Multi-million Atom Electronic Structure Calculations for Quantum Dots Muhammad Usman Network for Computational Nanotechnology (NCN) Electrical and Computer Engineering Department Purdue University. Major Advisor: Prof. Dr. Gerhard Klimeck NETWORK FOR COMPUTATIONAL NANOTECHNOLOGY ( Ph. D. Final Examination --- Date: )

Muhammad Usman – Ph.D. Dissertation E D(E) E E E Bulk Quantum Well Quantum Wire Quantum Dot “Man-made nanoscale structures in which electrons can be confined in all 3 dimensions” 1A o 10nm 100nm 1nm 1um 10um100um Animal Cell Bacterium Fluorescent Protein Small Dye Molecule Atom Quantum Dot What are Quantum Dots? Photon Absorption Detectors/ Input Photon Emission Lasers/ Output Tunneling/Transport Occupancy 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

Muhammad Usman – Ph.D. Dissertation QD Example Implementations Fabrication Self-assembled, InGaAs on GaAs. Pyramidal or dome shaped R.Leon,JPL(1998) Electrostatic Gates, GaAs, Si, Ge Create electron puddles Source: Colloidal, CdSe, ZnSe Fluorescence induced by exposure to ultraviolet light in vials containing various sized cadmium selenide (CdSe) quantum dots. Source: ß

Muhammad Usman – Ph.D. Dissertation Quantum Dots – Optical Devices and Quantum Computing Self Assembled Quantum Dots Laser Photo-detector/Amplifier Quantum Computation Fujitsu Temperature Independent QD laser 2004 Quantum Information Science is rapidly progressing, and Quantum Dot based optical devices are approaching the market ! S. J. Xu Dept. of Physics, University of Hong Kong

Muhammad Usman – Ph.D. Dissertation QDs for Optical Devices – Requirements? Single In(Ga)As QD InAs QD inside In x GaAs QW Bilayer InAs QD Stack μm 1.3 μm 1.5 μm Large InAs QD Stack (Columnar QD) InAsSb QD InGaNAs QD +Sb +N InAs QD Stack Inside In x GaAs QW +In x GaAs QW Requirement 2: Optical Emissions should be polarization insensitive Requirement 1: Optical Emissions at μm for optical fibers InGaBiAs QD +Bi

Muhammad Usman – Ph.D. Dissertation 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?

Muhammad Usman – Ph.D. Dissertation QD Stacks for 1500nm – Can we get polarization insensitivity too? Improved control of growth conditions (particularly temperature) for upper layer to achieve long wavelength emission o 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!

Muhammad Usman – Ph.D. Dissertation 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.ph p Applied Phys. Lett. 78, 3469 (2001)

Muhammad Usman – Ph.D. Dissertation How do we get QDs?  Stranski-Krastanov Growth Self-Assembly Process  InAs deposition on GaAs substrate InAs ( nm) GaAs ( nm) First Layer (wetting layer) ~ 1ML InAs GaAs InAs GaAs Capping Layer Substrate Wetting Layer Quantum Dot QDs grown by self-assembly process have: o Rough/Asymmetric Interface o Strain o Stress-induced Polarization

Muhammad Usman – Ph.D. Dissertation 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  Yes Piezo  No Strain  Yes Piezo  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? What we need:(1) Atomistic calculation of strain, piezoelectricity, and electronic structure (2) Large simulation domain ~ multi-million atoms? nanoHUB.org

Muhammad Usman – Ph.D. Dissertation Why Multi-Million Atoms, Large GaAs Buffer? 30nm 20nm 50nm ~50nm ~8 Million Atoms !

Muhammad Usman – Ph.D. Dissertation 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 Methodology 1 : o Experimental geometry in input deck o Strain is calculated using Valence Force Field (VFF) Method 2,3 o Linear and Quadratic Piezoelectric potentials by solving Poisson’s equation over polarization charge density 4 o Empirical tight binding parameters -- sp 3 d 5 s* band model with spin orbital coupling 5 Capabilities: o Arbitrary shape/size of quantum dot o Long range strain, piezoelectric fields o Interface roughness, atomistic representation of alloy o External Electrical/Magnetic fields o Zincblende/Wurtzite crystals [4] Phys. Rev. B 76, (2007) [5] Phys. Rev. B 66, (2002)

Muhammad Usman – Ph.D. Dissertation 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 Interface o Strain o Piezoelectricity o Optical Transitions 1500nm Optical Emissions o Level Anti-crossing Spectroscopy (LACS) o Exciton Tuning o Piezoelectricity o Single vs. Bilayers of QDs o nm Emissions o Polarization-resolved Optical Transitions

