Transcript Low-dimensional quantum confined semiconductor nanostructures

PART IV: EPITAXIAL
SEMICONDUCTOR
NANOSTRUCTURES
 Properties of low-dimensional quantum confined
semiconductor nanostructures
 Fabrication techniques of low-dimensional
semiconductor nanostructures
 Formation and properties of self-assembled QDs
 Growth of QWRs-QDs on patterned surfaces
 Mechanisms of self ordering in epitaxial growth
Properties of low-dimensional
quantum confined semiconductor
nanostructures
Effect of quantum confinement on
energy spectrum
 Energy spectrum for electrons confined in 1, 2 or 3D with infinitely
deep, rectangular potential wells with sizes tx, ty, tz:
2
2
2
h2 2l 2 h k y  k z 
El 

* 2
2m t x
2 m*
h2 2  l 2 m 2  h2 k z2
El ,m 
 2 
*  2
2 m  t x t y  2 m*
h2 2  l 2 m 2 n 2 
El ,m,n 
 2 2
*  2
2m  t x t y t z 
1D confinemen t
2 D confinemen t
3D confinemen t
Electron DOS in low-D systems
3D - bulk
2m

/ h2 
2 2
*
3/ 2
2D - QW
1D - QWR
m*

2 m* 
E   2    E  El   
h t x l
ht x t y
1/ 2
0D - QD
1 / 2
 E  El ,m    t t t   E  El ,m,n 
2
l ,m
x y z l ,m,n
Lower D  sharper DOS  potential advantage for optical
and electronic properties
Sizes needed to observe QC
 At T = 0K electrons occupy all energy states up to EF,
corresponding to de Broglie (Fermi) wavelength lF = 2 /
(32n)1/3, with n = electron density.
 Quantum confinement for ti ≤ lF
 Metals:  1 electron / atom  lF ≈ 0.5nm
 Semiconductors: much higher, depends on doping: e.g.,
n~1X1018cm-3  lF = 29nm, ti ≈ 10nm is sufficient
Subband population in QC systems
 If more subbands are populated, motion along
confinement direction results  only ground state must
be populated, i.e., DE12 > kBT
 For infinite square QW, this means
3h2 2
tx 
2 m * k BT
 For electrons in GaAs at T = 300K  tx < 20nm
 For holes, more complicated relations and mh>me 
smaller tx
 Equivalent sizes for other confinement dimensions
Uniformity requirements in QC structures
 Size non-uniformity  inhomogeneous broadening of DOS
 For ∞ wells, | Ei | / Ei = 2 ti / ti ; Ei << Ei  ti << ti
 Practical limit to observe QC: ti / ti < 10%  ti ≈ 1nm
15
0 meV
2 meV
5 meV
10 meV
15 meV
10
5
0
20
30
40
50
60
70
tates / nm
confinem e nt e ner gy (m e V)
Calculated electron DOS in a GaAs/AlGaAs QWR with different
Gaussian-shaped inhomogeneous broadening
Fabrication techniques of lowdimensional semiconductor
nanostructures
From Quantum Wells to Quantum Wires/Dots
Control over
lateral
composition
Planar (layer-by-layer) epitaxy
QWR
- QD
QW
Main approaches for creation of lateral
confinement
 Top-down:
Post growth patterning of epitaxially grown 2D quantum
wells
 Bottom-up:
Formation of QWR / QD during growth by special
epitaxial procedures
Post-growth patterning 1
 Selective removal of QW by lithography, etching
and regrowth
 Lithography: holo, e-beam, X-ray
 Etching: dry, wet depending on details of fabrication
process
 Regrowth: surface passivation
Advantages:
 Flexibility of design (lithographic patterns)
Disadvantages:
 Size: several 10nm
 Uniformity (size and shape): several nm
75-nm
SEM image
quantum
showing
wires narrow
fabricated
pillars
in
GaAs/AlGaAs
etched into a
material
GaAs substrate.
by e-beam
lithography
(horizontal
and bars
chemical
= 0.5etching
mm
(M. A. Reed
et L.
al.,Roukes
Phys. Rev.
(M.
et al.Lett. 60, 535
(1988))
Phys. Rev. Lett.
59, 3011 (1987))
 Etching defects  interface states
Post-growth patterning 2
 Selective disordering of QWs
  Patterning of QW band gap and
refractive index
 Methods: implantation or diffusion of
impurities through a mask or with focused
ion beams
Advantages:
 Flexibility of design (lithographic patterns)
Disadvantages:
 Size: several 10nm
 Uniformity (size and shape): several nm
 Impurities  material contamination
Post-growth patterning 3
Str essor
 Deposition of patterned “stressors” adjacent to the
QW
QW
  Lateral band-gap modulation via strain effects
Conduction Band
Advantages:
 Flexibility of design (lithographic patterns)
 Smooth, defect-free lateral interfaces
Disadvantages:
 Size: several 10nm
 Uniformity (size and shape): several nm
Post-growth patterning 4
 Lateral patterning of 2D electron gas structures
  Creation of QWRs, quantum point contacts (QPCs)
and QDs
 Methods:
 Depletion by deposition of a metallic split-gate (top)
 Wet chemical etching and depletion by in-plane
gates (bottom)
Advantages:
 Flexibility of design (lithographic patterns)
 Smooth, defect-free lateral interfaces
 Easy electric contacts
