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

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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**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**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.**As the title suggests…**…there are distinct topics tackled in this work.**The need for optimization**• Quantum Dot Lab www.nanoHUB.org**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.**The need for optimization**• MOSFET tool on ww.nanoHUB.org**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.**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!!**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!!**As the title suggests…**…there are distinct topics tackled in this work.**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**GA – aim and analogy**• Heuristic • Mimics biological genetic reproduction • Survival of the fittest Holland Darwin Image Ref. [1] and [2]**Comparison -1**• Gene E.g. Channel Length(nm) 23.2 Doping conc. 1e+18 /cm3 Image Ref. [3]**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]**GA - 1**• Input encoding • Binary • Real • Integer • Exponential • Combination of the above Choose an encoding suitable for your problem**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)**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**GA-4: Selection and reproduction**OLD Parents Mate Children are born NEW Unfit to live n-N n (Parents+Children) n N**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.**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.**Summary**• Optimization Process Initialization Physics Code Inputs Outputs Modify Evaluate Optimization Algorithm Selection, Crossover, Mutation, Replacement Fitness Evaluation, Sort Genetic Algorithm**As the title suggests…**…there are distinct topics tackled in this work.**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)**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**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)**TB bulk results**(a) (b) Fig. Bulk band structure of (a) GaAs and (b) InAs at 4K**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**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**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.**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**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!!**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 !!**Attempts at matching experiment**• Optical Gap = CBM - VBM • Coulombic correction not calculated (30-40 meV effect) • 2 Strain models in NEMO-3D (harmonic, Anharmonic)**In**In As As Harmonic Anharmonic dx dx Built in models in NEMO-3D for Atomic Structure**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.**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.**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!!!**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**As the title suggests…**…there are distinct topics tackled in this work.**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**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**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!**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!!**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