Muhammad Usman – Ph.D. Dissertation 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 Interface o Strain o Piezoelectricity o Optical Transitions 1500nm Optical Emissions o Level Anti-crossing Spectroscopy (LACS) o Exciton Tuning o Piezoelectricity o Single vs. Bilayers of QDs o nm Emissions o Polarization-resolved Optical Transitions

Muhammad Usman – Ph.D. Dissertation Electron P-state Anisotropy NEMO 3-D LensPyramid Height =4.6nm Diameter = 11.3nm Height = 4.6nm Base = 11.3nm dE p (meV) Can asymmetric interface lower the symmetry? dE p = |E1 – E2| ~ 0 from 8 band kp method Phys. Rev B 52, (1995) Continuum approach neglects interface asymmetry. QD Interfaces are not Equivalent ! NEMO 3-D – No Strain, No Piezo Phys. Rev. B 71, (2005) No strain, No piezoelectricity

Muhammad Usman – Ph.D. Dissertation Electron P-state Anisotropy NEMO 3-D LensPyramid Height = 4.6nm Diameter = 11.3nm Height = 4.6nm Base = 11.3nm dE p (meV)1.69   How Strain Changes the Electronic Spectra? o Band Gap Increases o HH and LH split o [110]---[-110] anisotropy is enhanced Ɛ xx + ɛ yy + ɛ z z Ɛ xx + ɛ yy - 2 ɛ zz

Muhammad Usman – Ph.D. Dissertation Electron P-state Anisotropy NEMO 3-D LensPyramid Height = 4.6nm Diameter = 11.3nm Height = 4.6nm Base = 11.3nm dE p (meV)5.73   What Piezoelectricity can do to Electronic Spectrum? + - o Small changes in energy levels o Optical Gap nearly unchanged o Electron P-states flipped!

Muhammad Usman – Ph.D. Dissertation Inter-band Optical Transitions 20nm 7nm TE TM E1 E2 E3 H1 H2 H3 E1-H1 E2-H1 E3-H1 QD Light 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

Muhammad Usman – Ph.D. Dissertation 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 Interface o Strain o Piezoelectricity o Optical Transitions 1500nm Optical Emissions o Level Anti-crossing Spectroscopy (LACS) o Exciton Tuning o Piezoelectricity o Single vs. Bilayers of QDs o nm Emissions o Polarization-resolved Optical Transitions

Muhammad Usman – Ph.D. Dissertation Ref: IEEE Trans. on Nanotechnology, vol. 8, No. 3, May 2009, pp Strain  Band Edge Deformations Hydrostatic strain relaxation  Band gap reduction  Red shift of spectra Biaxial strain reinforcement  LH bands move opposite of HH bands HH states dominate for large In concentrations! => Strong binding

Muhammad Usman – Ph.D. Dissertation Ref: IEEE Trans. on Nanotechnology, vol. 8, No. 3, May 2009, pp 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 spectra ΔB  blue shift of emission spectra RED SHIFT OF EMISSION SPECTRA Ref: Phys. Rev. B 74, (2006) AR + Strain Relaxation = Red Shift

Muhammad Usman – Ph.D. Dissertation Ref: IEEE Trans. on Nanotechnology, vol. 8, No. 3, May 2009, pp NEMO 3-D (red line) matches experiment’s non-linear behavior (black lines) ? δE c = -5.08ε H δE HH = ε H – 0.9 ε B 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?

Muhammad Usman – Ph.D. Dissertation Ref: IEEE Trans. on Nanotechnology, vol. 8, No. 3, May 2009, pp Non-linear biaxial Strain  Non-linear red shift in emission spectra  Non-linear biaxial strain comes from non-linear bond configuration a InGaAs = x.a InAs + (1-x).a GaAs X Bond 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)

Muhammad Usman – Ph.D. Dissertation Ref: IEEE Trans. on Nanotechnology, vol. 8, No. 3, May 2009, pp Soft Interface Ga and In diffusion at the interface  InAs QD interface is not sharp  shells of different In concentrations D 1  (x 1, x 2, x 3 ) = (1, 1, 1) D 2  (x 1, x 2, x 3 ) = (1, 0.9, 0.8) D 3  (x 1, x 2, x 3 ) = (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 ~120nm Device characteristics relatively insensitive towards experimental imperfections! -Small wavelength changes -Same non-linearity Experimental Imperfections does not Change our Conclusions !

