1. Network for Computational Nanotechnology (NCN) UC Berkeley, Univ.of Illinois, Norfolk State, Northwestern, Purdue, UTEP 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. Ganesh Hegde 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. Ganesh Hegde 3 As the title suggests… OptimizationThe Genetic Algorithm Tight Binding parameterization Other projects with GA + future work …there are distinct topics tackled in this work.

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

5. Ganesh Hegde 5 The need for optimization

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

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

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

9. Ganesh Hegde 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. All of the above affect the choice of solution method!! Linear/non-linear? Time required Constraints / Priorities Gradient?

10. Ganesh Hegde 10 Broad comparison of commonly used optimization techniques 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 Mathematical TechniquesHeuristics 01234 -0.5 0 0.5 1 x y = exp(-x)sin(8x) You need an optimum solution, not a mathematical way of getting from one point to another in search space!!

11. Ganesh Hegde 11 As the title suggests… OptimizationThe Genetic Algorithm Tight Binding parameterization Other projects with GA + future work …there are distinct topics tackled in this work.

12. Ganesh Hegde 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) General purpose, parallel, easy to interface your code Scores over other optim. Tools!

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

14. Ganesh Hegde 14 Comparison -1 Gene BiologicalAlgorithmic A unit of DNA. Represents a physical characteristic. A suitably encoded input parameter (binary, real, integer, exponential) E.g. Channel Length(nm)  23.2 Doping conc.  1e+18 /cm 3 Image Ref. [3]

15. Ganesh Hegde 15 Comparison -2 Chromosome BiologicalAlgorithmic Blueprint of an organismCollection of all inputs 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. Ganesh Hegde 16 GA - 1 Input encoding »Binary »Real »Integer »Exponential »Combination of the above Choose an encoding suitable for your problem

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

18. Ganesh Hegde 18 GA-3 Evaluation »Fitness – How ‘good’ is a potential solution? 15 C2 is fitter than C1 1 1 C1 030 0 1 1C2

19. Ganesh Hegde 19 GA-4: Selection and reproduction nN n-N Unfit to live OLDNEWParents MateChildren are born n (Parents+Children)

20. Ganesh Hegde 20 GA 5 - Crossover C1C1 C2C2 1 1 0 1 0 0 1 1 13 03 1 1 0 1 0 0 1 1 11 05 0 1 1 1 0 1 13 03 1 1 0 1 0 0 1 1 15 01 1 1 11 0 0 1 10 1 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. Ganesh Hegde 21 GA 6 - Mutation 1 1 1 11 1 115 0 1 1 11 1 107 Mutation is an Explorative operator!! Prevents getting stuck in a local optima. Allows for exploration of search space. Standard GA  In practice you can design your own operators

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

23. Ganesh Hegde 23 As the title suggests… OptimizationThe Genetic Algorithm Tight Binding parameterization Other projects with GA + future work …there are distinct topics tackled in this work.

24. Ganesh Hegde 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. Ganesh Hegde 25 TB as an optimization problem Vhh 1,Vhh 2,Vhh 3,….Vh h n Ec 1,Ec 2,Ec 3,….Ec n Eg 1,Eg 2,Eg 3,….Eg n P 1,P 2,P 3,….P n m* 1,m* 2,m* 3,….m* n 35 inputs/material, 100’s of outputs, unknown search space  Genetic Algorithm m* 1,m* 2,m* 3,….m* n Eg 1,Eg 2,Eg 3,….Eg n m* 1,m* 2,m* 3,….m* n Eg 1,Eg 2,Eg 3,….Eg n m* 1,m* 2,m* 3,….m* n

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

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

28. Ganesh Hegde 28

29. Ganesh Hegde 29 InAs bulk variation with hydrostatic strain ε xx = ε yy = ε zz Change lattice constant of material to correspond to required strain Fig. Gaps and edges at Gamma point for InAs at 4K versus hydrostatic strain Solid Lines – Theory Circles - calculated

30. Ganesh Hegde 30 GaAs bulk variation with hydrostatic strain Fig. Gaps and edges at Gamma point for GaAs at 4K versus hydrostatic strain Solid Lines – Theory Circles - calculated

31. Ganesh Hegde 31 InAs bulk variation with uniaxial (001) strain Fig. Gaps and edges at Gamma point for InAs at 4K versus uni-axial (001) strain. ε xx = ε yy != ε zz Solid Lines – Theory Circles - calculated

32. Ganesh Hegde 32 GaAs bulk variation with uniaxial (001) strain Fig. Gaps and edges at Gamma point for GaAs at 4K versus uniaxial strain Solid Lines – Theory Circles - calculated

33. Ganesh Hegde 33 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!!

34. Ganesh Hegde 34 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. GaAs InAs GaAs InAs lattice constant > GaAs (7%) Difficult to accurately model electronic structure of InAs/GaAs QD’s !!

35. Ganesh Hegde 35 Attempts at matching experiment Optical Gap = CBM - VBM Coulombic correction not calculated (30-40 meV effect) 2 Strain models in NEMO-3D (harmonic, Anharmonic)

36. Ganesh Hegde 36 Built in models in NEMO-3D for Atomic Structure AsInAsIn dx Harmonic dx Anharmonic

37. Ganesh Hegde 37 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.

38. Ganesh Hegde 38 The essential difference – an intuitive picture In NEMO3D we initially set the lattice constant = lattice constant of GaAs for both strain models! AsIn Harmonic InAs Anharmonic InAs Anharmonic model minimizes its strain more effectively than Harmonic model.

39. Ganesh Hegde 39 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!!!

40. Ganesh Hegde 40 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

41. Ganesh Hegde 41 As the title suggests… OptimizationThe Genetic Algorithm Tight Binding parameterization Other projects with GA + future work …there are distinct topics tackled in this work.

42. Ganesh Hegde 42 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

43. Ganesh Hegde 43 General purpose optimization engine for nanoHUB GUI Rappture – API Tool Rappture – API GUI Rappture Optimization API Tool Analyze Launch

44. Ganesh Hegde 44 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!

45. Ganesh Hegde 45 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!!

46. Ganesh Hegde 46 Images 1.http://user.uni- frankfurt.de/~scherers/blogging/AdventsKalenderPlots/GaAs/BandStru ctureGaAs_s_mark.jpghttp://user.uni- frankfurt.de/~scherers/blogging/AdventsKalenderPlots/GaAs/BandStru ctureGaAs_s_mark.jpg 2.http://www.mun.ca/computerscience/news/distinguished_lect.phphttp://www.mun.ca/computerscience/news/distinguished_lect.php 3.http://en.wikipedia.org/wiki/File:ADN_animation.gifhttp://en.wikipedia.org/wiki/File:ADN_animation.gif