PART II: MOLECULAR BEAM EPITAXY Description of the MBE equipment Reflection High Energy Electron Diffraction (RHEED) Analysis of the MBE growth process
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PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 2
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 3
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 4
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 5
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 6
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 7
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 8
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 9
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 10
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 11
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 12
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 13
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 14
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 15
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 16
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 17
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 18
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 19
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 20
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 21
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 22
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 23
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 24
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 25
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 26
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 27
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 28
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 29
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 30
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 31
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 32
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 33
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 34
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 35
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 36
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 37
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 38
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 39
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 40
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 41
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 42
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 43
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 44
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 45
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 46
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 47
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 48
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 49
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 50
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 51
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 52
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 53
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 54
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 55
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 56
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 57
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 58
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 59
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 60
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 61
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 62
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 63
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 64
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 65
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 66
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 67
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 68
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 69
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 70
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 2
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 3
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 4
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 5
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 6
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 7
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 8
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 9
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 10
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 11
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 12
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 13
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 14
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 15
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 16
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 17
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 18
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 19
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 20
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 21
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 22
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 23
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 24
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 25
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 26
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 27
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 28
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 29
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 30
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 31
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 32
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 33
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 34
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 35
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 36
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 37
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 38
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 39
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 40
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 41
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 42
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 43
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 44
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 45
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 46
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 47
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 48
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 49
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 50
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 51
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 52
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 53
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 54
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 55
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 56
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 57
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 58
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 59
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 60
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 61
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 62
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 63
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 64
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 65
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 66
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 67
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 68
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 69
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
http://www.bell-labs.com/org/physicalsciences/
projects/correlated/pop-up2-1.html
Slide 70
PART II: MOLECULAR BEAM
EPITAXY
Description of the MBE equipment
Reflection High Energy Electron Diffraction
(RHEED)
Analysis of the MBE growth process
Surface diffusion in MBE
MBE growth of III-V binary compounds and
alloys
MBE growth of lattice-matched and latticemismatched heterostructures
Doping in III-V materials
Molecular Beam Epitaxy (MBE)
Ultra-High-Vacuum (UHV)-based technique for producing high quality
epitaxial structures with monolayer (ML) control.
Introduced in the early 1970s as a tool for growing high-purity
semiconductor films.
One of the most widely used techniques for producing epitaxial layers
of metals, insulators and superconductors.
Research and industrial production applications (Al-containing, high
speed devices).
Simple principle: atoms or clusters of atoms, produced by heating up
a solid source, migrating in UHV onto a hot substrate surface, where
they can diffuse and eventually incorporate.
Despite the conceptual simplicity, a great technological effort is
required to produce systems that yield the desired quality in terms of
material purity, uniformity and interface control.
Description of the MBE equipment
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
MBE Facility
Growth, preparation and introduction chambers
Stainless steel, bake-out up to 200C for extended periods
of time
Image: Veeco Gen-II High-mobility MBE system at TASC
Research and production MBE systems
R&D
Riber Compact21 system:
Vertical reactor
Up to 1X3” wafer
6 to 11 source ports
Production
Riber MBE6000 system:
Up to 4X8”
model)
wafers
(MBE7000
10 large capacity source ports
Fully motorized wafer handling and
transfer
Schematics of an MBE system
Pumping
system
Effusion
cells
Substrate
manipulator
Liquid N2 cryopanels
around main walls and
source flange
thermal isolation among
Analysis tools:
RHEED
cells
prevent re-evaporation
RGA
from parts other than
the cells
Optical
(ellipsometry
, RDS...)
additional pumping
Cell
shutters
Pumping system
Minimization of impurities:
R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr
for nimp < 1015 cm-3 p < 10-13 Torr
In practice: p ~ 10-11 – 10-12 Torr, mostly H2
Used pumps: ion, cryo, Ti-sublimation.
Effusion cells
Thermocouple
Connector
Heat Shielding
Crucible
Power
Connector
Thermocouple
Filament
Head Assembly
Mounting Flange
and Supports
Principle of operation of the Knudsen cell.
