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

Stranski-KrastanovFrank-van der Merwe Volmer-Weber

used for „usual“ heterostructures:

unstrained material systems i.e. GaAs/AlAs

similar to rain drops on window

strained material systems i.e. In(Ga)As/GaAs

particular growth conditions i.e. temperature, In content, growth rate 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 surfacedensities:

0 - 1.000 µm-2

Growth on unrotated substrate

850 900 950 1000 1050 1100 1150 1200 1250 Wavelength (nm)

PL

inte

nsi

ty (

a.u.)

850 900 950 1000 1050 1100 1150 1200 1250

PL

inte

nsi

ty (

a.u.)

In

Ga

constantIn:Garatio

gradually changing

In:Garatio

further processing

Overgrowth for opticalapplication

Intermixing of materials

• no surface states• low band-gap material

surrounded by high band-gap matrix material

» 0-dimensional confinement

• occurs naturally• can also be driven by

thermal annealing» change of confinement

potential

Quantum Dots – artificial atoms

Band Gap (300K)– Eg,GaAs

= 1.411eV– Eg,InAs

= 0.356eV

» ΔEg up to ~ 1eVEEGG

3D D

OS

3D D

OS

2D D

OS

2D D

OS

1D D

OS

1D D

OS

0D D

OS

0D D

OS

EEGG

EEGG EEGG

EnergyEnergy EnergyEnergy

EnergyEnergyEnergyEnergyEE11 EE22 EE33

EE1111 EE1212 EE1313 EE111111 EE112112 EE113113

(a)(a) (b)(b)

(c)(c) (d)(d)

tz

tzty

tztytx

EEGG

3D D

OS

3D D

OS

2D D

OS

2D D

OS

1D D

OS

1D D

OS

0D D

OS

0D D

OS

EEGG

EEGG EEGG

EnergyEnergy EnergyEnergy

EnergyEnergyEnergyEnergyEE11 EE22 EE33

EE1111 EE1212 EE1313 EE111111 EE112112 EE113113

(a)(a) (b)(b)

(c)(c) (d)(d)

tz

tzty

tzty

tztytx"real atom"

single QD:"artificial atom"

SAQDs – confinement for excitons

» optically active exciton (X)states are bound

1280 1290 1300 1310

0.24

P (µW )L

0.20

0.15

0.11

0.08

0.06

0.05

0.04

0.03

0.02

0.015

2X

s-p p-s

s-Shell p-She ll

1X

E nergy (m eV )

PL

inte

nsity

(ar

b. u

nits

)

T=2 K=632.8 nm L

In G a A s/G aAs0.4 0 .6

E

x,y

X

x,y

z

» shell structure» parabolic

potential» few particle

interaction

n = 1n = 2

n = 1n = 2

gro

wth

dir

ect

ion

10nm

Electric fields on QDs

20)( FcFpEFE

QCSE:

Quantum Confined Stark Effect

vertical ( ) fields:• well investigated

• intrinsic dipole p 0• weak polarizability c

lateral ( ) fields:• not investigated in detail

• intrinsic dipole p = 0 expected

• high polarizability c

further investigation

p intrinsic dipolec polarizability

gro

wth

dir

ect

ion

10nm

Electric fields on QDs

20)( FcFpEFE

QCSE:

Quantum Confined Stark Effect

p intrinsic dipolec polarizability

F

ΔE(F)

Flateral

Fvertical

???

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

• Contact-Design– split-gates– standard optical lithography– contacts-on-top design (2µm gap)

2µm

First Approach

• put QDs in Capacitor

• 1. order approximation:homogeneous lateral field

• realisation of metal-semiconductor junction(pinning)

» expected field:

d

dUF

U

Stability Problems

-10 -5 0 5 10

0

1

2

PC

PC/[

a.u.]

bias voltage/ [V]

PL

PL/

[a.u

.]

excitation 632.8nm

-30 -20 -10 0 10

0

1

2

3

4

5

PC /

[a.

u.]

bias voltage / [V]

structure diedduring measurement

Model calculations on different Designs

GaAs

VacuumGaAs

Vacuum

GaAs

Vacuum

Model calculations on different Designs

ElateralEvertical

0 1 2 3 4 5

-4

-3

-2

-1

0

1

2

3

4

0 1 2 3 4 5

-4

-3

-2

-1

0

1

2

3

4

contact on top buried contact

Ev

ert

ica

l / [a

.u.]

x / [µm]

Ela

tera

l / [a

.u.]

x / [µm]

Model calculations – contacts on top

• decreasing d increases field• considering homogeneity

» trade-off: d = 2µm

0 1 2 3 4 5

0

1

2

3

4

5

6

7

1µm gap 2µm gap

Ela

tera

l / [

a.u.]

x / [µm]

• extraction of geometry factor

» fmidgap ≈ 0.75

0 1 2 3 4 5

0

1

2

3

4

5

contacts on top

Ela

tera

l / [

a.u.]

x / [µm]

field in simple capacitor

temperature dependent IV-Curves

0 50 100 150 200 250 300

5

10

15

20

25

Onse

t Voltag

e (V

)

Temperature (K)

0 10 20 30

0,00

0,25

0,50

0,75

1,00 305 K 250 K 200 K 150 K 100 K 75 K 50 K 15,5 K

Curr

ent (µ

A)

bias voltage (V)

max. fields: 80-130 kV/cm

Dark current measurement

µPL/µPC - Setup

• Spatial Resolution (1µm Spot)

• Bias dependent optical spectroscopy(PL and PC)

• Temperature: down to 4.2K

U

Crash course PL & PC

electric field (kV/cm)20 30 40 50 60 70 80 90 100 110

1.296

1.298

1.300

1.302

1.304

1.306

1.308

PL PC

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

negative external voltage (V)

en

erg

y (

eV

)860 880 900 920 940 960 980 1000 1020 1040

Phot

o Lu

min

esce

nce

/ [c

ps]

Wavelength / [nm]

WL

Ensemble of QDs

single QD

Bias dependent PL-Spectra

• HeNe-excitation (632.8nm)

• PL disappears @ 13 kV/cm (3.5V)

880 900 920 940 960 980 1000 1020

Photo

Lum

ines

cence

/ [

a.u.]

Wavelength / [nm]

Bias dependent PL-Spectra (-5V..5V)

Bias dependent PL & PC

0.0 0.5 1.0 1.5 2.0

GaAs PL

bias voltage (V)

QD PL

PC

WL PL

HeNe excitation (632.8nm)

PC resonant excitation

19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5

0

2

4

6

8

10

PC (

a.u.)

bias voltage (V)

» 4-terminal-µCapacitor– different crystal directions– top and back contacts

foreseen

Sample Design – future plans

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:X0 in QD |10 empty QD |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:

Applying lateral fieldmeans control of ΔE

10nm

10nm

E|11 = E|01 + E|10 + ΔE

CNOT Gate

1

1

0

0

00 --> 0001 --> 0110 --> 11

11 --> 100

10on

off

control bitswitches

NOT-operationon target bit control bit

unaffected by CNOT

target bitchanged if control bit is 1

initializationapplying gate operation readout

on

off

target bit

consideration purely classical and logic so far:

quantum mechanical implementation

Implementation

PC-Meas

control of dotoccupation• Rabi-oscillation• different

X0-GS-energies

a

1,1

0,0

1,00,1

ba nn ,

a b

baab

b

a b

The above term scheme can be taylored for our needs by applying vertical & lateral fields!!!

initialization applying gate operation readout

Rabi Oscillation