1 / 39

Multi-million Atom Electronic Structure Calculations for Quantum Dots

Multi-million Atom Electronic Structure Calculations for Quantum Dots. Muhammad Usman Network for Computational Nanotechnology (NCN) Electrical and Computer Engineering Department Purdue University. Email: usman@purdue.edu Major Advisor: Prof. Dr. Gerhard Klimeck.

papina
Download Presentation

Multi-million Atom Electronic Structure Calculations for Quantum Dots

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Multi-million Atom Electronic Structure Calculations for Quantum Dots Muhammad Usman Network for Computational Nanotechnology (NCN) Electrical and Computer Engineering Department Purdue University. Email: usman@purdue.edu Major Advisor: Prof. Dr. Gerhard Klimeck NETWORK FOR COMPUTATIONAL NANOTECHNOLOGY (Ph. D. Final Examination --- Date: 07-15-2010)

  2. Photon Absorption Tunneling/Transport Occupancy of states Photon Emission Detectors/ Input Lasers/ Output Logic / Memory What are Quantum Dots? “Man-made nanoscale structures in which electrons can be confined in all 3 dimensions” Quantum Well Quantum Dot Bulk Quantum Wire Atom Small Dye Molecule Fluorescent Protein Animal Cell Bacterium • Electronic structure: • Electron energy is quantized -> artificial atoms (coupled QD->molecule) • Contains a countable number of electrons 10um 100um 1um 100nm 1Ao 1nm 10nm D(E) D(E) D(E) D(E) Quantum Dot E E E E Quantum dots are artificial atoms that can be custom designed for a variety of applications

  3. Colloidal, CdSe, ZnSe http://www.research.ibm.com/journal/rd/451 ElectrostaticGates, GaAs, Si, Ge Create electron puddles 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 Source: http://www.spectrum.ieee.org/WEBONLY/wonews/aug04/0804ndot.html QD Example Implementations Fabrication Self-assembled, InGaAs on GaAs. Pyramidal or dome shaped R.Leon,JPL(1998)

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

  5. QDs for Optical Devices – Requirements? Requirement 1: Optical Emissions at 1.3-1.5μm for optical fibers 1.1-1.2 μm Single In(Ga)As QD +InxGaAs QW +Sb +N +Bi Bilayer InAs QD Stack InAs QD inside InxGaAs QW InAsSb QD InGaNAs QD 1.3 μm InGaBiAs QD InAs QD Stack Inside InxGaAs QW Large InAs QD Stack (Columnar QD) 1.5 μm Requirement 2: Optical Emissions should be polarization insensitive

  6. InAs QDs in InGaAs QWs – Can they emit at 1500nm? Experiment without Theory • Questions • What shifts the optical peak to 1500nm? • Why nonlinear dependence on In composition? • What is role of strain, piezoelectricity? • How is wavelength related to size/composition of QD?

  7. 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 • suppress In/Ga intermixing  • maintain QD size  • Question asked to me by the experimentalists: • Optically active layer of QDs, upper/lower? • Increased size of QDs in upper layer: will it enhance TM mode? • InGaAs cap on the upper layer: How it effects the polarization response? • 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!

  8. How Can Theory, Modeling, and Computation Help? • 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 AFM micrograph of InAs QD Experiment Diagnostic data • Quantum dots grow in different shapes and sizes • PL intensity is measured to determine light spectrum • Experimentalists need to understand the PL spectrum Source: cqd.eecs.northwestern.edu/research/qdots.php Simulation Missing Physics Comparison Applied Phys. Lett. 78, 3469 (2001)

  9. How do we get QDs?  Stranski-Krastanov Growth Self-Assembly Process  InAs deposition on GaAs substrate First Layer (wetting layer) ~ 1ML InAs (0.60583 nm) GaAs (0.56532 nm) Capping Layer Quantum Dot GaAs Wetting Layer InAs InAs • QDs grown by self-assembly process have: • Rough/Asymmetric Interface • Strain • Stress-induced Polarization GaAs GaAs Substrate

  10. What is required in a theoretical model for QDs? Quantum Dots grown by self-assembly process have atomistic granularity! • Interface roughness and assymetry • Arbitrary alloy configuration • Long range strain • Non-parabolic dispersion • Piezoelectricity GaAs 60nm InAs InGaAs nanoHUB.org Biaxial Strain IEEE Trans. on Nanotechnology (2009) GaAs buffer Strain  Yes Piezo  No InAs Dome QD In proc. of the IEEE NEMS (2008) What we need: (1) Atomistic calculation of strain, piezoelectricity, and electronic structure (2) Large simulation domain ~ multi-million atoms? Strain  Yes Piezo  Yes In proc. of the IEEE Nano (2008)