Features of an effusion cell
The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen
• 6 –or10K-cells,
cell ininareference
source to
flange
cells,
the evaporation sources used by Knudsen in his studies of molecular
• Co-focused
onto
substrate
uniformity
effusion.
However,
a “true”
Knudsen
cellflux
has a
small diameter orifice (<1mm) to maintain high pressure within
the
crucible.
With certain
practice
• Flux
stability
<1% /exceptions,
day DTthis
< 1ºC
@ isT undesirable
~ 1000 ºCin MBE because it limits deposition rates.
Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit
• Temperature regulation by high-precision PID regulators
aperture. The crucible and source material are heated by radiation from a resistively heated filament. A
• Minimization
of flux
drift
as material
is depleted
thermocouple
is used
to allow
closed
loop feedback
control. choice of geometry
Crucibles
Cylindrical Crucible
+ Good charge capacity
+ Excellent long term flux stability
- Uniformity decreases as charge depletes
- Large shutter flux transients possible
Conical Crucible
- Reduced charge capacity
- Poor long term flux stability
+ Excellent uniformity
- Large shutter flux transients possible
SUMO® Crucible
+ Excellent charge capacity
+ Excellent long term flux stability
+ Excellent uniformity
+ Minimal shutter-related flux transients
Evaporation flux
The flux J at the substrate a distance d (cm) from the tip of the cell and on its
axis can be calculated, assuming that the evaporant is in equilibrium with its
vapor at pressure p (Torr) (cosine law of effusion, see lecture 1):
h e atin g b lock
su b stra te
J
J 1 . 12 10
p (T ) A
22
d
log P
A
2
MT
B log T C
at
cm 2 s
d
T
A
M: molecular weight in amu
T: source temperature in K
A: source area in cm2
p
M
T
Vapor pressure chart
As4
Ga
Al
TAs4 < Tsubstr < TGa,Al As re-evaporation growth in As4 overpressure
Numerical Application:
Estimation of the GaAs growth rate r
Typical values:
T (Ga cell) =1000oC=1273oK P ~ 10-3 Torr
J 1 . 12 10
p (T ) A
22
d
J 1 . 18 10
15
2
MT
at
cm 2 s d 10cm, A 3.14cm
at
2
cm s
r J 0 , 0 ( GaAs ) 2 . 27 10
r 2 . 67 Å/s 0.96 m / h
23
cm
3
2
, M 70
Cell shutters
Function: flux triggering
Materials: Ta – Mo
Mechanical or pneumatic actuators
Operation (~50ms) much faster
than ML deposition time (~1s)
Designed for more than 1 million
cycles
Not outgassing from cell heating
Minimization of heat shield no
flux transients
Computer control for reproducibility
Substrate manipulator
Continuous azimuthal rotation uniformity
Heater behind sample (Ta, W, C):
temperature uniformity, small outgassing
Beam flux monitor (BFM) opposite to sample
for flux calibration
Temperatures up to >1000C
Wafer holders
Mo- or Ta- made holders
Bonding: In (Ga), or In-free
(clamped)
Quick and easy transfer
Image: In-free, 3-inch sample
holder fitting a quarter of a 2-inch
wafer
Residual Gas Analyzer
Filament: Atoms and molecules are ionized in a signal ion source following electron
impact.
Electrons are emitted from the hot filaments.
Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a
combination of DC and RF voltages to each quadrupole.
Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors.
