Simulation of Transport in Nanodevices

François Triozon, Researcher at Laboratoire d'Electronique et de Technologies de l'Information (LETI) of CEA/Grenoble, France.

Philippe Dollfus, CNRS Research Director, France.

List of Symbols xv

List of Abbreviations xvii

Chapter 1 Introduction: Nanoelectronics, Quantum Mechanics, and Solid State Physics 1
Philippe Dollfus and François Triozon

1.1 Nanoelectronics 1

1.2 Basic notions of solid-state physics 4

1.3 Quantum mechanics and electronic transport 20

1.4 Conclusion 29

1.5 Bibliography 30

Chapter 2 Electronic Transport: Electrons, Phonons and Their Coupling within the Density Functional Theory 31
Nathalie Vast, Jelena Sjakste, Gaston Kané and Virginie Trinité

2.1 Introduction 31

2.2 Electronic structure 34

2.3 Phonons 46

2.4 Electron-phonon coupling 52

2.5 Semiclassical transport properties 62

2.6 Quantum transport 70

2.7 Conclusion 84

2.8 Appendix A 85

2.9 Blbiography 86

Chapter 3 Electronic Band Structure: Empirical Pseudopotentials, k . p and Tight-Binding Methods 97
Denis Rideau, François Triozon and Philippe Dollfus

3.1 Band structure problem 97

3.2 Empirical pseudopotentials method 102

3.3 the k . p method 109

3.4 The TB method 115

3.5 Optimization of empirical models 122

3.6 Bibliography 126

Chapter 4 Relevant Semiempirical Potentials for Phonon Properties 131
Sebastian Volz

4.1 Introduction 131

4.2 Generic pair potentials: the Lennard-Jones potential 134

4.3 Semiconductors: Stillinger-Weber and Tersoff potentials 136

4.4 Oxydes: Van Beest, Kramer and van Santen potential 143

4.5 Metals - isotropic many-body pair-functional potentials for metals: the modified embedded-atom method 148

4.6 Polymers and carbon-based compounds: adaptive intermolecular reactive bond order, adaptive intermolecular REBO and Dreiding potentials 149

4.7 Water: TIP3P potential 156

4.8 Conclusion 158

4.9 Bibliography 158

Chapter 5 Introduction to Quantum Transport 163
François Triozon, Stephan Roche and Yann-Michel Niquet

5.1 Quantum transport from the point of view of wavepacket propagation 164

5.2 The transmission formalism for the conductance 177

5.3 The Green's function method for quantum transmission 185

5.4 Conclusion 219

5.5 Matlab/Octave codes 219

5.6 Bibliography 220

Chapter 6 Non-Equilibrium Green's Function Formalism 223
Michel Lannoo and Marc Bescond

6.1 Second quantization and time evolution pictures 223

6.2 General definition of the Green's functions, their physical meaning and their perturbation expansion 225

6.3 Stationary Green's functions and fluctuation-dissipation theorem 229

6.4 Dyson's equation and self-energy: general formulation 232

6.5 Some examples 237

6.6 The ballistic regime 240

6.7 The electron-photon interaction 245

6.8 Bibliography 257

Chapter 7 Electron Devices Simulation with Bohmian Trajectories 261
Guillermo Albareda, Damiano Marian, Abdelilah Benali, Alfonso Alarcon, Simeon Moises and Xavier Oriols

7.1 Introduction: why Bohmian mechanics? 261

7.2 Theoretical framework: Bohmian mechanics 267

7.3 The BITLLES simulator: time-resolved electron transport 276

7.4 Computation of the electrical current and its moments with BITLLES 291

7.5 Conclusion 299

7.6 Acknowlegments 301

7.7 Appendix A: Pratical algorithm to compute Bohmian trajectories 301

7.8 Appendix B: Ramo-Shockley-Pellegrini theorems 306

7.9 Appendix C: Bohmian mechanics with operators 307

7.10 Appendix D: Relation between the Wigner distribution function and the Bohmian trajectories 310

7.11 Bibliography 314

Chapter 8 The Monte Carlo Method for Wigner and Boltzmann Transport Equations 319
Philippe Dollfus, Damien Querlioz and Jérôme Saint Martin

8.1 The WTE 320

8.2 The semiclassical limit: BTE 325

8.3 Scattering in Boltzmann and Wigner equations 329

8.4 The MC method for solving the BTE 341

8.5 Extension of the MC method for solving the WBTE 352

8.6 Bibliography 360

List of Authors 371

Index 373

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