Disadvantages:
 Size: several 10nm
 Uniformity (size and shape): several nm
Cleaved-edge overgrowth
 Overgrowth on the Cleaved (011) Edge of a (multiple)
QW or 2DEG structure (CEO)
 Cleave of the 2DEG in the MBE chamber
 Overgrowth of 2DEG on top of the cleaved edge 
QWR at the point where the two 2DEGs intersect
  lateral variation in the potential energy
 1 regrowth: QWRs; 2 regrowths: QDs
Growth direction
Growth direction
AlGaAs
Cleave here
The process begins with
the usual growth of a
high-mobility
heterojunction
After this the sample
is cleaved inside the
vacuum chamber
GaAs
GaAs
AlGaAs
GaAs
AlGaAs
A. R. Goni et al.
APL. 61, 1956 (1992)
After cleavage the sample
is reoriented and growth
is then resumed on top
of the cleaved surface
Cleaved-edge overgrowth
W. Wegscheider et al.
PRL 71, 4071 (1993)
Advantages:
 Size, uniformity: ML scale
 Smooth, defect-free lateral interfaces
Disadvantages:
 Low flexibility (difficult contacts on cleaved edge)
Spontaneous self-ordering 1
 Growth of fractional-layer SLs on vicinal substrates
Tilted SL
 Species-dependent surface diffusion and preferential
attachment of adatoms to the step edges  lateral and
vertical definition, alignment
 QWR formation: serpentine SL (growth rate
Vicinal Substr ate
modulations), accumulation at step bunches
Advantages:
 1-step process (no processing)
 Size: <10nm
 Lateral interfaces formed during growth
Disadvantages:
Stacked GaAs/AlGaAs QWR SL
formed on step bunches on 3o off
(110) GaAs.
(T. Kato et al., APL 72, 465 (1998)
 Uniformity: 10-20% (imperfect step
configuration and spacing, incomplete
adatom segregation, growth rate
variations)
Spontaneous self-ordering 2
 Stranski - Krastanov growth of QDs in latticeStr ain field in the cap layer
mismatched system (e.g., InGaAs/GaAs)
Par tiall y
strained
island
Str ain field in the substrate
Advantages:
1-step
process (no
Improvement: growth
on misoriented
substrates  QD formation on quasi step
Size:
<10nm
periodic
edges
processing)
 Lateral interfaces formed during growth
Disadvantages:
STM image of self-assembled InAs
QDs on a GaAs substrate
(M. E. Rubin et al. Phys. Rev. Lett. 77, 5268
(1996))
 Uniformity: 10-20% in size and position
(randomness of nucleation process)
 Difficult contacting for transport
Seeded self-ordering
 Growth of QWs on lithographically patterned substrates
 Dielectric masks
 Nonplanar surfaces
 Mechanisms: selective (masks) or anisotropic
(nonplanar) growth rates  material accumulation on
preferential sites (“seeds”)
Advantages:
 Size: <10nm
AlGaAs
barriers
 Uniformity: 5% (seeds)
GaAs
QWR
 Lateral interfaces formed during growth
Disadvantages:
100nm
GaAs
V-shaped
substrate
 2-step process (pre-patterning)
 Nanostructures depend on growth habit
TEM X-section of a stack of GaAs/AlGaAs
QWRs grown on a V-grooved substrate
Formation and properties of selfassembled QDs
Atomic arrangement in a QD
 High resolution TEM of an uncapped InAs/GaAs QD
(Chu et al., JAP85, 2355
(1999))
 The lateral lattice constant in the upper part of the QD is clearly larger
than in the lower part: strain relaxation in the 3D island.
 When too much island material is deposited, the strain cannot be totally
relieved elastically through islanding, and dislocations occur via plastic
relaxation.
Formation stages of InAs/GaAs(001) QDs
 a) Low coverages:
InAs step-flow
growth.
 b)-c): ~1.7ML:
pseudomorphic,
defect free QDs,
10% uniformity. c):
Higher density,
smaller size than b).
Self-limiting effect
1X1mm2 AFM scans of different InAs coverages (1 to 4
ML) on GaAs (001) (Leonard et al., PRB 50, 11687 (1994))
 d)-f): >2ML:
dislocated islands by
QD aggregation or by
dislocations in a
single QD.
Critical thickness for QD formation
 QD density = 0 below critical layer thickness QC
 Sharp density increase after QC
 QD density  = 0 (Q- QC)a, QC = 1.5ML, a = 1.76: 1st order phase
transition with  an order parameter (Leonard et al., PRB 50, 11687 (1994))
Size distribution of QDs
1.6ML
 Diameter and height
distribution for increasing
InAs coverage
1.65ML
 10% height and 7%
uniformity for initial stages of
QD formation (a)
 Degraded uniformity for
higher Q
1.75ML
 Increasing Q: diameter
decrease (~30nm to ~
20nm), density increase
 (Leonard et al., PRB 50, 11687 (1994))
1.9ML
Optical properties of QDs
 RT PL spectra for different Q
 2-3 peaks corresponding to ground and excited states
 Size distribution of the QDs  -like DOS  broad lines
(inhomogeneous broadening)