  11. Why Multi-Million Atoms, Large GaAs Buffer? 30nm ~50nm 20nm 50nm ~8 Million Atoms !

  12. NEMO 3-D – A fully atomistic simulation tool • Methodology1: • Experimental geometry in input deck • Strain is calculated using Valence Force Field (VFF) Method2,3 • Linear and Quadratic Piezoelectric potentials by solving Poisson’s equation over polarization charge density4 • Empirical tight binding parameters -- sp3d5s* band model with spin orbital coupling5 Input Deck Geometry Construction Eigen Solver Atomistic Relaxation Piezoelectric Potential Strain Hamiltonian Construction Electrical / Magnetic field • Capabilities: • Arbitrary shape/size of quantum dot • Long range strain, piezoelectric fields • Interface roughness, atomistic representation of alloy • External Electrical/Magnetic fields • Zincblende/Wurtzite crystals Optical Transition Strengths Single Particle Energies Excitons [1] IEEE Trans. Electron Devices,54, 9. (2007) [2] Phys. Rev. 145, no. 2, pp.737 (1966) [3] Appl. Phys. Lett. 85, 4193 (2004) [4] Phys. Rev. B 76, 205324 (2007) [5] Phys. Rev. B 66, 125207 (2002)

  13. Thesis Outline (2) Single Quantum Dot inside InGaAs-SRCL (1) Single Quantum Dot • Atomistic Interface • Strain • Piezoelectricity • Optical Transitions 1500nm Optical Emissions Include one cool breakthrough image (3) Bilayer Quantum Dot Stack (4) Polarization Resolved Optical Emissions • Level Anti-crossing Spectroscopy (LACS) • Exciton Tuning • Piezoelectricity • Single vs. Bilayers of QDs • 1300-1500nm Emissions • Polarization-resolved Optical Transitions

  14. Thesis Outline (2) Single Quantum Dot inside InGaAs-SRCL (1) Single Quantum Dot • Atomistic Interface • Strain • Piezoelectricity • Optical Transitions 1500nm Optical Emissions Include one cool breakthrough image (3) Bilayer Quantum Dot Stack (4) Polarization Resolved Optical Emissions • Level Anti-crossing Spectroscopy (LACS) • Exciton Tuning • Piezoelectricity • Single vs. Bilayers of QDs • 1300-1500nm Emissions • Polarization-resolved Optical Transitions

  15. Can asymmetric interface lower the symmetry? dEp = |E1 – E2| ~ 0 from 8 band k•p method QD Interfaces are not Equivalent ! Phys. Rev B 52, 11969 (1995) Continuum approach neglects interface asymmetry. NEMO 3-D – No Strain, No Piezo Phys. Rev. B 71, 045318 (2005) No strain, No piezoelectricity

  16. How Strain Changes the Electronic Spectra? Ɛxx+ɛyy+ɛzz Ɛxx+ɛyy-2ɛzz No strain With strain • Band Gap Increases • HH and LH split • [110]---[-110] anisotropy is enhanced

  17. What Piezoelectricity can do to Electronic Spectrum? + - Strain Strain+piezo • Small changes in energy levels • Optical Gap nearly unchanged • Electron P-states flipped!

  18. Inter-band Optical Transitions E3-H1 E3 E2 TE E2-H1 TM E1 E1-H1 H1 H2 H3 First few VB states are HH states due to biaxial strain 7nm 20nm A typical Experimental Setup QD TM[001] TE[110] Light A single flat QD is very polarization sensitive i.e. TE Mode >> TM Mode [-110]

  19. Thesis Outline (2) Single Quantum Dot inside InGaAs-SRCL (1) Single Quantum Dot • Atomistic Interface • Strain • Piezoelectricity • Optical Transitions 1500nm Optical Emissions Include one cool breakthrough image (3) Bilayer Quantum Dot Stack (4) Polarization Resolved Optical Emissions • Level Anti-crossing Spectroscopy (LACS) • Exciton Tuning • Piezoelectricity • Single vs. Bilayers of QDs • 1300-1500nm Emissions • Polarization-resolved Optical Transitions

