François Triozon has been a permanent researcher since 2005 at CEA-LETI, in Grenoble, France. His research focuses on the simulation of electron transport in nanodevices, using semi-classical and quantum methods.Philippe Dollfus is currently Director of Research (CNRS) at the Center for Nanoscience and Nanotechnology, Orsay, France. His research activity covers different fields of computational nanoelectronics.

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• Preface xiii List of Symbols xvList of Abbreviations xviiChapter 1 Introduction: Nanoelectronics, Quantum Mechanics, and Solid State Physics 1Philippe Dollfus and François Triozon1.1 Nanoelectronics 11.2 Basic notions of solid-state physics 41.3 Quantum mechanics and electronic transport 201.4 Conclusion 291.5 Bibliography 30Chapter 2 Electronic Transport: Electrons, Phonons and Their Coupling within the Density Functional Theory 31Nathalie Vast, Jelena Sjakste, Gaston Kané and Virginie Trinité2.1 Introduction 312.2 Electronic structure 342.3 Phonons 462.4 Electron-phonon coupling 522.5 Semiclassical transport properties 622.6 Quantum transport 702.7 Conclusion 842.8 Appendix A 852.9 Blbiography 86Chapter 3 Electronic Band Structure: Empirical Pseudopotentials, k . p and Tight-Binding Methods 97Denis Rideau, François Triozon and Philippe Dollfus3.1 Band structure problem 973.2 Empirical pseudopotentials method 1023.3 the k . p method 1093.4 The TB method 1153.5 Optimization of empirical models 1223.6 Bibliography 126Chapter 4 Relevant Semiempirical Potentials for Phonon Properties 131Sebastian Volz4.1 Introduction 1314.2 Generic pair potentials: the Lennard-Jones potential 1344.3 Semiconductors: Stillinger-Weber and Tersoff potentials 1364.4 Oxydes: Van Beest, Kramer and van Santen potential 1434.5 Metals - isotropic many-body pair-functional potentials for metals: the modified embedded-atom method 1484.6 Polymers and carbon-based compounds: adaptive intermolecular reactive bond order, adaptive intermolecular REBO and Dreiding potentials 1494.7 Water: TIP3P potential 1564.8 Conclusion 1584.9 Bibliography 158Chapter 5 Introduction to Quantum Transport 163François Triozon, Stephan Roche and Yann-Michel Niquet5.1 Quantum transport from the point of view of wavepacket propagation 1645.2 The transmission formalism for the conductance 1775.3 The Green's function method for quantum transmission 1855.4 Conclusion 2195.5 Matlab/Octave codes 2195.6 Bibliography 220Chapter 6 Non-Equilibrium Green's Function Formalism 223Michel Lannoo and Marc Bescond6.1 Second quantization and time evolution pictures 2236.2 General definition of the Green's functions, their physical meaning and their perturbation expansion 2256.3 Stationary Green's functions and fluctuation-dissipation theorem 2296.4 Dyson's equation and self-energy: general formulation 2326.5 Some examples 2376.6 The ballistic regime 2406.7 The electron-photon interaction 2456.8 Bibliography 257Chapter 7 Electron Devices Simulation with Bohmian Trajectories 261Guillermo Albareda, Damiano Marian, Abdelilah Benali, Alfonso Alarcon, Simeon Moises and Xavier Oriols7.1 Introduction: why Bohmian mechanics? 2617.2 Theoretical framework: Bohmian mechanics 2677.3 The BITLLES simulator: time-resolved electron transport 2767.4 Computation of the electrical current and its moments with BITLLES 2917.5 Conclusion 2997.6 Acknowlegments 3017.7 Appendix A: Pratical algorithm to compute Bohmian trajectories 3017.8 Appendix B: Ramo-Shockley-Pellegrini theorems 3067.9 Appendix C: Bohmian mechanics with operators 3077.10 Appendix D: Relation between the Wigner distribution function and the Bohmian trajectories 3107.11 Bibliography 314Chapter 8 The Monte Carlo Method for Wigner and Boltzmann Transport Equations 319Philippe Dollfus, Damien Querlioz and Jérôme Saint Martin8.1 The WTE 3208.2 The semiclassical limit: BTE 3258.3 Scattering in Boltzmann and Wigner equations 3298.4 The MC method for solving the BTE 3418.5 Extension of the MC method for solving the WBTE 3528.6 Bibliography 360List of Authors 371Index 373

François Triozon has been a permanent researcher since 2005 at CEA-LETI, in Grenoble, France. His research focuses on the simulation of electron transport in nanodevices, using semi-classical and quantum methods.Philippe Dollfus is currently Director of Research (CNRS) at the Center for Nanoscience and Nanotechnology, Orsay, France. His research activity covers different fields of computational nanoelectronics.