(Chu et al., JAP85, 2355 (1999))
Optical properties of QDs
 RT PL intensity, energy and FWHM as
a function of Q
 Intensity: maximum for Q ~ 2.3ML
 Energy: broad minimum for Q ~ 2.32.7ML ( largest QDs)
 FWHM: minimum for Q ~ 2.6ML (3035meV)
  larger islands: better optical quality,
higher homogeneity
 Q > 2.7ML: formation of dislocations:
decreased intensity, energy shift,
broader lines.

(Chu et al., JAP85, 2355 (1999))
Previous experiment: higher
homogeneity, slightly higher size
for lower Q (first stages of QD
formation)  high influence of
experimental conditions!
Effect of growth temperature (MBE)
(Chu et al., JAP85, 2355
(1999))
 Increasing T (480-530C)  decreasing energy  larger QDs
 Explanation: larger diffusion length  there is a larger nucleation-free area
around islands ( nucleation centers, adatom sinks) where adatoms can
be collected by the island
 550C: In desorption (smaller QDs), In-Ga intermixing  higher energy
 Increasing T: stronger, narrower lines  better material quality
 Ground state – 1st subband separation (530C): ~ 70meV
Effect of V/III ratio (MBE)
(Chu et al., JAP85, 2355
(1999))
 T=480, different As4 flux: enhanced In diffusion for lower As4/In ratios
 Lower As4 fluxes: increased QD quantum efficiency
 Lower As4 fluxes: small redshift  increased QD size ( larger diffusion
length, coherent with T dependence)
Lithographic positioning of SA QDs
 Self-assembled Ge islands on
Si(001) pre-patterned with oxide
lines
 Increased uniformity in size and
separation
 Possible mechanisms:
 Diffusion barrier on the stripe
edge
 Reduced strain energy at the
stripe edge
T. I. Kamins and R. S. Williams, APL 71, 1201
(1997)
Lithographic positioning of SA QDs
 Preferential formation of InAs QDs in
shallow, sub-mm-size GaAs holes
defined by electron-beam (a) 1.4ML,
b) 1.8ML InAs)
 Holes with (111)A and B faces, QDs
formed on B faces (favorable
nucleation sites for In atoms).
S Kohmoto, MSEB 88, 292 (2002)
Vertical stacking of QDs
 Coherent InAs islands separated by GaAs spacer layers exhibit
self-organized growth along the growth direction.
 The island-induced evolving strain fields provide the driving force
for self-assembly provided the spacer is not too thick
Bright field TEM pictures taken along
[011] azimuth of five sets of InAs
islands separated by 36 ML GaAs
spacer layers.
Q. Xie et al., PRL 75, 2542 (1995)
X-STM constant current topography
image of two stacks of InAs QDs.
D. M. Bruls et al., APL 82, 3758 (2003)
Lithographic positioning of stacked QDs
 Twofold stacked InGaAs/GaAs QD
layers grown on GaAs(001)
substrates patterned with square
arrays of shallow holes ((a)(-d):
100-200nm period).
 The second QD layer responds to
the lateral strain-field interferences
generated by the buried periodic
QD array: vertically-aligned QDs or
satellite QDs placed on strain
energy minima.
 Base size and shape, and lateral
orientation are predefined by the
Estr distribution on the underlying
surface.
H. Heidemeyer et al., PRL 91, 196103 (2003)
Growth of QWRs and QDs on
patterned surfaces
Grating fabrication for QWRs
5 µm
MOCVD on V-grooved substrates
Stable facets forming in the groove:
 sidewalls:
(100)
{111}A ~ 5-10° off towards (100)
 top and bottom regions:
(100) + {311}A
Different surface crystalline structure

