Multi-million Atom Electronic Structure Calculations for Quantum Dots

Multi-million Atom Electronic Structure Calculations for Quantum Dots

Muhammad UsmanNetwork for Computational Nanotechnology (NCN)

Electrical and Computer Engineering DepartmentPurdue University.

Email: [email protected]

Major Advisor: Prof. Dr. Gerhard Klimeck

NETWORK FOR COMPUTATIONAL NANOTECHNOLOGY

(Ph. D. Final Examination --- Date: 07-15-2010)

Muhammad Usman – Ph.D. Dissertation

E

D(E)

E

D(E)

E

D(E)

E

D(E)

Bulk Quantum Well Quantum Wire Quantum Dot

“Man-made nanoscale structures in which electrons can be confined in all 3 dimensions”

1Ao 10nm 100nm1nm 1um 10um 100um

Animal CellBacteriumFluorescent ProteinSmall Dye MoleculeAtom

Quantum Dot

What are Quantum Dots?

PhotonAbsorption

Detectors/Input

PhotonEmission

Lasers/Output

Tunneling/TransportOccupancy of states

Logic / Memory

Electronic structure:• Electron energy is quantized -> artificial atoms (coupled QD->molecule) • Contains a countable number of electrons

Quantum dots are artificial atoms that can be custom designed for a variety of applications


QD Example Implementations

Fabrication

Self-assembled , InGaAs on GaAs.

Pyramidal or domeshaped

R.Leon,JPL(1998)

ElectrostaticGates, GaAs, Si, GeCreate electron puddles

Source: http://www.spectrum.ieee.org/WEBONLY/wonews/aug04/0804ndot.html

Colloidal, CdSe, ZnSe

http://www.research.ibm.com/journal/rd/451

Fluorescence induced by exposure to ultraviolet light in vials containing various sized cadmium selenide (CdSe) quantum dots.Source: http://en.wikipedia.org/wiki/Fluorescent ß

http://en.wikipedia.org/wiki/Image:Fluorescence_in_various_sized_CdSe_quantum_dots.png


Quantum Dots – Optical Devices and Quantum Computing

Self Assembled Quantum Dots

Laser Photo-detector/Amplifier Quantum Computation

Fujitsu Temperature Independent QD laser2004

Quantum Information Science is rapidly progressing, and Quantum Dot based optical devices are approaching the market !

S. J. XuDept. of Physics , University of Hong Kong


QDs for Optical Devices – Requirements?

Single In(Ga)As QD

InAs QD inside

InxGaAs QW

Bilayer InAs QD Stack

1.1-1.2μm

1.3μm

1.5μm

Large InAs QD Stack(Columnar

QD)

InAsSb QD

InGaNAs QD

+Sb +N

InAs QD StackInside

InxGaAs QW

+InxGaAs QW

Requirement 2: Optical Emissions should be polarization insensitive

Requirement 1: Optical Emissions at 1.3-1.5μm for optical fibers

InGaBiAs QD

+Bi


InAs QDs in InGaAs QWs – Can they emit at 1500nm?

Experiment without Theory

Questions

o What shifts the optical peak to 1500nm?

o Why nonlinear dependence on In composition?

o What is role of strain, piezoelectricity?

o How is wavelength related to size/composition of QD?


QD Stacks for 1500nm – Can we get polarization insensitivity too?

Improved control of growth conditions (particularly temperature) for upper layer to achieve long wavelength emissiono suppress In/Ga intermixing o maintain QD size

Question asked to me by the experimentalists:

o Optically active layer of QDs, upper/lower?

o Increased size of QDs in upper layer: will it

enhance TM mode?

o InGaAs cap on the upper layer: How it effects the

polarization response?

o What are the polarization properties when we

consider one hole level vs. multiple hole levels?Theoretical modeling explores the vast design space of QDs and helps us to narrow

it down for the experimentalists!


How Can Theory, Modeling, and Computation Help?