Functions: leak detection, measure of the system cleanliness (quality of bake and
pumping, impurities from outgassing...), studies of growth mechanisms
Reflection High Energy Electron
Diffraction (RHEED)
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996)
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Reflection High Energy Electron Diffraction
Si(001) RHEED patterns
sputter-cleaned surface
• Cells substrate
RHEED // substrate
• Control of the
crystallographic structure
of the growing epitaxial
surface
perfect surface
• Pattern for 2D surface:
series of // lines
high density of steps
rough surface
Surface sensitivity of RHEED
Ek = 5-40KeV
l = 0.17-0.06Å
Q = 1-3o
l
12 . 247
Å
EK
d(penetration) = lesin q
le 10ML d = 0.5ML Surface sensitivity
Diffraction: 3D vs 2D
3D
DK = G
2D
(1st layer of perfectly flat surface)
G // ∞ rods
a=5.65Å G=2p/a=1.1 Å-1
Ek=5KeV
k1/l=36.5Å-1
k >> G
Ideal RHEED Pattern
Ewald sphere
Projected image
on screen
Sample
Perfect 2D
crystalline surface
Perfectly monochromatic,
collimated beam
Intersection of Ewald
sphere with G vectors
Ideal pattern: series of
points on a half circle (for
each nth-order Laue zone)
Diffraction in real case
Thermal vibrations, lattice imperfections
finite thickness of reciprocal lattice rods
Divergence and dispersion of e-beam
finite thickness of Ewald sphere
Diffraction spots streaks with modulated intensity even for 2D surfaces
Non-ideal Surfaces
Ideal surface circular arrays of
(elongated) spots
Ideal surface
Amorphous layers no diffraction
pattern, diffuse background
Polycrystallyne – textured surface
diffuse rings (Debye-Sherrer
construction)
Polycrystal
3D surface electrons transmitted
through surface asperities and
scattered in different directions
spotty RHEED pattern
Rough surface
Non-ideal Surfaces: Example
RHEED
De-oxidized GaAs substrate
+ 15nm epitaxial GaAs
Lateral, periodic
intensity modulation!
+ 1m epitaxial GaAs
A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1
SEM
GaAs (001): (2x4) RHEED Pattern
2x ([110] direction )
4x ([-110] direction)
Reciprocal space
GaAs (2x4) Reconstruction
Original model:
GaAs(001) (2x4) unit cell: 3 As
dimers along [-110] + 1 dimer
vacancy surface energy
reduction
Top As layer
Top Ga layer
2nd As layer
Direct space
GaAs (2x4) Reconstruction
Top As layer
Top Ga layer
2nd As layer
Further studies (total energy calculation,
STM: 4 phases with As coverage 0.25
→ 0.75 and different dimer distribution.
Right: STM of GaAs(001)-b2(2X4)
V. P. LaBella et al., Phys. Rev. Lett. 83, 2989
(1999)
GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75
Lower T, higher As4/Ga: As-rich c(4X4) with additional As
dimers
Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along
[110]
Even higher T, lower
As4/Ga: Ga droplets
Other reconstructions
exist, maybe as
interference between
domains
Growth dynamics: RHEED Oscillations
RHEED maximum spot intensity indicate
completion of growing layers
layer-by-layer control of the growing
crystal surface
# of deposited atomic layers = #
of maxima
growth rate = 1ML / t
GaAs Growth
shutters open
shutters closed
RHEED intensity (Arb. Units)
GaAs
AlAs
0
10
20
30
40
50
Time (s)
Shutter closed:
Oscillation dumping: statistical
distribution of growth front → constant
surface roughness.
Persistence of RHEED oscillations
layer-by-layer epitaxial quality
GaAs: 2D rearrangement of
mobile Ga adatoms intensity
recovery
AlAs: low surface mobility of Al
adatoms no recovery
Analysis of the MBE growth process
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental
and Current status”, Springer (1996).
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Three-phases model
heating block
1. Gas phase (molecular beam
generation + vapor mixing zones):
complete lack of order, no
homogeneous reactions (ballistic
transport).
2. Crystalline
phase
epilayer): complete
long-range order.
(substrate,
short- and
3. Near-surface
transition
layer
(substrate crystallization zone):
area where all processes leading
to epitaxy occur (heterogeneous
reactions on hot surface). Layer
geometry and processes strongly
dependent on growth conditions.
substrate
substrate
crystallization zone
vapor elements
mixing zone
molecular beam
generation zone
Atomic-scale mechanisms of epitaxial growth
chemisorption
physisorption
a. Surface diffusion
b. Thermal desorption
c. Formation of two-dimensional
clusters
d. Incorporation at steps
e. Step diffusion
f. Incorporation at kinks
All steps (a-f) strongly dependent
on kinetics (T, r, V/III ratio, crystal
orientation...)
