| Preface ix 1 Introduction 1.1 A hierarchy of semiconductor models 1.2 Quasi-hydrodynamic semiconductor models 2 Basic Semiconductor Physics 2.1 Homogeneous semiconductors 2.2 Inhomogeneous semiconductors 3 The Isentropic Drift-diffusion Model 3.1 Derivation of the model 3.1.1 Semiconductor equations based on Fermi-Dirac statistics 3.1.2 The isentropic model-scaling 3.1.3 The convergence result 3.2 Existence of transient solutions 3.2.1 Assumptions and existence result 3.2.2 Proof of the existence result 3.3 Uniqueness of transient solutions 3.4 Localization of vacuum solutions 3.4.1 Main results 3.4.2 Proofs of the main results 3.4.3 Numerical examples 3.5 Numerical approximation 3.5.1 The mixed finite element discretization in one space dimension 3.5.2 Numerical examples in one space dimension 3.5.3 The mixed finite element discretization in two space dimensions 3.5.4 Numerical examples in two space dimensions 3.6 Current-voltage characteristics 3.6.1 Numerical current-voltage characteristics 3.6.2 High-injection current-voltage characteristics 4 The Energy-transport Model 4.1 Derivation of the model 4.1.1 General non-parabolic band diagrams 4.1.2 A drift-diffusion formulation for the current densities 4.1.3 A non-parabolic band approximation 4.1.4 Parabolic band approximation 4.2 Symmetrization and entropy function 4.3 Existence of transient solutions 4.3.1 Assumptions and main results 4.3.2 Semidiscretization 4.3.3 Proof of the existence result 4.4 Long-time behavior of the transient solution 4.5 Regularity and uniqueness 4.5.1 Regularity of transient solutions 4.5.2 Uniqueness of transient solutions 4.6 Existence of steady-state solutions 4.7 Uniqueness of steady-state solutions 4.8 Numerical approximation 4.8.1 The mixed finite element discretization in one space dimension 4.8.2 Numerical results 5 The Quantum Hydrodynamic Model 5.1 Derivation of the model 5.2 Existence and positivity 5.2.1 Existence of steady-state solutions 5.2.2 Positivity and non-positivity properties 5.3 Uniqueness of steady-state solutions 5.4 A non-existence result …… References Index |
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