• Quantum dots grow in different shapes and sizes• PL intensity is measured to determine light spectrum• Experimentalists need to understand the PL spectrum

Experiment

Diagnostic data

Simulation

Comparison

• Why Theory, Modeling and Computation? Modeling can provide essential insight into the physical

data Obtain information where experimental data is not

readily available Can help experimentalists to design their experiments

Missing Physics

AFM micrograph of InAs QD

Source: cqd.eecs.northwestern.edu/research/qdots.php

Applied Phys. Lett. 78, 3469 (2001)

http://cqd.eecs.northwestern.edu/research/qdots.php




How do we get QDs? Stranski-Krastanov Growth

Self-Assembly Process InAs deposition on GaAs substrate

InAs (0.60583 nm)

GaAs (0.56532 nm)

First Layer (wetting layer) ~ 1ML

InAs

GaAs

InAs

GaAs

GaAsCapping Layer

Substrate

Wetting Layer

Quantum Dot

QDs grown by self-assembly process have:

o Rough/Asymmetric Interfaceo Straino Stress-induced Polarization


IEEE Trans. on Nanotechnology (2009)

InGaAs

GaAs

InAs

What is required in a theoretical model for QDs?

Interface roughness and assymetry

Arbitrary alloy configuration

Long range strain

Non-parabolic dispersion

Piezoelectricity

Quantum Dots grown by self-assembly process have atomistic granularity!

Strain YesPiezo No

Strain YesPiezo Yes

In proc. of the IEEE NEMS (2008)

Biaxial Strain

InAs Dome QD

GaAs buffer

60nm

In proc. of the IEEE Nano (2008)What we need: (1) Atomistic calculation of strain, piezoelectricity, and electronic structure

(2) Large simulation domain ~ multi-million atoms?

nanoHUB.org


Why Multi-Million Atoms, Large GaAs Buffer?

30nm

20nm

50nm

~50nm

~8 Million Atoms !


NEMO 3-D – A fully atomistic simulation tool

[1] IEEE Trans. Electron Devices,54, 9. (2007)[2] Phys. Rev. 145, no. 2, pp.737 (1966)[3] Appl. Phys. Lett. 85, 4193 (2004)

Geometry Construction

Atomistic Relaxation

Strain

Single Particle Energies

Eigen Solver

Hamiltonian Construction

Input Deck

Electrical / Magnetic field

Piezoelectric Potential

Optical Transition Strengths

Excitons

Methodology1:

o Experimental geometry in input deck

o Strain is calculated using Valence Force Field (VFF) Method2,3

o Linear and Quadratic Piezoelectric potentials by solving Poisson’s equation over polarization charge density4

o Empirical tight binding parameters -- sp3d5s* band model with spin orbital coupling5

Capabilities:

o Arbitrary shape/size of quantum doto Long range strain, piezoelectric fieldso Interface roughness, atomistic representation of alloyo External Electrical/Magnetic fieldso Zincblende/Wurtzite crystals

[4] Phys. Rev. B 76, 205324 (2007)[5] Phys. Rev. B 66, 125207 (2002)


Thesis Outline

Include one cool breakthrough image

(1) Single Quantum Dot

(2) Single Quantum Dot inside InGaAs-SRCL

(3) Bilayer Quantum Dot Stack

(4) Polarization Resolved Optical Emissions

o Atomistic Interfaceo Straino Piezoelectricityo Optical Transitions 1500nm Optical Emissions

o Level Anti-crossing Spectroscopy (LACS)

o Exciton Tuningo Piezoelectricity

o Single vs. Bilayers of QDso 1300-1500nm Emissionso Polarization-resolved

Optical Transitions


Thesis Outline










Optical Transitions


Electron P-state

Anisotropy

NEMO 3-D

Lens Pyramid

Height =4.6nmDiameter = 11.3nm

Height = 4.6nmBase = 11.3nm

dEp (meV) 1.69 2.02

Can asymmetric interface lower the symmetry?

dEp = |E1 – E2| ~ 0 from 8 band k•p method

Phys. Rev B 52, 11969 (1995)

Continuum approach neglects interface asymmetry.

QD Interfaces are not Equivalent !

NEMO 3-D – No Strain, No Piezo

Phys. Rev. B 71, 045318 (2005)

No strain, No piezoelectricity


ElectronP-state

Anisotropy

NEMO 3-D

Lens Pyramid

Height = 4.6nmDiameter = 11.3nm


dEp (meV) 1.69 5.73 2.0210.85

How Strain Changes the Electronic Spectra?

o Band Gap Increaseso HH and LH split o [110]---[-110] anisotropy is enhanced

No

stra

inW

ith s

trai

n

Ɛxx+ɛyy+ɛzz

Ɛxx+ɛyy-2ɛzz


ElectronP-state

Anisotropy

NEMO 3-D

Lens Pyramid

Height = 4.6nmDiameter = 11.3nm


dEp (meV) 5.73-7.7 10.85-10.11

What Piezoelectricity can do to Electronic Spectrum?