  20. 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 Ref: IEEE Trans. on Nanotechnology, vol. 8, No. 3, May 2009, pp.330-344

  21. QD Aspect Ratio Changes • SRCL introduces large in-plane strain • vertical strain is relaxed •  Base decreases •  Height increases Aspect Ratio of QD Increase ! ΔH  red shift of emission spectra ΔB  blue shift of emission spectra RED SHIFT OF EMISSION SPECTRA AR + Strain Relaxation = Red Shift Ref: Phys. Rev. B 74, 245331 (2006) Ref: IEEE Trans. on Nanotechnology, vol. 8, No. 3, May 2009, pp.330-344

  22. What is the reason for nonlinearity in experiment and theory? NEMO 3-D (red line) matches experiment’s non-linear behavior (black lines) ? Hole energy levels change nonlinearly Electron energy levels change linearly Nonlinearity Comes from Holes ! δEc = -5.08εH δEHH = εH – 0.9 εB Biaxial Strain causes Nonlinearity ! Ref: IEEE Trans. on Nanotechnology, vol. 8, No. 3, May 2009, pp.330-344

  23. Nonlinear Bond Length Distortion  Nonlinear Biaxial Strain Non-linear biaxial Strain  Non-linear red shift in emission spectra  Non-linear biaxial strain comes from non-linear bond configuration Ref: Phys. Rev. Lett. 79, 5026 (1997) Bond length in strained alloys is non-linear! X aInGaAs = x.aInAs + (1-x).aGaAs 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: IEEE Trans. on Nanotechnology, vol. 8, No. 3, May 2009, pp.330-344

  24. Experimental Imperfections does not Change our Conclusions ! Soft Interface Size Variation • QD size is not exactly knownnominally D=20nm, H=5nm • Base increase D=21nm  red shift ~40nm • Height increase H=5.5nm  red shift ~120nm • 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 • Device characteristics relatively insensitive towards experimental imperfections! • Small wavelength changes • Same non-linearity Ref: IEEE Trans. on Nanotechnology, vol. 8, No. 3, May 2009, pp.330-344

  25. Thesis Outline (2) Single Quantum Dot inside InGaAs-SRCL (1) Single Quantum Dot • Atomistic Interface • Strain • Piezoelectricity • Optical Transitions 1500nm Optical Emissions Include one cool breakthrough image (3) Bilayer Quantum Dot Stack (4) Polarization Resolved Optical Emissions • Level Anti-crossing Spectroscopy (LACS) • Exciton Tuning • Piezoelectricity • Single vs. Bilayers of QDs • 1300-1500nm Emissions • Polarization-resolved Optical Transitions

  26. Bilayer Quantum Dot Stack Device Model Experiment Source: Walter Schottky Institute Hydrostatic Strain Biaxial Strain In Quantum Dot Stacks, Strain can penetrate deep and couple adjacent layers! Ref: in proc. of IEEE Nano 2008.

  27. Quantum Dot Molecule As “d ” increases, coupling reduces! 4 5 7 9 10 6 8 11 Is this quantum mechanical coupling between the quantum dots at some fixed “d” controllable by an external field? Ref: in proc. of IEEE Nano 2008.

  28. Is it possible to control this coupling by the external fields? Experiment with First Order Theory Single band effective mass study • Qualitative match with experiment • Have to significantly adjust the QD dimensions to get close to the experiment • Only lowest two electron levels (E1, E2) are considered • No Quadratic Piezoelectric Component • No optical transition strength calculations GaInAs ~5nm ~21nm GaInAs ~10 nm ~4nm ~19nm 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 GaAs

  29. ‘Bright’ – ‘Dark’ Excitons F Fixed External Field (F) can turn the Excitons ‘ON’ or ‘OFF’ ! E3-H1 = Bright, E1-H1=E2-H1= Dark E1-H1 = Bright, E2-H1= Dark Ref: under review ACS Nano 2010

  30. Match With Experiment e4 E=17kV/cm h1 e3 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 ! Ref: under review ACS Nano 2010 e3 h1 e4

  31. Level Anti-crossing Spectroscopy (LACS): • Spectroscopic probing of electronic energy levels of one quantum dot through anti-crossings with second quantum dot. • Determination of intra-dot spatial separation between electron and hole. • Determination of dot-to-dot separation. • Piezoelectricity is of critical importance! Ref: under review ACS Nano 2010