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• Preface xiii List of Symbols xvList of Abbreviations xviiChapter 1 Introduction: Nanoelectronics, Quantum Mechanics, and Solid State Physics 1Philippe Dollfus and François Triozon1.1 Nanoelectronics 11.2 Basic notions of solid-state physics 41.3 Quantum mechanics and electronic transport 201.4 Conclusion 291.5 Bibliography 30Chapter 2 Electronic Transport: Electrons, Phonons and Their Coupling within the Density Functional Theory 31Nathalie Vast, Jelena Sjakste, Gaston Kané and Virginie Trinité2.1 Introduction 312.2 Electronic structure 342.3 Phonons 462.4 Electron-phonon coupling 522.5 Semiclassical transport properties 622.6 Quantum transport 702.7 Conclusion 842.8 Appendix A 852.9 Blbiography 86Chapter 3 Electronic Band Structure: Empirical Pseudopotentials, k . p and Tight-Binding Methods 97Denis Rideau, François Triozon and Philippe Dollfus3.1 Band structure problem 973.2 Empirical pseudopotentials method 1023.3 the k . p method 1093.4 The TB method 1153.5 Optimization of empirical models 1223.6 Bibliography 126Chapter 4 Relevant Semiempirical Potentials for Phonon Properties 131Sebastian Volz4.1 Introduction 1314.2 Generic pair potentials: the Lennard-Jones potential 1344.3 Semiconductors: Stillinger-Weber and Tersoff potentials 1364.4 Oxydes: Van Beest, Kramer and van Santen potential 1434.5 Metals - isotropic many-body pair-functional potentials for metals: the modified embedded-atom method 1484.6 Polymers and carbon-based compounds: adaptive intermolecular reactive bond order, adaptive intermolecular REBO and Dreiding potentials 1494.7 Water: TIP3P potential 1564.8 Conclusion 1584.9 Bibliography 158Chapter 5 Introduction to Quantum Transport 163François Triozon, Stephan Roche and Yann-Michel Niquet5.1 Quantum transport from the point of view of wavepacket propagation 1645.2 The transmission formalism for the conductance 1775.3 The Green's function method for quantum transmission 1855.4 Conclusion 2195.5 Matlab/Octave codes 2195.6 Bibliography 220Chapter 6 Non-Equilibrium Green's Function Formalism 223Michel Lannoo and Marc Bescond6.1 Second quantization and time evolution pictures 2236.2 General definition of the Green's functions, their physical meaning and their perturbation expansion 2256.3 Stationary Green's functions and fluctuation-dissipation theorem 2296.4 Dyson's equation and self-energy: general formulation 2326.5 Some examples 2376.6 The ballistic regime 2406.7 The electron-photon interaction 2456.8 Bibliography 257Chapter 7 Electron Devices Simulation with Bohmian Trajectories 261Guillermo Albareda, Damiano Marian, Abdelilah Benali, Alfonso Alarcon, Simeon Moises and Xavier Oriols7.1 Introduction: why Bohmian mechanics? 2617.2 Theoretical framework: Bohmian mechanics 2677.3 The BITLLES simulator: time-resolved electron transport 2767.4 Computation of the electrical current and its moments with BITLLES 2917.5 Conclusion 2997.6 Acknowlegments 3017.7 Appendix A: Pratical algorithm to compute Bohmian trajectories 3017.8 Appendix B: Ramo-Shockley-Pellegrini theorems 3067.9 Appendix C: Bohmian mechanics with operators 3077.10 Appendix D: Relation between the Wigner distribution function and the Bohmian trajectories 3107.11 Bibliography 314Chapter 8 The Monte Carlo Method for Wigner and Boltzmann Transport Equations 319Philippe Dollfus, Damien Querlioz and Jérôme Saint Martin8.1 The WTE 3208.2 The semiclassical limit: BTE 3258.3 Scattering in Boltzmann and Wigner equations 3298.4 The MC method for solving the BTE 3418.5 Extension of the MC method for solving the WBTE 3528.6 Bibliography 360List of Authors 371Index 373

François Triozon has been a permanent researcher since 2005 at CEA-LETI, in Grenoble, France. His research focuses on the simulation of electron transport in nanodevices, using semi-classical and quantum methods.Philippe Dollfus is currently Director of Research (CNRS) at the Center for Nanoscience and Nanotechnology, Orsay, France. His research activity covers different fields of computational nanoelectronics.