+

-

o Small changes in energy levelso Optical Gap nearly unchanged o Electron P-states flipped!

Str

ain

Stra

in+p

iezo


Inter-band Optical Transitions

20nm

7nm

TETM

E1

E2E3

H1H2H3

E1-H1

E2-H1

E3-H1

QDLight

TE[110]

TM[001]

[-110]

A typical Experimental Setup

A single flat QD is very polarization sensitive i.e. TE Mode >> TM Mode

First few VB states are HH states due to biaxial strain


Thesis Outline










Optical Transitions

Muhammad Usman – Ph.D. Dissertation Ref: IEEE Trans. on Nanotechnology, vol. 8, No. 3, May 2009, pp.330-344

Strain Band Edge Deformations

Hydrostatic strain relaxation Band gap reduction Red shift of spectraBiaxial strain reinforcement LH bands move opposite of HH bandsHH states dominate for large In concentrations! => Strong binding


• SRCL introduces large in-plane strain

• vertical strain is relaxed

• Base decreases

• Height increases

QD Aspect Ratio Changes

Aspect Ratio of QD Increase !

ΔH red shift of emission spectraΔB blue shift of emission spectra

35.0

AR

BE

HE

RED SHIFT OF EMISSION SPECTRA

Ref: Phys. Rev. B 74, 245331 (2006)AR + Strain Relaxation = Red Shift


NEMO 3-D (red line) matches experiment’s non-linear behavior (black lines) ?

δEc = -5.08εH

δEHH = εH – 0.9 εB

Electron energy levels change linearly

Nonlinearity Comes from Holes !

Biaxial Strain causes Nonlinearity !

Hole energy levels change nonlinearly

What is the reason for nonlinearity in experiment and theory?


Non-linear biaxial Strain Non-linear red shift in emission spectra

Non-linear biaxial strain comes from non-linear bond configuration

aInGaAs = x.aInAs + (1-x).aGaAsXBond length in strained alloys is non-linear!

Nonlinear Bond Length Distortion Nonlinear Biaxial Strain

Simple virtual crystal approximation is failed in strained alloys!Better theoretical approximation of bond lengths is required!

NEMO 3-D quantitatively modeled the non-linearity in the experiment!

Ref: Phys. Rev. Lett. 79, 5026 (1997)


Soft Interface• Ga and In diffusion at the interface

InAs QD interface is not sharp shells of different In concentrations• D1 (x1, x2, x3) = (1, 1, 1)• D2 (x1, x2, x3) = (1, 0.9, 0.8)• D3 (x1, x2, x3) = (1, 0.7, 0.6)• Blue shift of emission spectra

peak shift ~47nm

Size Variation

• QD size is not exactly known

nominally D=20nm, H=5nm

• Base increase D=21nm

red shift ~40nm

• Height increase H=5.5nm

red shift ~120nmDevice characteristics relatively insensitive towards experimental imperfections!- Small wavelength changes- Same non-linearity

Experimental Imperfections does not Change our Conclusions !


Thesis Outline






o Atomistic Interfaceo Straino Piezoelectricityo Optical Transitions

1500nm Optical Emissions




Optical Transitions


Bilayer Quantum Dot Stack

Experiment

In Quantum Dot Stacks, Strain can penetrate deep and couple adjacent layers!

Ref: in proc. of IEEE Nano 2008.

Source: Walter Schottky Institute

Hydrostatic Strain Biaxial Strain

Device Model


As “d ” increases, coupling reduces!

Quantum Dot Molecule

Ref: in proc. of IEEE Nano 2008.

4 5 6 7 8 9 10 11

Is this quantum mechanical coupling between the quantum dots at some fixed “d” controllable by an external field?


Is it possible to control this coupling by the external fields?

Single band effective mass studyExperiment with First Order Theory

o Qualitative match with experiment

o Have to significantly adjust the QD dimensions to get close to the experiment

o Only lowest two electron levels (E1, E2) are considered

o No Quadratic Piezoelectric Component

o No optical transition strength calculations

GaInAs

GaInAs~10 nm

GaAs

~21nm

~19nm

~5nm

~4nm

Goals: 1) Atomistic Modeling+(Linear+Quadratic) piezoelectricity+Optical Transition Strengths2) Identify electron and hole states in excitonic spectra without geometry tuning3) Characterize excitons as “dark” and “bright” and demonstrate field controlled tuning


‘Bright’ – ‘Dark’ Excitons

FixedF

E1-H1 = Bright, E2-H1= Dark E3-H1 = Bright, E1-H1=E2-H1= Dark

External Field (F) can turn the Excitons ‘ON’ or ‘OFF’ !

