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Ganesh Hegde Network for Computational Nanotechnology (NCN) Electrical and Computer Engineering
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Ganesh Hegde Network for Computational Nanotechnology (NCN) Electrical and Computer Engineering

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  1. Generation and optimization of Tight Binding parameters using Genetic Algorithms and their validation using NEMO-3D Ganesh Hegde Network for Computational Nanotechnology (NCN) Electrical and Computer Engineering Committee Prof. Gerhard Klimeck (Major Prof.) Dr. Michael McLennan Prof. Supriyo Datta

  2. Key points I wish to make in this presentation • Need for optimization. • Genetic Algorithm (GA) – general purpose technique. • Tight Binding with GA • InAs and GaAs at Low Temperature (4K) • Validation  Electronic Structure of InAs/GaAs Quantum Dots.

  3. As the title suggests… …there are distinct topics tackled in this work.

  4. The need for optimization • Quantum Dot Lab www.nanoHUB.org

  5. The need for optimization

  6. The need for optimization • Forward procedure • Input  Output • Reverse procedure • Output  Input Fig: Optical absorption plot obtained from Quantum Dot Lab tool on www.nanoHUB.org with parameters shown before.

  7. The need for optimization • MOSFET tool on ww.nanoHUB.org

  8. The need for optimization Give me the input that gives me the output I want Fig: Id-Vg plot obtained MOSFet tool on www.nanoHUB.org with parameters shown before. Fig: Id-Vg plot obtained MOSFet tool on www.nanoHUB.org with parameters shown before.

  9. Common features • Input  Output mapping. • ‘N’ Input parameters • N-dimensional search space. • Desired output(s) • Optimum solution(s) may exist • Nature of Search space • Holes/Singularities/Discontinuities. Linear/non-linear? Time required Constraints / Priorities Gradient? All of the above affect the choice of solution method!!

  10. Point - to - Point mathematical formulation E.g. Gradient-based, Gauss-Newton, Powell etc. Iterative Y(i) = a.Y(i-1) + b.dY(i-1)/dx etx Local Depend on nature of search space Intuitive approach Analogy E.g. GA, SA, PSO, ACO. etc. Parallel Global General purpose 1 0.5 y = exp(-x)sin(8x) 0 -0.5 -1 0 1 2 3 4 x Broad comparison of commonly used optimization techniques Mathematical Techniques Heuristics You need an optimum solution, not a mathematical way of getting from one point to another in search space!!

  11. As the title suggests… …there are distinct topics tackled in this work.

  12. The Genetic Algorithm – why choose it? • Shares all +ve characteristics of heuristics • PGAPack - Parallel Genetic Algorithm Package • David Levine, Argonne National Labs • Parallel (MPI) • Well documented, easy to interface. • Previous experience with TB. • Klimeck et al. (1999) Scores over other optim. Tools! General purpose, parallel, easy to interface your code

  13. GA – aim and analogy • Heuristic • Mimics biological genetic reproduction • Survival of the fittest Holland Darwin Image Ref. [1] and [2]

  14. Comparison -1 • Gene E.g. Channel Length(nm)  23.2 Doping conc.  1e+18 /cm3 Image Ref. [3]

  15. Comparison -2 • Chromosome E.g. [23.2 1e+19 1e+18….] [1101 1011 1111 0001 1110…] [1 23 34 56 -9 -345 999 10247….] Image Ref. [4]

  16. GA - 1 • Input encoding • Binary • Real • Integer • Exponential • Combination of the above Choose an encoding suitable for your problem

  17. GA-2 • Initialization (Playing God) • Population is created by ‘randomly’ sampling the search space 0010(2) 1111(15) 1010(10) N individuals. N is usually large enough to accommodate memory constraints. 1101(13)

  18. GA-3 • Evaluation • Fitness – How ‘good’ is a potential solution? C1 15 1 1 1 1 C2 03 0 0 1 1 C2 is fitter than C1

  19. GA-4: Selection and reproduction OLD Parents Mate Children are born NEW Unfit to live n-N n (Parents+Children) n N

  20. C1 13 1 1 0 1 1 1 0 1 0 1 1 11 C2 03 0 0 1 1 0 0 1 1 1 0 1 05 13 1 1 0 1 1 1 1 1 1 15 03 0 0 1 1 0 0 1 1 0 1 01 GA 5 - Crossover Crossover is an ‘exploitative’ operator!! It exploits the strengths of two chromosomes to form new chromosomes. Weaker children are discarded in the next evaluation. Stronger ones improve fitness further.

  21. 1 1 1 1 1 1 1 15 0 1 1 1 1 1 1 07 GA 6 - Mutation Standard GA  In practice you can design your own operators Mutation is an Explorative operator!! Prevents getting stuck in a local optima. Allows for exploration of search space.

  22. Summary • Optimization Process Initialization Physics Code Inputs Outputs Modify Evaluate Optimization Algorithm Selection, Crossover, Mutation, Replacement Fitness Evaluation, Sort Genetic Algorithm

  23. As the title suggests… …there are distinct topics tackled in this work.

  24. Tight Binding • Electronic Structure Method • LCAO • Potential and material variation  atomic scale • Atomistic basis  nearest neighbor  sparse Hamiltonian • sp3d5s* (Image from http://cobweb.ecn.purdue.edu/~gekco)

  25. TB as an optimization problem m*1 ,m*2 ,m*3,….m*n m*1 ,m*2 ,m*3,….m*n m*1 ,m*2 ,m*3,….m*n m*1 ,m*2 ,m*3,….m*n m*1 ,m*2 ,m*3,….m*n Eg1 ,Eg2 ,Eg3,….Egn Eg1 ,Eg2 ,Eg3,….Egn Eg1 ,Eg2 ,Eg3,….Egn Ec1 ,Ec2 ,Ec3,….Ecn Vhh1,Vhh2,Vhh3,….Vhhn P1 ,P2 ,P3,….Pn 35 inputs/material, 100’s of outputs, unknown search space Genetic Algorithm

