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AuthorMarkowich, Peter A. author
TitleSemiconductor Equations [electronic resource] / by Peter A. Markowich, Christian A. Ringhofer, Christian Schmeiser
ImprintVienna : Springer Vienna, 1990
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Descript X, 248 p. online resource


In recent years the mathematical modeling of charge transport in semiยญ conductors has become a thriving area in applied mathematics. The drift diffusion equations, which constitute the most popular model for the simulaยญ tion of the electrical behavior of semiconductor devices, are by now matheยญ matically quite well understood. As a consequence numerical methods have been developed, which allow for reasonably efficient computer simulations in many cases of practical relevance. Nowadays, research on the drift diffuยญ sion model is of a highly specialized nature. It concentrates on the exploraยญ tion of possibly more efficient discretization methods (e.g. mixed finite elements, streamline diffusion), on the improvement of the performance of nonlinear iteration and linear equation solvers, and on three dimensional applications. The ongoing miniaturization of semiconductor devices has prompted a shift of the focus of the modeling research lately, since the drift diffusion model does not account well for charge transport in ultra integrated devices. Extensions of the drift diffusion model (so called hydrodynamic models) are under investigation for the modeling of hot electron effects in submicron MOS-transistors, and supercomputer technology has made it possible to employ kinetic models (semiclassical Boltzmann-Poisson and Wignerยญ Poisson equations) for the simulation of certain highly integrated devices


1 Kinetic Transport Models for Semiconductors -- 1.1 Introduction -- 1.2 The (Semi-)Classical Liouville Equation -- 1.3 The Boltzmann Equation -- 1.4 The Quantum Liouville Equation -- 1.5 The Quantum Boltzmann Equation -- 1.6 Applications and Extensions -- Problems -- References -- 2 From Kinetic to Fluid Dynamical Models -- 2.1 Introduction -- 2.2 Small Mean Free Pathโ{128}{148}The Hilbert Expansion -- 2.3 Moment Methodsโ{128}{148}The Hydrodynamic Model -- 2.4 Heavy Doping Effectsโ{128}{148}Fermi-Dirac Distributions -- 2.5 High Field Effectsโ{128}{148}Mobility Models -- 2.6 Recombination-Generation Models -- Problems -- References -- 3 The Drift Diffusion Equations -- 3.1 Introduction -- 3.2 The Stationary Drift Diffusion Equations -- 3.3 Existence and Uniqueness for the Stationary Drift Diffusion Equations -- 3.4 Forward Biased P-N Junctions -- 3.5 Reverse Biased P-N Junctions -- 3.6 Stability and Conditioning for the Stationary Problem -- 3.7 The Transient Problem -- 3.8 The Linearization of the Transient Problem -- 3.9 Existence for the Nonlinear Problem -- 3.10 Asymptotic Expansions on the Diffusion Time Scale -- 3.11 Fast Time Scale Expansions -- Problems -- References -- 4 Devices -- 4.1 Introduction -- 4.2 P-N Diode -- 4.3 Bipolar Transistor -- 4.4 PIN-Diode -- 4.5 Thyristor -- 4.6 MIS Diode -- 4.7 MOSFET -- 4.8 Gunn Diode -- Problems -- References -- Physical Constants -- Properties of Si at Room Temperature

Mathematics Chemometrics Mathematical analysis Analysis (Mathematics) Physics Optics Electrodynamics Computational intelligence Electronics Microelectronics Mathematics Analysis Optics and Electrodynamics Theoretical Mathematical and Computational Physics Math. Applications in Chemistry Computational Intelligence Electronics and Microelectronics Instrumentation


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