tet rameric
molecule
interaction potential
Adsorption (physi-chemisorbtion)
of the costituent atoms or
molecules impinging on the
substrate surface
Ea
Edp
Edc
distance to the
substrate surface
physisorbed precursor
state
chemisorbed state
rc
rp
b
a
c
a
f
e
d
Surface diffusion in MBE
nucleation of 2D islands
step-flow growth
2D nucleation–surface diffusion: RHEED analysis
High T l > l0
l0
Critical T:
Tc ≈ 590C
l ≈ l0
Low T l < l0
l0
Neave et al, APL 47 (1985) 100
Growth modes: GaAs homoepitaxy
60 0°C
T=520°C
55 0°C
a)
b)
c)
70 0°C
750°C
650°C
d)
e)
f)
Transition from 2D island nucleation to step flow growth (MOCVD).
5X5m2 post-growth AFM scans, heigth scale 2-5nm
Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans
B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997)
http://www.kfa-juelich.de/video/voigtlaender/
T = 550C
Step-flow growth
T = 450C
island nucleation growth
Determination of diffusion coefficient
l = l(T, r, V/III)
Einstein relation: l2 = 2Dt
Exactly: t = tnuc
Assumption: t = 1/r
(upper limit)
D = diffusion coefficient, t =
characteristic time for diffusion
D = l2 / (2t), D = D0 exp (-ED / kT)
ED = activation energy for Ga surface
diffusion
Experiment: measurement of Tc(r) at
fixed misorientation (l(Tc) = l)
Arrhenius plot
ED = 1.3±0.1eV
D0 = 0.85 X 10-5 cm2 s-1
Neave et al, APL 47 (1985) 100
Surface diffusion: a more rigorous approach
Assumptions:
Vicinal surface with uniform step separation l0
Rough step edge negligible step diffusion 1D problem
JAs >> JGa As disregarded except for reaction at step edge
Basic diffusion equation (steady-state)
dn s
dt
2
Ds
d ns
dy
2
J
ns
ts
0
ns = adatom surface concentration
Ds = surface diffusion coefficient
J = flux from Knudsen cell
ts = re-evaporation (residence) time
ls = sqrt (Dsts) = re-evaporation
diffusion length
T. Nishinaga, in “Handbook of crystal growth”, vol.3,
p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.
Solution of diffusion equation
Surface concentration :
ns ( y )
J t s n step J t s
n step
cosh y / l s
cosh l 0 / 2 l s
2
2y
Jl
1
8 D s l 0
2
0
(for ls >> l0 (typical for MBE)
Close to step edges, adatoms reach the step and incorporate before reevaporation lower density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Incorporation flow ( step supersaturation):
l 0 n step D step
Js
step
k BT
2
a
Js =
nstep =
ne =
Dstep =
a
=
tstep =
Nernst-Einstein relation
n step n e
t step
surface lateral flux
concentration at step edge
equilibrium concentration
a2/ tstep = step diff. coeff.