  26. TB parameterization - methodology Fitness Extraction Physics Code (NEMO-1D) Initialization (Random) Masses, Band Edges, Gaps, etc (from experiment/theory) Solve [H]{Ψ}= E{Ψ} Inputs (Hamiltonian Terms) Outputs (Band structure) Modify Evaluate Optimization Algorithm Selection, Crossover, Mutation, Replacement Fitness Evaluation, Sort Genetic Algorithm (PGAPACK)

  27. TB bulk results (a) (b) Fig. Bulk band structure of (a) GaAs and (b) InAs at 4K

  28. InAs bulk variation with hydrostatic strain εxx = εyy = εzz Change lattice constant of material to correspond to required strain Solid Lines – Theory Circles - calculated Fig. Gaps and edges at Gamma point for InAs at 4K versus hydrostatic strain

  29. GaAs bulk variation with hydrostatic strain Solid Lines – Theory Circles - calculated Fig. Gaps and edges at Gamma point for GaAs at 4K versus hydrostatic strain

  30. InAs bulk variation with uniaxial (001) strain Solid Lines – Theory Circles - calculated εxx = εyy != εzz Fig. Gaps and edges at Gamma point for InAs at 4K versus uni-axial (001) strain.

  31. GaAs bulk variation with uniaxial (001) strain Solid Lines – Theory Circles - calculated Fig. Gaps and edges at Gamma point for GaAs at 4K versus uniaxial strain

  32. Numerical experiment in NEMO-3D • Free standing InAs box • 5nm X 5nm X 5 nm • Hydrostatic Strain • Energy gap measured L, X valleys moved below Gamma valley  calculated gap at Gamma NOT true gap!!

  33. Validation of TB parameters – Electronic Structure of InAs/GaAs Dots • Self – Assembly • Experimental Uncertainties • GA diffusion (increases gap) • Size • Atomic Structure • Previous theoretical studies  +/- 10% error. InAs lattice constant > GaAs (7%) GaAs InAs GaAs GaAs Difficult to accurately model electronic structure of InAs/GaAs QD’s !!

  34. Attempts at matching experiment • Optical Gap = CBM - VBM • Coulombic correction not calculated (30-40 meV effect) • 2 Strain models in NEMO-3D (harmonic, Anharmonic)

  35. In In As As Harmonic Anharmonic dx dx Built in models in NEMO-3D for Atomic Structure

  36. Atomic Structure of QD’s – procedure and consequences • Aim • To understand why the harmonic model always gives a larger band gap than the anharmonic model • Procedure • Lattice constant of GaAs entire structure. • Minimize total strain energy. • Calculate bond length deviations • Result • Both strain models InAs is only compressively strained. (-1 to -5%) • Strain in Anharmonic model < Strain in harmonic model.

  37. Harmonic In As In In As As Anharmonic The essential difference – an intuitive picture In NEMO3D we initially set the lattice constant = lattice constant of GaAs for both strain models! Anharmonic model minimizes its strain more effectively than Harmonic model.

  38. Attempts at matching experiment • Optical Gap = CBM - VBM • Coulombic correction not calculated (30-40 meV effect) • 2 Strain models in NEMO-3D (harmonic, Anharmonic) Atomic Structure effects are extremely important in validation!!!

  39. Summary • Genetic Algorithm • General purpose • Parallel • Easy to implement and interface • TB is a non-trivial optimization problem • TB parameterization and results • Effect of strain on bulk electronic structure • Matching to experiment for InAs/GaAs dot system is non-trivial • Experimental uncertainties • Atomic structure effects

  40. As the title suggests… …there are distinct topics tackled in this work.

  41. Additional projects with the GA • Tight Binding Parameters • Si (4K) • AlAs (4K and 300K) • InSb, AlSb and GaSb at 300K. (Intend to publish Sb parameters) • Force Field Optimization (collaboration with Strachan group) • Energy, Force and Stress minimization (Ni,Ti) • Force Field parameters • Replace ab-initio calculations

  42. General purpose optimization engine for nanoHUB GUI GUI Rappture – <Language>API Rappture Optimization API Launch Tool Tool Tool Tool Tool Analyze Rappture – <Language>API Rappture Optimization API

  43. Future Work • Arbitrariness of TB parameters • Parameters for Surfaces/Interfaces  scope for work in this area. • Fitness = single number. • Alternate optimization techniques. • Atomic Structure effects greater accuracy required!

  44. Acknowledgments • Committee Members • Prof Klimeck for guidance, constant encouragement (+ve and -ve) and funding support. • Dr. McLennan for his initial guidance with the optimization API and for funding support. • Prof. Datta for agreeing to be a part of my committee in spite of the confusion and for ECE 495 and 659, both excellent courses from which I’ve learned a lot. • George Howlett for helping me out whenever I needed it. (If I have problems with my code, I’m coming back for more help!!) • All EE-350 lab-mates – in particular Sunhee, Usman and Sebastian. Everyone else for the long hours of discussion – technical and non-technical. (…and for tolerating me!!) • Cheryl Haines, Vicki Johnson – Mother Hens of EE-350!!

  45. Images • http://user.uni-frankfurt.de/~scherers/blogging/AdventsKalenderPlots/GaAs/BandStructureGaAs_s_mark.jpg • http://www.mun.ca/computerscience/news/distinguished_lect.php • http://en.wikipedia.org/wiki/File:ADN_animation.gif