Muhammad Usman – Ph.D. Dissertation 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 Interface o Strain o Piezoelectricity o Optical Transitions 1500nm Optical Emissions o Level Anti-crossing Spectroscopy (LACS) o Exciton Tuning o Piezoelectricity o Single vs. Bilayers of QDs o nm Emissions o Polarization-resolved Optical Transitions

Muhammad Usman – Ph.D. Dissertation Bilayer Quantum Dot Stack Experiment In Quantum Dot Stacks, Strain can penetrate deep and couple adjacent layers! Ref: in proc. of IEEE Nano Source: Walter Schottky Institute Hydrostatic Strain Biaxial Strain Device Model

Muhammad Usman – Ph.D. Dissertation As “d ” increases, coupling reduces! Quantum Dot Molecule Ref: in proc. of IEEE Nano Is this quantum mechanical coupling between the quantum dots at some fixed “d” controllable by an external field?

Muhammad Usman – Ph.D. Dissertation Is it possible to control this coupling by the external fields? Single band effective mass study Experiment 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 ~10 nm GaAs ~21nm ~19nm ~5nm ~4nm Goals: 1)Atomistic Modeling+(Linear+Quadratic) piezoelectricity+Optical Transition Strengths 2)Identify electron and hole states in excitonic spectra without geometry tuning 3)Characterize excitons as “dark” and “bright” and demonstrate field controlled tuning

Muhammad Usman – Ph.D. Dissertation ‘Bright’ – ‘Dark’ Excitons Fixed F 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 h1e3 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!

Muhammad Usman – Ph.D. Dissertation Thesis Outline (1)Single Quantum Dot (2) Single Quantum Dot inside InGaAs-SRCL (3)Bilayer Quantum Dot Stack(4)Polarization Resolved Optical Emissions o Atomistic Interface o Strain o Piezoelectricity o Optical Transitions 1500nm Optical Emissions o Level Anti-crossing Spectroscopy (LACS) o Exciton Tuning o Piezoelectricity o Single vs. Bilayers of QDs o nm Emissions o Polarization-resolved Optical Transitions

Muhammad Usman – Ph.D. Dissertation 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

Muhammad Usman – Ph.D. Dissertation Multiple Valence Band Energy Levels Contribute at RT Experimental Measurement: TE[110] = TE[-110] Hole Energy Level H1 is oriented along [110] direction Top view of upper QD in bilayer QD stack H1-H3 ~ 12.5meV < 1/2 k T ~ 12.9meVHole energy levels are closely packed  NEMO 3-D Calculations: TE[110] ~11.4 TE[-110] Multiple valence band energy levels should be considered for RT ground state optical emissions! NEMO 3-D Calculations: TE[110] ~11.4  1.52 TE[-110] NEMO 3-D Calculations: TE[110] ~11.4  1.52  1.07 TE[-110]

Muhammad Usman – Ph.D. Dissertation 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 QD Light TE[110] TM[001] [-110] Semiconductor Optical Amplifiers operate with cleaved-edge excitation:

Muhammad Usman – Ph.D. Dissertation Summary (1)Single Quantum Dot (2) Single Quantum Dot inside InGaAs-SRCL (3)Bilayer Quantum Dot Stack(4)Polarization Resolved Optical Emissions o Atomistic Interface o Strain o Piezoelectricity o Optical Transitions 1500nm Optical Emissions o Level Anti-crossing Spectroscopy (LACS) o Exciton Tuning o Piezoelectricity o Single vs. Bilayers of QDs o nm Emissions o Polarization-resolved Optical Transitions Outlook

Muhammad Usman – Ph.D. Dissertation Outlook (1) – Short term projects Columnar Quantum DotsLaterally Coupled QD Molecules phys. stat. sol. (c) 0, No. 4, 1137– 1140 (2005) PHYSICAL REVIEW B 81, (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 QDs o [001] confinement is relaxed o QDL ~ 11  TE ~ TM o Theoretical design recipe for devices NEMO 3-D Results

Muhammad Usman – Ph.D. Dissertation QDs Grown on (111) Substrates Growth Simulation  NEMO 3-D Outlook (2) – Long term projects Appl. Phys. Lett. 96, (2010) o QDs grown on [111] substrate are potential candidates for entangled photons i.e. biexciton  exciton  0 o Lowest symmetry is C 3v 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 geometry o Shape, Size, Composition, ‘In’ Segregation? o Electronic/Optical Spectra have strong dependence on geometry of QDs o Possibility to drive fully atomistic electronic structure calculations of NEMO 3-D by simulations of the Self-assembly growth process?

Muhammad Usman – Ph.D. Dissertation 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 ( ) 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 !