  32. Thesis Outline (2) Single Quantum Dot inside InGaAs-SRCL (1) Single Quantum Dot • Atomistic Interface • Strain • Piezoelectricity • Optical Transitions 1500nm Optical Emissions (3) Bilayer Quantum Dot Stack (4) Polarization Resolved Optical Emissions • Level Anti-crossing Spectroscopy (LACS) • Exciton Tuning • Piezoelectricity • Single vs. Bilayers of QDs • 1300-1500nm Emissions • Polarization-resolved Optical Transitions

  33. 1300nm+ Quantum Dot Devices • Upper QD is optically active • ~77nm red shift for QD Stack • ~122nm red shift for QD Stack with SRCL • Stacks of QDs provide red shifts of emission spectra

  34. Multiple Valence Band Energy Levels Contribute at RT Experimental Measurement: TE[110] ------------ = 1 + 0.1 TE[-110] Top view of upper QD in bilayer QD stack Hole Energy Level H1 is oriented along [110] direction Hole energy levels are closely packed  H1-H3 ~ 12.5meV < 1/2kT ~ 12.9meV NEMO 3-D Calculations: TE[110] ------------- ~11.4 TE[-110] NEMO 3-D Calculations: TE[110] ------------- ~11.4  1.52  1.07 TE[-110] NEMO 3-D Calculations: TE[110] ------------- ~11.4  1.52 TE[-110] Multiple valence band energy levels should be considered for RT ground state optical emissions!

  35. TE[110]/TM[001] Ratio Tailoring: Semiconductor Optical Amplifiers operate with cleaved-edge excitation: • QD Stack exhibit lesser polarization sensitivity • SRCL  HH-LH splitting increases • SRCL increases polarization sensitivity • NEMO 3-D trends match experimental measurements QD TM[001] TE[110] Light [-110]

  36. Summary (2) Single Quantum Dot inside InGaAs-SRCL (1) Single Quantum Dot • Atomistic Interface • Strain • Piezoelectricity • Optical Transitions 1500nm Optical Emissions Outlook (3) Bilayer Quantum Dot Stack (4) Polarization Resolved Optical Emissions • Level Anti-crossing Spectroscopy (LACS) • Exciton Tuning • Piezoelectricity • Single vs. Bilayers of QDs • 1300-1500nm Emissions • Polarization-resolved Optical Transitions

  37. Outlook (1) – Short term projects Laterally Coupled QD Molecules Columnar Quantum Dots phys. stat. sol. (c) 0, No. 4, 1137– 1140 (2005) PHYSICAL REVIEW B 81, 205315 (2010) NEMO 3-D Results • Laterally coupled QDs for Quantum Information Science • External Electrical Field determine the dot-to-dot coupling • Little theoretical guidance available to-date • Large Stacks of InAs QDs • [001] confinement is relaxed • QDL ~ 11  TE ~ TM • Theoretical design recipe for devices

  38. Outlook (2) – Long term projects Growth Simulation  NEMO 3-D QDs Grown on (111) Substrates Appl. Phys. Lett. 96, 093112 (2010) Cryst. Res. Technol., 1-6 (2009), Wiley Inter Science • Only little is known about QD geometry • Shape, Size, Composition, ‘In’ Segregation? • Electronic/Optical Spectra have strong dependence on geometry of QDs • Possibility to drive fully atomistic electronic structure calculations of NEMO 3-D by simulations of the Self-assembly growth process? • QDs grown on [111] substrate are potential candidates for entangled photons i.e. biexciton  exciton  0 • Lowest symmetry is C3v • Piezoelectricity is along the growth direction and does not lower the symmetry!

  39. Acknowledgements: • Major Advisor: Prof. Dr. Gerhard Klimeck • Advisory Committee: Prof. Dr. Timothy Sands, Prof. Dr. M. Ashraful Alam, • Prof. Dr. R. Edwin Garcia, Prof. Dr. Alejandro H. Strachan • Prof. Shaikh S. Ahmed (SIU), Prof. Timothy B. Boykin (UAH) • Prof. Edmund Clarke, Dr. Susannah Heck (Imperial College London) • “Klimeck” group members and NCN colleagues, our collaborators and sponsors • USA Department of States (USAID) for Fulbright Fellowship (2005-2010) • Network for Computational Nanotechnology, Rosen Center for Advanced Computing • Purdue University, Electrical and Computer Engineering Department (ECE) • My family for their moral support and patience • Thank you All !

More Related