Transcript Folie 1 - TU Muenchen

Tuning eigenstate-energies of InGaAs
Quantum-Dots using lateral electric fields
W. Prestel, H. Krenner, J. J. Finley
St. Petersburg – JASS 2004
Outline
• Introduction
– Growth of self-assembled Quantum Dots (SAQDs)
– electric fields on QDs
• Work in progress:
single QDs in lateral electric fields
• Benefit of lateral electric fields
– structural information about QDs
– Implementation of CNOT Gate
Self-Assembly of Quantum Dots

Frank-van der Merwe

Stranski-Krastanov
used for „usual“
heterostructures:
 strained material systems
i.e. In(Ga)As/GaAs
 unstrained material
systems
i.e. GaAs/AlAs
 particular growth conditions
i.e. temperature, In content,
growth rate
Volmer-Weber
 similar to rain drops
on window
 formation of pseudomorpic layer:
Wetting Layer (WL)
 growth of islands:
strain relaxes in islands
In(Ga)As Quantum Dots
Lattice constant:
– GaAs: 0.57nm
– InAs: 0.61nm
Lattice mismatch ε = 7%
typical surface
densities:
0 - 1.000 µm-2
gradually
changing
In:Ga
ratio
850
900
950
850
900
950
1000
1050
1100
1150
1200
1250
PL intensity (a.u.)
constant
In:Ga
ratio
PL intensity (a.u.)
Growth on unrotated substrate
1000 1050 1100 1150 1200 1250
Wavelength (nm)
further processing
Overgrowth for optical
application
• occurs naturally
• can also be driven by
thermal annealing
» change of confinement
potential
• no surface states
• low band-gap material
surrounded by high bandgap matrix material
» 0-dimensional confinement
Intermixing of materials
Quantum Dots – artificial atoms
Band Gap (300K)
tz
2D DOS
» ΔEg up to ~ 1eV
(b)
3D DOS
– Eg,GaAs = 1.411eV
– Eg,InAs = 0.356eV
(a)
EG
EG
E1
E2
Energy
(c)
"real atom"
Energy
(d)
tz
tz
ty tx
EG
0D DOS
ty
1D DOS
single QD:
"artificial atom"
E3
E11
E12
Energy
E13
EG
E111
E112
Energy
E113
SAQDs – confinement for excitons
» optically active exciton (X)
states are bound
T=2 K
 L=632.8 nm
In0.4Ga0.6As/GaAs
s-Shell
p-Shell
PL(µW)
0.24
z
0.20
X
x,y
n=2
n=1
E
n=1
n=2
» shell structure
» parabolic
potential
» few particle
interaction
PL intensity (arb. units)
0.15
0.11
0.08
s-p
p-s
0.06
0.05
2X
0.04
0.03
1X
0.02
0.015
x,y
1280
1290
1300
Energy (meV)
1310
Electric fields on QDs

2
 
E(F )  E0  p  F  cF
Quantum
Confined
Stark
Effect
growth direction
QCSE:
p intrinsic dipole
c polarizability
10nm
vertical ( ) fields:
lateral (
• well investigated
• not investigated in detail
• intrinsic dipole p 0
• intrinsic dipole p = 0
expected
• weak polarizability c
) fields:
• high polarizability c
further investigation
Electric fields on QDs

