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-Krastanov Frank-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 surface densities: µm -2

Growth on unrotated substrate In Ga constant In:Ga ratio gradually changing In:Ga ratio

further processing Overgrowth for optical application 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) –E g,GaAs = 1.411eV –E g,InAs = 0.356eV » ΔE g up to ~ 1eV "real atom" single QD: "artificial atom"

SAQDs – confinement for excitons »optically active exciton (X) states are bound E x,y X z »shell structure »parabolic potential »few particle interaction n = 1 n = 2 n = 1 n = 2

growth direction 10nm Electric fields on QDs 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 dipole c polarizability

growth direction 10nm Electric fields on QDs QCSE: Quantum Confined Stark Effect p intrinsic dipole c polarizability F ΔE(F) F lateral F vertical ???

Work in progress Sample Design –model calculations –strength of electrical field Setup + crash course in PL & PC Characterization of sample

Sample Design Substrate: –In 0.5 Ga 0.5 As – QDs in GaAs –surface density: ~ QDs/µm 2 –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 U

Stability Problems structure died during measurement

Model calculations on different Designs GaAs Vacuum GaAs Vacuum GaAs Vacuum

Model calculations on different Designs E lateral E vertical

Model calculations – contacts on top decreasing d increases field considering homogeneity »trade-off: d = 2µm extraction of geometry factor »f midgap 0.75

temperature dependent IV-Curves max. fields: 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 WL Ensemble of QDs single QD

Bias dependent PL-Spectra HeNe-excitation (632.8nm) PL 13 kV/cm (3.5V)

Bias dependent PL & PC HeNe excitation (632.8nm)

PC resonant excitation

»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: X 0 in QD | 1 0 empty QD | 0 -2-Qbit-System: Quantum Dot Molecule (QDM): empty dots | 00 ; X 0 in lower dot | 10 ; … | 01 ; … | 11 -coupling of X 0 in QDM via dipole-dipole interaction: Applying lateral field means control of ΔE 10nm E |11 = E |01 + E |10 + ΔE

CNOT Gate > > > > on off control bit switches NOT-operation on target bit control bit unaffected by CNOT target bit changed if control bit is 1 initializationapplying gate operationreadout on off target bit consideration purely classical and logic so far: quantum mechanical implementation

Implementation PC-Meas control of dot occupation Rabi-oscillation different X 0 -GS-energies a a b ba ab b The above term scheme can be taylored for our needs by applying vertical & lateral fields!!! initializationapplying gate operationreadout

Rabi Oscillation