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Preface xiii <p>List of Symbols xv</p> <p>List of Abbreviations xvii</p> <p><b>Chapter 1 Introduction: Nanoelectronics, Quantum Mechanics, and Solid State Physics 1</b><br /><i>Philippe Dollfus and François Triozon</i></p> <p>1.1 Nanoelectronics 1</p> <p>1.2 Basic notions of solid-state physics 4</p> <p>1.3 Quantum mechanics and electronic transport 20</p> <p>1.4 Conclusion 29</p> <p>1.5 Bibliography 30</p> <p><b>Chapter 2 Electronic Transport: Electrons, Phonons and Their Coupling within the Density Functional Theory 31</b><br /><i>Nathalie Vast, Jelena Sjakste, Gaston Kané and Virginie Trinité</i></p> <p>2.1 Introduction 31</p> <p>2.2 Electronic structure 34</p> <p>2.3 Phonons 46</p> <p>2.4 Electron-phonon coupling 52</p> <p>2.5 Semiclassical transport properties 62</p> <p>2.6 Quantum transport 70</p> <p>2.7 Conclusion 84</p> <p>2.8 Appendix A 85<br /><br />2.9 Blbiography 86</p> <p><b>Chapter 3 Electronic Band Structure: Empirical Pseudopotentials, k . p and Tight-Binding Methods 97</b><br /><i>Denis Rideau, François Triozon and Philippe Dollfus</i></p> <p>3.1 Band structure problem 97</p> <p>3.2 Empirical pseudopotentials method 102</p> <p>3.3 the k . p method 109</p> <p>3.4 The TB method 115</p> <p>3.5 Optimization of empirical models 122</p> <p>3.6 Bibliography 126</p> <p><b>Chapter 4 Relevant Semiempirical Potentials for Phonon Properties 131</b><br /><i>Sebastian Volz</i></p> <p>4.1 Introduction 131</p> <p>4.2 Generic pair potentials: the Lennard-Jones potential 134</p> <p>4.3 Semiconductors: Stillinger-Weber and Tersoff potentials 136</p> <p>4.4 Oxydes: Van Beest, Kramer and van Santen potential 143</p> <p>4.5 Metals - isotropic many-body pair-functional potentials for metals: the modified embedded-atom method 148</p> <p>4.6 Polymers and carbon-based compounds: adaptive intermolecular reactive bond order, adaptive intermolecular REBO and Dreiding potentials 149</p> <p>4.7 Water: TIP3P potential 156</p> <p>4.8 Conclusion 158</p> <p>4.9 Bibliography 158</p> <p><b>Chapter 5 Introduction to Quantum Transport 163</b><br /><i>François Triozon, Stephan Roche and Yann-Michel Niquet</i></p> <p>5.1 Quantum transport from the point of view of wavepacket propagation 164</p> <p>5.2 The transmission formalism for the conductance 177</p> <p>5.3 The Green's function method for quantum transmission 185</p> <p>5.4 Conclusion 219</p> <p>5.5 Matlab/Octave codes 219</p> <p>5.6 Bibliography 220</p> <p><b>Chapter 6 Non-Equilibrium Green's Function Formalism 223</b><br /><i>Michel Lannoo and Marc Bescond</i></p> <p>6.1 Second quantization and time evolution pictures 223</p> <p>6.2 General definition of the Green's functions, their physical meaning and their perturbation expansion 225</p> <p>6.3 Stationary Green's functions and fluctuation-dissipation theorem 229</p> <p>6.4 Dyson's equation and self-energy: general formulation 232</p> <p>6.5 Some examples 237</p> <p>6.6 The ballistic regime 240</p> <p>6.7 The electron-photon interaction 245</p> <p>6.8 Bibliography 257</p> <p><b>Chapter 7 Electron Devices Simulation with Bohmian Trajectories 261</b><br /><i>Guillermo Albareda, Damiano Marian, Abdelilah Benali, Alfonso Alarcon, Simeon Moises and Xavier Oriols</i></p> <p>7.1 Introduction: why Bohmian mechanics? 261</p> <p>7.2 Theoretical framework: Bohmian mechanics 267</p> <p>7.3 The BITLLES simulator: time-resolved electron transport 276</p> <p>7.4 Computation of the electrical current and its moments with BITLLES 291</p> <p>7.5 Conclusion 299</p> <p>7.6 Acknowlegments 301</p> <p>7.7 Appendix A: Pratical algorithm to compute Bohmian trajectories 301</p> <p>7.8 Appendix B: Ramo-Shockley-Pellegrini theorems 306</p> <p>7.9 Appendix C: Bohmian mechanics with operators 307</p> <p>7.10 Appendix D: Relation between the Wigner distribution function and the Bohmian trajectories 310</p> <p>7.11 Bibliography 314</p> <p><b>Chapter 8 The Monte Carlo Method for Wigner and Boltzmann Transport Equations 319</b><br /><i>Philippe Dollfus, Damien Querlioz and Jérôme Saint Martin</i></p> <p>8.1 The WTE 320</p> <p>8.2 The semiclassical limit: BTE 325</p> <p>8.3 Scattering in Boltzmann and Wigner equations 329</p> <p>8.4 The MC method for solving the BTE 341</p> <p>8.5 Extension of the MC method for solving the WBTE 352</p> <p>8.6 Bibliography 360</p> <p>List of Authors 371</p> <p>Index 373</p>

<p><strong>François Triozon</strong>, Researcher at Laboratoire d'Electronique et de Technologies de l'Information (LETI) of CEA/Grenoble, France. <p><strong>Philippe Dollfus</strong>, CNRS Research Director, France.

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