lattice constant
adatom relaxation time to enter the step
tstep depends on activation energy to enter the step and on kink
density
Boundary condition at step edge
nstep given by balance of incorporation flow at the step and
surface diffusion flow
Surface diffusion flow
l0
Js
2
dn s
Ds
l
dy
y 0
2
n step
J
ts
(for ls >> l0)
l0
2
Supersaturation ratio at step edge
a
step
where
n step
ne
ne
ts
n step n e
t step
ne
t s
n step
J
ts
l 0t step
1
2at s
1
l0
2
l 0t step
ne
J
ts
2at s
pe
2 p mkT
pe = equilibrium pressure of growth atom with the surface
m = mass of growth atom
Step edge activity
step
n step
ne
n
e
t s
l 0t step
1
2at s
• J, l0 decreased
(small Ga flux to the step)
• Temperature increased
(tstep decreased)
Step edge very active to accept
Ga atoms, nstep → ne
1
l 0t step
n
J e
ts
2at s
• J, l0 increased
(high Ga flux to the step)
• Temperature decreased
(tstep increased)
Negligible incorporation of Ga
atoms at steps, nstep → n∞
Critical supersaturation for 2D nucleation
Nucleation theory:
2
phs
c exp
65 ln I c kT
Where
= atomic (cell) volume
h = step height
s = free energy of 2D nucleus side surface
Ic = nucleation rate
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
max > c 2D nucleation
( y)
ns y
n step
1
Jl
2
0
8 D s n step
2y
1
l
0
1
(for n step n e )
max < c step flow
2
2D nucleation vs. step flow
Jl0
8 D s ne
2
At the middle of the terrace
max
1
(for n step n e )
Applications: GaAs (001): larger flux, smaller miscut
larger max
Higher Tc for 2D nucleation
MBE growth of III-V binary compounds
and alloys
Modulated molecular beam techniques
Experimental
technique:
Modulated-Beam
Mass
Spectrometry
(MBMS)
Applications: studies of growth process chemistry in GaAs MBE on
(001) surfaces
Basic method: evaporation of neutral atoms beam onto substrate;
detection of desorbing flux with RGA mass spectrometer
Problem: discrimination beteen background and desorbing species
Solution: modulation of incident beam or desorbing flux.
C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
Binary III-V compounds
Group III (Al, Ga, In): monomers, low vapor pressure at
typical substrate growth temperatures sticking
coefficient = 1 (no desorption or re-evaportation)
group-III flux determines growth rate.
Group V (P, As, Sb): dimers-tetramers, high vapor
pressure sticking coefficient < 1 need for
overpressure to maintain stoichiometry.
As2 growth kinetics
Supplied by GaAs or As cracker
source
Adsorbed as mobile precursor
(physisorption)
No Ga:
Fast desorption as As2 or
As4 (low T)
With Ga:
Dissociative chemisorption
(1st order reaction)
Sticking coefficient Ga
flux (max = 1)
Desorption of excess As
stoichiometry
As4 growth kinetics
No Ga: fast desorption
With Ga:
2nd order reaction
between pairs of As4
on Ga sites 4
incorporated As atoms
+ 1 desorbed As4
Max. sticking
coefficient = 0.5
Second-order
dependence of As4
desorption rate on
adsorption rate
Similar behavior for other
III-V compounds or alloys
Simulation of GaAs (001)-(2X4) growth
P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional
theory (DFT) chemical bonding on atomic level and surface morphology at
the large length and time scales characteristic for growth.
GaAs (001)-(2X4) growth from Ga and As2; topmost As dimerized along [110] unless Ga atom in between
> 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by
DFT
Surface mobility: Ga, As2 (no As)
Ga flux: 0.1ML/s
Ga diffusion: anisotropic, 10 hopping processes
Ga incorporation for strongly bound configurations stop diffusion
As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga
As2 desorption: 3 events with different rates depending on environment
Simulation results
AxB1-x-V alloys
Standard temperatures: sticking coefficient = 1 growth
rate r = rA + rB, composition x = rA/(rA+rB)
High temperatures:
Transition from group-V stable surface (i.e. (2X4) in
GaAs) to metal-rich surface high group-V flux to
keep surface stoichiometry.
Desorption of more volatile group-III element (In > Ga
> Al) deviations from ideal r and x
Surface segregation of more volatile group-III element
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
III-AxB1-x alloys
More complicated situation, no easy relation between x
(vapor) and x (solid):
Difference in adsorption efficiency
Difference in vapor pressure (P > As > Sb) (at low T
preferential incorporation of low vapor pressure dimer
or tetramer)
Mutual interference of the sticking coefficients
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994
Elsevier Science B.V
MBE growth of lattice-matched and
lattice-mismatched heterostructures
GaAs/AlxGa1-xAs heterostructures
shutters open
RHEED intensity (Arb. Units)
GaAs
shutters closed
Lattice-matched system for 0 < x < 1
AlAs
Interface atomic structure influences optical and
electronic properties of HS, QW and 2DEG-based
devices
0
10
20
30
40
50
Time (s)
lGa >> lAl intrinsic asymmetry between morphology of
“normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-onAlGaAs) interfaces
High reactivity of Al segregation of impurities towards
the inverted interface
Growth interruptions: effects on the optical
properties of GaAs/AlGaAs QWs
M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987)
Growth
interruption
x = 0.33
x=1
A
above-below
B An exciton is a bound state of an electron and a hole in an insulator (or
semiconductor), or in other words, a Coulomb correlated electron/hole pair.