different diffusion & nucleation rates

growth rate R depends on orientation
GaAs
substrate
Rtop, Rbottom < Rsidewall

expansion at top,
sharpening at bottom
BUT: profile stabilizes at the
bottom at the 10nm-level
QWR formation on V-grooved substrates
AlGaAs self-limiting profile
GaAs QW profile
independent of lithographic details
bottom region thickens and expands
recovers after QWR deposition
 ~ 10nm
QWR formation
AlGaAs
Barriers
Patterned
GaAs
Substrate
[100]
[011]
[011]
AlGaAs vertical
QW
20 nm
lateral
GaAs QW
GaAs
QWR
Profile evolution during self-limiting growth
G. Biasiol et al., APL 71, 1831 (1997).
R(100) > R{ijk}

conformal growth
R(100) > R{ijk}

(100) expanding
layer A: t100 > t311 > ts  expansion of (100) and {311}A facets
layer B: t100 = t311 = ts  stable facets, self-limiting growth
Optical Properties of GaAs-AlGaAs QWRs*
Photoluminescence
1
Photoluminescence Excitation
1
QWR - 2.5nm
8K
e 6 -h6
e 3 -h3
e 4 -h4 e -h
e 2 -h2
5 5
LUMINESCENCE INTENSITY
LUMINESCENCE INTENSITY
QW
QWR
AlGaAs
Barrier
0
e 8 -h8
QWR - 2.5nm
e 1 -h1
e 9 -h9
e 7 -h7
e 1 -"lh1 "
PLE, Excit. pol. //
PLE, Excit. pol. 
PL
0
1.4
1.5
1.6
1.7
1.8
1.9
2
PHOTON ENERGY (eV)
PL FWHM of QWR ~ 6meV
*F.
Vouilloz et al. ICPS 23, Berlin, 1996
2.1
1.55
1.6
1.65
1.7
1.75
PHOTON ENERGY (eV)
•hh and lh related transitions observed
•polarization anisotropy in e-lh/e-hh ratio
Mechanisms of self ordering in
epitaxial growth
Driving force for lateral epitaxy
Chemical potential (driving force for epitaxy  supersaturation):
0
mstrain
m(capillarit
mi  m
m00  D
( x)2  0D
)   "y( )
 ( xD
)
k B T ln X i ( x)
mmixing
2E
0  unit cell volum e   surfacefreeeneggy
E  elastic m odulus
  surfaceangle
   tangential stress
X i  com position of com ponenti
  surfacecurvature
Lateral variations of m  lateral variations of growth rate
Chemical potential  growth rate
Nernst-Einstein relation
nD m( x)
j ( x)  
k BT x
n  adatom surfacedensity
D  surfacediffusion coefficient
x  lateralcoordinate
Continuity equation
j ( x) 

R( x)  0  J 0 ( x) 

x 

J 0  growth flux
Diffusion towards areas of lower m
2

nD

m( x) 

R( x)   0 J 0 ( x) 
2 

k
T

x
B


Growth rate: increased at lower m,
decreased at higher m
Example: sinusoidal chemical potential
j
j
j
j
 m(x) = sin (x)
 j(x)  - m’(x) = -cos(x)
 R(x)  m”(x) = -sin(x)
How self-ordering is established
Need for an equilibrating action between non-uniform
chemical potential (stress, shape, composition) and another
factor that drives atoms away from chemical potential
minima.
As growth proceeds, this should bring to steady-state
growth profile.
Any change in growth parameters (materials, temperature,
fluxes, growth rates...) should bring to a new steady-state
profile, independent of the initial one.
Stressed surface  self-ordering of QDs
1. SK growth mode: adatom flux towards
islands  island coarsening
2. Strain energy (chemical potential) Es:
 Flux away from islands
 Es larger for larger islands 
dissolution rate larger as island size
increases
3. 1 + 2: kinetic mechanism stabilizing the
f=
7.5% ()
5 ()
2.5% ()
0% ()
island size: slowing of the growth rate of
large islands and increase of the adatom
density away from them, thus enhancing
nucleation of new islands (with small Es 
faster growth).
4.  narrow island size distribution in the
system (for f = 5 and 7.5%).
1D KMC model, A.L. Barabasi, APL 70, 2565 (1997)
Vertical self-ordering of stacked QDs
 Pairing probability between 1st and 2nd layer of
dots decreases with thicker spacers
 Model: atoms of 2nd InAs layer arrive on
stressed region (I) of width 2ls ( strain-driven
diffusion towards top of 1st islands) or
unstressed region (II) of width l-2ls ( random
island formation)
 ls increases as GaAs spacer is thinner
0
  ( x)2
2E
Surface diffusion model  pairing probability as
a function spacer thickness, dependent on
island size and density (measured), lattice
mismatch and strain (calculated) and In
diffusion length LD (fit parameter)
 m  m0 

