Multigroup Equations for the Description of the Particle Transport in Semiconductors (Advances in Mathematics for Applied Sciences)

Deterministic simulation of the particle transport in semiconductor devices is an interesting alternative to the common Monte Carlo approach. In this book, a state-of-the-art technique called the multigroup approach is presented and applied to a variety of transport problems in bulk semiconductors and semiconductor devices. High-field effects as well as hot-phonon phenomena in polar semiconductors are studied in detail. The mathematical properties of the presented numerical method are studied, and the method is applied to simulating the transport of a two-dimensional electron gas formed at a semiconductor heterostructure. Concerning semiconductor device simulation, several diodes and transistors fabricated of silicon and gallium arsenide are investigated. For all of these simulations, the numerical techniques employed are discussed in detail. This unique study of the application of direct methods for semiconductor device simulation provides the interested reader with an indispensable reference on this growing research area. Contents......Page 10 Preface......Page 8 1. Introduction......Page 14 2.2 Electrons in Semiconductors......Page 18 2.3 Phonons in Semiconductors......Page 22 2.4 Scattering Mechanisms......Page 24 2.4.1 General Theory of Scattering......Page 25 2.4.2 Phonon Scattering......Page 27 2.4.2.1 Non-polar Phonon Scattering......Page 28 2.4.2.2 Polar Phonon Scattering......Page 32 2.4.3 Ionized Impurity Scattering......Page 35 2.5 Semiclassical Dynamics of Electrons......Page 37 2.6 The Bloch-Boltzmann-Peierls Equations......Page 39 2.7 Mathematical Properties of the BBP Equations......Page 45 3.1 Introduction......Page 50 3.2 Multigroup Equations to the Bloch-Boltzmann-Peierls Equations......Page 51 3.2.1 The Electron Boltzmann Equation......Page 53 3.2.2 The LO Phonon Boltzmann Equation......Page 58 3.2.3 The Coupling POP Interaction Term......Page 60 3.2.4 The Evaluation of the Collision Coefficients......Page 64 3.3 Conservation Laws......Page 66 4.2 Two-valley Model......Page 74 4.2.1 Validation of the Method......Page 77 4.2.2 Electron Distribution Function......Page 79 4.2.3 Phonon Distribution Function......Page 81 4.2.4 Transport Parameters......Page 82 4.3 Three-valley Model......Page 84 5.1 Introduction......Page 90 5.2 Transport in a Time-dependent Electric Field......Page 91 5.3 The Stationary-state Electron Distribution......Page 95 6.1 Introduction......Page 100 6.2 The Bloch-Boltzmann-Peierls Equations......Page 101 6.3 The Multigroup Model Equations......Page 102 6.4.1 Boundedness of the Solution......Page 106 6.4.2 Conservation Laws......Page 108 6.4.3 H-theorem......Page 109 6.4.4 Equilibrium Solution......Page 111 6.5 Numerical Results......Page 113 7.2.1 Dispersion Laws......Page 120 7.2.2 Scattering Mechanisms......Page 124 7.2.2.1 Acoustic Deformation Potential Scattering......Page 125 7.2.2.2 Piezoelectric Scattering......Page 127 7.2.2.3 Polar Optical Phonon Scattering......Page 128 7.2.2.4 Screening Effects......Page 131 7.2.3 BBP Equations for 2D Systems......Page 133 7.3 Multigroup Equations to the 2D-BBP Equations......Page 137 7.4 Transport in A1xGa1-xN/GaN......Page 145 7.4.1 Self-consistent Solution for Confining Potential......Page 148 7.4.2 Transport Properties......Page 152 7.4.3 Distribution Functions......Page 158 8.1 Introduction......Page 160 8.2 The Boltzmann-Poisson System......Page 161 8.3 The Multigroup-WENO Scheme......Page 163 9.1 Introduction......Page 168 9.2 Transport in Bulk Silicon......Page 170 9.3 The Silicon n+ – n – n+ Diode......Page 171 9.4 The Si-MESFET......Page 175 9.5 The Si-MOSFET......Page 185 10.1 Introduction......Page 204 10.2 Bulk GaAs......Page 206 10.3 The GaAs n+ – ni – n+ Diode......Page 208 10.4 The GaAs-MESFET......Page 213 11. Conclusion......Page 226 Bibliography......Page 230 Related Publications of the Author......Page 236 Index......Page 238