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• Preface xiii List of Symbols xvList of Abbreviations xviiChapter 1 Introduction: Nanoelectronics, Quantum Mechanics, and Solid State Physics 1Philippe Dollfus and François Triozon1.1 Nanoelectronics 11.2 Basic notions of solid-state physics 41.3 Quantum mechanics and electronic transport 201.4 Conclusion 291.5 Bibliography 30Chapter 2 Electronic Transport: Electrons, Phonons and Their Coupling within the Density Functional Theory 31Nathalie Vast, Jelena Sjakste, Gaston Kané and Virginie Trinité2.1 Introduction 312.2 Electronic structure 342.3 Phonons 462.4 Electron-phonon coupling 522.5 Semiclassical transport properties 622.6 Quantum transport 702.7 Conclusion 842.8 Appendix A 852.9 Blbiography 86Chapter 3 Electronic Band Structure: Empirical Pseudopotentials, k . p and Tight-Binding Methods 97Denis Rideau, François Triozon and Philippe Dollfus3.1 Band structure problem 973.2 Empirical pseudopotentials method 1023.3 the k . p method 1093.4 The TB method 1153.5 Optimization of empirical models 1223.6 Bibliography 126Chapter 4 Relevant Semiempirical Potentials for Phonon Properties 131Sebastian Volz4.1 Introduction 1314.2 Generic pair potentials: the Lennard-Jones potential 1344.3 Semiconductors: Stillinger-Weber and Tersoff potentials 1364.4 Oxydes: Van Beest, Kramer and van Santen potential 1434.5 Metals - isotropic many-body pair-functional potentials for metals: the modified embedded-atom method 1484.6 Polymers and carbon-based compounds: adaptive intermolecular reactive bond order, adaptive intermolecular REBO and Dreiding potentials 1494.7 Water: TIP3P potential 1564.8 Conclusion 1584.9 Bibliography 158Chapter 5 Introduction to Quantum Transport 163François Triozon, Stephan Roche and Yann-Michel Niquet5.1 Quantum transport from the point of view of wavepacket propagation 1645.2 The transmission formalism for the conductance 1775.3 The Green's function method for quantum transmission 1855.4 Conclusion 2195.5 Matlab/Octave codes 2195.6 Bibliography 220Chapter 6 Non-Equilibrium Green's Function Formalism 223Michel Lannoo and Marc Bescond6.1 Second quantization and time evolution pictures 2236.2 General definition of the Green's functions, their physical meaning and their perturbation expansion 2256.3 Stationary Green's functions and fluctuation-dissipation theorem 2296.4 Dyson's equation and self-energy: general formulation 2326.5 Some examples 2376.6 The ballistic regime 2406.7 The electron-photon interaction 2456.8 Bibliography 257Chapter 7 Electron Devices Simulation with Bohmian Trajectories 261Guillermo Albareda, Damiano Marian, Abdelilah Benali, Alfonso Alarcon, Simeon Moises and Xavier Oriols7.1 Introduction: why Bohmian mechanics? 2617.2 Theoretical framework: Bohmian mechanics 2677.3 The BITLLES simulator: time-resolved electron transport 2767.4 Computation of the electrical current and its moments with BITLLES 2917.5 Conclusion 2997.6 Acknowlegments 3017.7 Appendix A: Pratical algorithm to compute Bohmian trajectories 3017.8 Appendix B: Ramo-Shockley-Pellegrini theorems 3067.9 Appendix C: Bohmian mechanics with operators 3077.10 Appendix D: Relation between the Wigner distribution function and the Bohmian trajectories 3107.11 Bibliography 314Chapter 8 The Monte Carlo Method for Wigner and Boltzmann Transport Equations 319Philippe Dollfus, Damien Querlioz and Jérôme Saint Martin8.1 The WTE 3208.2 The semiclassical limit: BTE 3258.3 Scattering in Boltzmann and Wigner equations 3298.4 The MC method for solving the BTE 3418.5 Extension of the MC method for solving the WBTE 3528.6 Bibliography 360List of Authors 371Index 373