above It is an elementary excitation, or a quasiparticle of a solid.
l(roughness) <<
A vivid picture of exciton formation is as follows: a photon enters
a
l(exciton);
the
C semiconductor, exciting an electron from the valence band into
l(roughness)
>>
conduction band, leaving a hole behind, to which it is attracted by the
l(exciton) sharp
below
Coulomb force. The exciton results from the binding of the electron with its
PL and
hole the exciton has slightly less energy than the unbound electron
D hole. The wavefunction of the bound state is hydrogenic. However, the
≈
binding energy is much smaller and the size much bigger than al(roughness)
hydrogen
none
atom because of the effects of screening and the effective mass
of the
l(exciton)
broad
constituents in the material.
PL
Impurity segregation in AlGaAs
High reactivity of Al atoms (with
respect to Ga).
higher
incorporation
of
impurities, with segregation to the
surface.
inverted interface is more
contaminated than normal one.
Left: SIMS profiles of O impurities
in an AlxGa1-xAs multilayer, where
1. O concentration is higher for
higher x.
2. O segregates at interfaces
where lower x material is
grown on higher x one.
S.Naritsuka et al., J. Cryst.
Growth 254, 310 (2003)
Lattice-mismatched heterostructures
Needed to expand flexibility in
materials choice (e.g., InxGa1xAs/GaAs)
Misfit:
fi = (asi-aoi)/aoi
i = x,y (growth plane)
a = lattice constant
s = substrate
o = overlayer
fx,y (InAs/GaAs) ≈ 7%
Ee > ED
Relaxation
through dislocations
Ee = ED
Ee < ED
Pseudomorphic growth
ED
Ee
Energy
Separate bulk layers of
materials A and B, with
a(B) > a(A)
Epitaxy of thin layer of B on substrate A:
pseudomorphic (strained) growth for Ee
(increasing) < ED (constant),
dislocations for Ee > ED.
Layer thickness
Growth mode for small lattice mismatch
Dislocations
Edge dislocation: line defect that occurs when there is a missing row
of atoms. The crystal arrangement is perfect on the top and on the
bottom. The defect is the row of atoms missing from region b. This
mistake runs in a line that is perpendicular to the page and places a
strain on region a.
ENERGY per unit area
Critical thickness and dislocations
Thin epilayer grown on substrate with
different lattice parameter
strain
Ee
dislocations
ED
Energetics:
Strain: increases with thickness
Dislocations: thickness independent
Energetic
fo
ENERGY per unit area
LATTICE MISFIT
Ee
ED
ho
LAYER THICKNESS
trade-off
between
pseudomorphic and dislocated epilayers:
beyond a critical lattice misfit f0 the
adjustement of the two lattices by
dislocations is energetically more
favorable than by strain
for thicknesses exceeding the critical
thickness
h0
dislocations
are
energetically more favorable than strain
H. Luth, “Surfaces and Interfaces of Solid
Materials”, 3° ed., Springer, Berlin, 1995
Critical thickness: energetic calculations
Minimization of energy for the epitaxial system
Critical thickness in units of as as a function of f, for
the introduction of 60o misfit dislocations on (111)
glide
planes
in
a
(001)
interface
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current
status”, Springer (1996)
Strained epitaxy: experiment
Existence of kinetic barriers
critical thicknesses much larger
than predicted by energetic
balance.
Methods to increase t0:
Reduction of surface diffusion GaAs
(Low T, Ga-stabilized surfaces
(InGaAs on GaAs),
surfactants)
Gradual lattice accommodation
(graded buffer layers (BL))
Image: TEM cross section of a metamorphic In0.75Ga0.25As/
In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate
(f ~ 5%) by insertion of a ~1m-thick InxAl1-xAs step-graded BL
(F. Capotondi et al., Thin Solid Films 484, 400 (2005).))
