Optimal Device Design

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 11
Acknowledgements......Page 13
1.1.1 The past success of ad hoc design......Page 15
1.1.2 Looking beyond ad hoc design......Page 16
1.2 Example: Optimal design of atomic clusters......Page 17
1.3 Design in the age of quantum technology......Page 20
1.3.1 High performance heterostructure bipolar transistors......Page 21
1.3.2 Control of electron transmission through a tunnel barrier......Page 22
1.3.3 The need for improved  physical models......Page 27
1.4 Exploring nonintuitive  design space......Page 28
1.5 Mathematical formulation of optimal device design......Page 29
1.6 Local optimization using the adjoint method......Page 32
1.7.1 Example: Genetic algorithm......Page 35
1.7.2 Constraints......Page 38
1.7.2.1 Interior point method......Page 39
1.7.2.2 Exterior point method......Page 40
1.7.3 Advanced optimization......Page 41
1.8 Summary......Page 42
1.9 References......Page 43
2.1 Manmade nanostructures......Page 46
2.2 Long-range tight-binding model......Page 49
2.3 Target functions and convergence criterion......Page 50
2.4 Atoms-up design of tight-binding clusters in continuous configuration space......Page 52
2.5 Optimal design in discrete configuration space......Page 56
2.6 Optimization and search algorithms......Page 59
2.7 Summary......Page 62
2.8 References......Page 63
3.1 Introduction......Page 65
3.1.1 Example: A transistor that requires ballistic electron transport to operate......Page 68
3.2 Elastic electron transport and tunnel current......Page 71
3.3.1 Parameterization of the design space......Page 75
3.3.2 Mathematical formulation of the design problem......Page 76
3.3.3 Derivative of objective function with respect to design parameters......Page 77
3.3.4 Local optimization......Page 80
3.3.5 Convergence......Page 82
3.3.6 Natural objective functions and efficient parallel search......Page 83
3.4 Inelastic electron transport......Page 85
3.4.1 Incoherent transport and rate equations......Page 86
3.4.2 Coherent inelastic electron transport......Page 92
3.4.3 Coherent current continuity......Page 94
3.4.4 Examples of calculating coherent inelastic electron transmission......Page 96
3.5 Summary......Page 99
3.6 References......Page 100
4.1 Introduction......Page 102
4.2 Calculation of the scattered field......Page 103
4.2.1 Fourier-Bessel based electromagnetic solver......Page 104
4.3 Optimization......Page 105
4.3.1 Cost function......Page 106
4.4 Results......Page 107
4.4.1 Top hat objective function......Page 108
4.4.2 Cosine squared objective function......Page 109
4.4.3 Computing resources......Page 111
4.4.5 Sensitivity analysis......Page 113
4.5 Efficient local optimization using the adjoint method......Page 117
4.6 Finite difference frequency domain electromagnetic solver......Page 118
4.7 Cost functional......Page 121
4.8 Gradient-based optimization using the adjoint method......Page 122
4.9 Results and comparison with experiment......Page 123
4.9.1 Finite-sized periodic structure......Page 124
4.9.2 Aperiodic dielectric structure for a top hat objective function......Page 125
4.9.3 Sensitivity analysis......Page 127
4.9.4 Further discussion......Page 129
4.9.5 Comparison with photonic crystal inspired devices......Page 133
4.10 References......Page 134
5.1 Introduction......Page 137
5.2 Non-local linear response theory......Page 138
5.3 Dielectric response of a diatomic molecule......Page 140
5.4 Dielectric response of small clusters......Page 143
5.5 Dielectric response of a metallic rod......Page 149
5.6 Response of inhomogeneous structures......Page 151
5.7.1 Static response......Page 155
5.7.2 Dynamic response and screening......Page 156
5.7.3 Optimal static response......Page 158
5.7.4 Optimal dynamic response......Page 160
5.9 References......Page 161
6.1 Introduction......Page 163
6.2.1 Problem definition......Page 166
6.2.2  Robust local search algorithm......Page 167
6.2.3.1 Problem description......Page 170
6.2.3.2 Computation results......Page 172
6.2.4 Example in chirped mirrors......Page 174
6.2.4.1 Computation of cost function......Page 176
6.2.4.3 Implementation errors......Page 177
6.2.4.4 Restricted search space......Page 178
6.2.4.5 Results......Page 180
6.3.1 Constrained problem under implementation errors......Page 184
6.3.1.1 Problem definition......Page 185
6.3.1.2 Robust local search for problems with constraints......Page 186
6.3.1.3 Enhancements when constraints are convex......Page 188
6.3.2.1 Problem definition......Page 190
6.3.2.2 Generalized constrained robust local search algorithm......Page 191
6.3.3.1 Problem description......Page 194
6.3.3.2 Computation results......Page 195
6.3.3.3 When constraints are linear......Page 197
6.3.4 Summary......Page 198
6.4 References......Page 200
7.1 Introduction......Page 203
7.2 Constrained local optimal design......Page 208
7.3 Local optimal design of an electronic device......Page 218
7.3.1 The optimal design problem......Page 219
7.3.2 Approximation......Page 223
7.3.3 Computing gradients using the static adjoint method......Page 225
7.3.4 An alternative approach involving the dynamic adjoint......Page 228
7.3.5 Convergence......Page 233
7.3.6 A numerical example......Page 241
7.4 Techniques for global optimization......Page 242
7.4.1 First-order test......Page 248
7.4.2 Second-order test......Page 249
7.5  Database of search iterations......Page 251
7.5.2 Procession flow of EGS......Page 253
7.5.4 A randomly generated test problem......Page 255
7.5.5 EGS performance on the test function......Page 256
7.7 References......Page 258
8.1 Introduction......Page 260
8.2 Example: System complexity in a small laser......Page 261
8.3 Sensitivity to atomic configuration......Page 265
8.3.1 Reproducibility in manufacturing......Page 268
8.3.2 Robustness......Page 270
8.4 Realtime optimal design of molecules......Page 271
8.5 The path to quantum engineering......Page 272
8.6 Summary......Page 273
8.7 References......Page 274
A.2 Tabu search......Page 276
A.3 Particle swarm algorithm......Page 277
A.4 Simulated annealing......Page 279
A.5.1 Multiple starting points......Page 282
A.6  Clustering algorithms......Page 283
A.7.1 Direct elimination of local minimizers......Page 286
A.8 Global smoothing......Page 287
A.9 Stopping rules......Page 288
A.10 References......Page 289
About the authors......Page 291
 Index......Page 295