 Very good match with exp data for LD = 280nm
(@ T=400C)
Full calculations in Q. Xie et al., PRL 75, 2542 (1995)
Surface chemical potential on a patterned,
faceted substrate
 0
mt  m0 
;
lt
ms  m0 ;
lt
µt
lb
nD m
j(x)  
k B T x

j(x)
R(x)   0 J 0 (x) 

x 
µs
µb
 0
mb  m0 
lb
Ozdemir and Zangwill,
JVSTA 10, 684 (1992)
Diffusion towards the bottom
Growth rate: increased at the
bottom, decreased at the top
Mechanism of self-limiting growth
Capillarity
=
Growth rate anisotropy
Self-limiting growth
G. Biasiol and E. Kapon, PRL 81, 2962 (1998),
G. Biasiol et al., PRB 65, 205306 (2002).
Self-Limiting Growth: AlxGa1-xAs
AFM cross section of a Vgroove AlxGa1-xAs
heterostructure
x=0.21
VQW
Ls(Ga) > Ls(Al)
 stronger Ga capillarity to
the bottom
 Ga-rich AlxGa1-xAs vertical
quantum well
Nonuniform composition
x=0.49
 ordered phase
 increase of the entropy of
mixing
 to be included in the model
200 nm
0
1.5 nm
G. Biasiol and E. Kapon, PRL 81, 2962 (1998),
G. Biasiol et al., PRB 65, 205306 (2002).
Composition dependence of self-limiting bottom
width
 Evidence for entropic contributions
140
120
without entropy
of mixing
lbsl (nm)
100
AlXGa1-XAs;
T = 700°C
80
60
exp. data
40
with entropy
of mixing
20
0
0.2
0
0.4
0.8
0.6
x
l  l X;l , l , Dr ,Dr , L
sl
b
sl
b
G. Biasiol and E. Kapon, PRL 81, 2962 (1998),
G. Biasiol et al., PRB 65, 205306 (2002).
A
sl
G
sl
A
fixed by
experiment
G
G
s
1

fitted, LsG =175±20nm
Temperature dependence
 Arrhenius plots
 sl ~ lsl (nm)
30
10
8
x=0
x=.19
x=.29
x=.47
6
4
11.5
12
12.5
13
1/k B T (eV)
GaAs:
AlXGa1-XAs:
1 /3
l slG  DsG
e xpEBG / 3k BT 
l sl  X   lsl X;DsA , DsG 
G. Biasiol and E. Kapon, PRL 81, 2962 (1998),
G. Biasiol et al., PRB 65, 205306 (2002).
fit: EBG = 1.9±0.3eV
fit: EBA = 2.3±0.2eV
Evolution to self-limiting profiles
 sl
dlb
l
 Dr 0  b
 lb
dt

GaAs:
AlXGa1-XAs:
3


  1




 sl
dlb
l
0
 Dr  X  b
 lb
dt

3


  1  b lb  lbsl

 lb3




Modeling of experimental data; T = 700°C
120
From experiment
100
GaAs
Al0.3Ga0.7As
lbsl (nm)
129±3
31.6±1.1
Dr0
0.22±0.05
0.19±0.05
LsG (nm)
Fitted

l b (nm)
Parameters
l bsl (GaAs)
80
60
40
145±20
l bsl (Al 0.3 Ga 0.7 As)
20
0
G. Biasiol and E. Kapon, PRL 81, 2962 (1998),
G. Biasiol et al., PRB 65, 205306 (2002).
50
100
z n (nm)
150
200
QDs on etched tetrahedral pyramids
Top view
QDs at the intersection of 3 QWRs
 3D diffusion model [ µ(x,y) ]
A. Hartmann et al.
APL 71, 1314 (1997)