2
 
E(F )  E0  p  F  cF
Quantum
Confined
Stark
Effect
growth direction
QCSE:
p intrinsic dipole
c polarizability
10nm
ΔE(F)
F
Fvertical
???
Flateral
Work in progress
• Sample Design
– model calculations
– strength of electrical field
• Setup + crash course in PL & PC
• Characterization of sample
Sample Design
• Substrate:
– In0.5Ga0.5As – QDs in GaAs
– surface density: ~ 1.000 QDs/µm2
– undoped substrate
2µm
• Contact-Design
– split-gates
– standard optical lithography
– contacts-on-top design (2µm gap)
First Approach
• put QDs in Capacitor
• 1. order approximation:
homogeneous lateral field
d
• realisation of metalsemiconductor junction
(pinning)
» expected field:
U
F U
d
Stability Problems
5
PC / [a.u.]
4
structure died
during measurement
3
2
1
2
PL/[a.u.]
PC/[a.u.]
0
1
PC
PL
0
excitation 632.8nm
-10
-5
0
bias voltage/[V]
5
10
-30
-20
-10
bias voltage / [V]
0
10
Model calculations on different Designs
Vacuum
Vacuum
GaAs
Vacuum
GaAs
GaAs
Model calculations on different Designs
4
4
3
3
2
2
Elateral / [a.u.]
Evertical / [a.u.]
contact on top
buried contact
1
0
-1
1
0
-1
-2
-2
-3
-3
-4
-4
0
1
2
3
x / [µm]
Evertical
4
5
0
1
2
3
4
x / [µm]
Elateral
5
Model calculations – contacts on top
7
1µm gap
2µm gap
5
4
• decreasing d increases field
• considering homogeneity
3
» trade-off: d = 2µm
2
1
0
0
1
2
3
4
5
x / [µm]
5
• extraction of geometry factor
» fmidgap ≈ 0.75
4
Elateral / [a.u.]
Elateral / [a.u.]
6
3
2
1
contacts on top
field in simple capacitor
0
0
1
2
3
x / [µm]
4
5
temperature dependent IV-Curves
305 K
250 K
200 K
150 K
100 K
75 K
50 K
15,5 K
0,75
0,50
Dark current measurement
0,25
25
0,00
0
10
20
30
bias voltage (V)
max. fields: 80-130 kV/cm
Onset Voltage (V)
Current (µA)
1,00
20
15
10
5
0
50
100
150
200
Temperature (K)
250
300
µPL/µPC - Setup
U
• Spatial Resolution
(1µm Spot)
• Bias dependent
optical
spectroscopy
(PL and PC)
• Temperature:
down to 4.2K
Crash course PL & PC
negative external voltage (V)
860
880
900
Ensemble of QDs
1.308
single QD
1.306
920
940
960
980 1000 1020 1040
Wavelength / [nm]
energy (eV)
Photo Luminescence / [cps]
WL
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
1.304
1.302
1.300
1.298
PL
1.296
20
30
PC
40
50
60
70
80
90 100 110
electric field (kV/cm)
Bias dependent PL-Spectra
Photo Luminescence / [a.u.]
Bias dependent PL-Spectra (-5V..5V)
• HeNe-excitation
(632.8nm)
• PL disappears
@ 13 kV/cm
(3.5V)
880
900
920
940
960
Wavelength / [nm]
980
1000
1020
Bias dependent PL & PC
GaAs PL
WL PL
QD PL
PC
HeNe excitation (632.8nm)
0.0
0.5
1.0
bias voltage (V)
1.5
2.0
PC resonant excitation
10
PC (a.u.)
8
6
4
2
0
19.0
19.5
20.0
20.5
21.0
21.5
bias voltage (V)
22.0
22.5
Sample Design – future plans
» 4-terminal-µCapacitor
– different crystal directions
– top and back contacts
foreseen
top view
Application
1) Investigation of shape and alloy profile
of buried Dots
2) Goal in further future:
Implementation of CNOT gate
Shape and alloy profile of QDs
• no non-invasive characterization of overgrown QDs possible
• structural properties determine electro-optical properties
Definition of Qubits
QM implementation of CNOT
- 1-Qbit-System:
in QD

0 empty QD 
X0
10nm
10nm
|1
|0
- 2-Qbit-System: Quantum Dot Molecule (QDM):
empty dots  |00; X0 in lower dot  |10; …  |01; …  |11
- coupling of X0 in QDM via dipole-dipole interaction:
E|11 = E|01 + E|10 + ΔE
 Applying lateral field means control of ΔE
CNOT Gate
initialization
applying gate operation
1
0
1
0
on
readout
off
control bit
switches
NOT-operation
on target bit
0
on
off
target bit
00
01
10
11
-->
-->
-->
-->
00
01
11
10
control bit
unaffected by CNOT
1
0
target bit
changed if control bit is 1
consideration purely classical and logic so far:
 quantum mechanical implementation
Implementation
initialization
applying gate operation
na , nb
control of dot
occupation
• Rabi-oscillation
• different
X0-GS-energies
readout
1,1
w
wab
wba
wa  wb
0,1
1,0
wa
b
a
wb
PC-Meas
0,0
The above term scheme can be
taylored for our needs by applying
vertical & lateral fields!!!
Rabi Oscillation