Strained growth: Onset of 3D growth (S-K)
Very
large
mismatch:
strain
relaxation
energetically
more
favorable by 3D islanding, rather
than dislocations.
Right: critical thicknesses as a
function
of
x
in
InxGa1xAs/In.53Ga.47As for the onset of 3D
growth (t3D) and misfit dislocations
(tc), at T = 525C. Transition from
dislocations to 3D occurs (TRM) at x
~ .75, i.e., f = 1.7% (M. Gendry et al.,
tc
TRM
Appl. Phys. Lett. 60, 2249 (1992))
t3D
M. A. Herman, H. Sitter, “Molecular Beam Epitaxy,
Fundamental and Current status”, Springer (1996); original
data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).
Doping in III-V materials
C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By
D.T.J. Hurle, 1994 Elsevier Science B.V
G. Biasiol and L. Sorba, in “Crystal growth of materials for energy
production and energy-saving applications”, R. Fornari, L. Sorba,
Eds. (Edizioni ETS, Pisa, 2001) pp. 66-83 (http://www.tascinfm.it/research/amd/file/school.pdf).
Doping in III-V materials
Doping necessary
for carrier transport
inTop:
electronic
or optoelectronic
devices
Group-IV
atoms amphoteric:
donors
(if
incorporated
ondensities
group-III
sites)
free-carrier
in
Si-
acceptors
(onII group-V
sites)
doped
and
(100) GaAs at
or
Doping
by group
(p-type), IV
(p- or n- type)
and{311}A
VI atoms
(n-type)
Compositional
300pressure,
K as a function
the VT4 /III
C: acceptor, but very low vapour
veryofhigh
dependence
of Si (>
Group II
ratio. Dotted line: NSi.
2000C)
donor
activation
II-b atoms (Zn, Cd): too high vapour pressure at usual
growth
Ge:
amphoteric
behavior
energy in
temperatures
not
used in difficult
MBE to control
Bottom: Phase diagram (V4 /III
AlxGa1-xAs
II-a
Sn: atoms
too high
segregation
(Besurface
in particular):
the universal
choice
ratio
–
T)
for
the
conduction
K.Kohler
et al.,
JCG
127,
720
(1993).
(N.
Chand
et al., PRB
SIMS
profiles
of
Si-d
doped
Si: universal
n-type dopant
in (Ga,In,Al)As
(001)
Group-VI
atoms uncommon
(surface
segregation,
re-evaporation)
type of Si
doped
{311}A
30,
4481 (1984)GaAs.
GaAs
grown
at
different
T
(A.
-3 before compensation (substitution on As
– n up to ~1019 cm
Dot88,size
activation efficiency.
P. Mills et al., JAP
4056(2000)
sites, Si-vacancy complexes, Si clusters…)
(N. Sakamoto et al., APL 67, 1444 (1995)
– Diffusivity towards the surface at doping levels higher than
about 2X1018 cm-3 problem in sharp doping profiles
– Donor ionization energy increases in AlGaAs reduced
doping efficiency
– GaAs(311)A surfaces : n- to p-type transition depending on T
and III/V ratio can be used as p-type dopant
Modulation doping and the two-dimensional
electron gas
Bulk doping
Electrical conduction (otherwise semi-insulating)
BUT
Introduction of impurities source of scattering,
limitation of mobility at low temperatures
Temperature dependence of mobility in
n-type GaAs. The dashed curves are the
corresponding calculated contributions
from various mechanisms.
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors
(Springer-Verlag, Berlin, 1996).
Modulation doping and the two-dimensional
electron gas
Solution: spatial separation between doping layer and conducting
channel
m odulatio n d oping
(d dop ing)
G aA s
G aA s
substrate epila yer
A lG a A s
e
-
+
G aA s
cap
Increase of
mobility
E nerg y
conduction ban d
EF
2 DEG
H. Störmer, Surf. Sci.132 (1983) 519
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