Ref: under review ACS Nano 2010

Muhammad Usman – Ph.D. Dissertation Ref: under review ACS Nano 2010

Match With Experiment

h1 e3

e4

h1

e3

e4

E=17kV/cm

E=19.5kV/cm

• Anti-crossing field (F) from NEMO 3-D match experimental value• Bright Excitons are E3-H1 and E4-H1, NOT E1-H1 !

Muhammad Usman – Ph.D. Dissertation Ref: under review ACS Nano 2010

Level Anti-crossing Spectroscopy (LACS):

o Spectroscopic probing of electronic energy levels of one quantum dot through anti-crossings with second quantum dot.

o Determination of intra-dot spatial separation between electron and hole.

o Determination of dot-to-dot separation.

o Piezoelectricity is of critical importance!


Thesis Outline










Optical Transitions


1300nm+ Quantum Dot Devices

o Upper QD is optically active

o ~77nm red shift for QD Stack

o ~122nm red shift for QD Stack with SRCL

o Stacks of QDs provide red shifts of emission spectra


Multiple Valence Band Energy Levels Contribute at RT

Experimental Measurement:

TE[110]------------ = 1 + 0.1TE[-110]

Hole Energy Level H1 is oriented along [110] direction

Top view of upper QD in bilayer QD stack

H1-H3 ~ 12.5meV < 1/2kT ~ 12.9meVHole energy levels are closely packed

NEMO 3-D Calculations:

TE[110]------------- ~11.4TE[-110]

Multiple valence band energy levels should be considered for RT ground state optical emissions!


TE[110]------------- ~11.4 1.52TE[-110]


TE[110]------------- ~11.4 1.52 1.07TE[-110]


TE[110]/TM[001] Ratio Tailoring:

o QD Stack exhibit lesser polarization sensitivity

o SRCL HH-LH splitting increases

o SRCL increases polarization sensitivity

o NEMO 3-D trends match experimental measurements

QDLight

TE[110]

TM[001]

[-110]

Semiconductor Optical Amplifiers operate with cleaved-edge excitation:


Summary(1) Single Quantum Dot









Optical Transitions

Outlook


Outlook (1) – Short term projects

Columnar Quantum Dots Laterally Coupled QD Moleculesphys. stat. sol. (c) 0, No. 4, 1137– 1140 (2005)

PHYSICAL REVIEW B 81, 205315 (2010)

o Laterally coupled QDs for Quantum Information Science

o External Electrical Field determine the dot-to-dot coupling

o Little theoretical guidance available to-date

o Large Stacks of InAs QDso [001] confinement is relaxedo QDL ~ 11 TE ~ TMo Theoretical design recipe for devices

NEMO 3-D Results


QDs Grown on (111) Substrates Growth Simulation NEMO 3-D

Outlook (2) – Long term projects

Appl. Phys. Lett. 96, 093112 (2010)

o QDs grown on [111] substrate are potential candidates for entangled photons i.e. biexciton exciton 0

o Lowest symmetry is C3v

o Piezoelectricity is along the growth direction and does not lower the symmetry!

Cryst. Res. Technol., 1-6 (2009), Wiley Inter Science

o Only little is known about QD geometryo Shape, Size, Composition, ‘In’ Segregation?o Electronic/Optical Spectra have strong

dependence on geometry of QDso Possibility to drive fully atomistic electronic

structure calculations of NEMO 3-D by simulations of the Self-assembly growth process?


Acknowledgements:

o Major Advisor: Prof. Dr. Gerhard Klimeck

o Advisory Committee: Prof. Dr. Timothy Sands, Prof. Dr. M. Ashraful Alam,

Prof. Dr. R. Edwin Garcia, Prof. Dr. Alejandro H. Strachan

o Prof. Shaikh S. Ahmed (SIU), Prof. Timothy B. Boykin (UAH)

o Prof. Edmund Clarke, Dr. Susannah Heck (Imperial College London)

o “Klimeck” group members and NCN colleagues, our collaborators and sponsors

o USA Department of States (USAID) for Fulbright Fellowship (2005-2010)

o Network for Computational Nanotechnology, Rosen Center for Advanced Computing

o Purdue University, Electrical and Computer Engineering Department (ECE)

o My family for their moral support and patience

Thank you All !

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Multi-million Atom Electronic Structure Calculations for Quantum Dots

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