Description
Book SynopsisThis volume provides a recent study of mathematical research on semiconductor equations. With recent developments in semiconductor technology, several mathematical models have been established to analyze and to simulate the behavior of electron flow in semiconductor devices. Among them, a hydrodynamic, an energy-transport and a drift-diffusion models are frequently used for the device simulation with the suitable choice, depending on the purpose of the device usage. Hence, it is interesting and important not only in mathematics but also in engineering to study a model hierarchy, relations among these models. The model hierarchy has been formally understood by relaxation limits letting the physical parameters, called relaxation times, tend to zero. The main concern of this volume is the mathematical justification of the relaxation limits. Precisely, we show that the time global solution for the hydrodynamic model converges to that for the energy-transport model as a momentum relaxation time tends to zero. Moreover, it is shown that the solution for the energy-transport model converges to that for the drift-diffusion model as an energy relaxation time tends to zero. For beginners' help, this volume also presents the physical background of the semiconductor devices, the derivation of the models, and the basic mathematical results such as the unique existence of time local solutions.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets
Table of ContentsIntroduction: Structure of Semiconductor Device; Mathematical Models; Review of Previous Results; Notation; Mathematical Problem and Main Results: Intial Boundary Value Problem for Hydrodynamic Model; Formal Computation of Relaxation Limits; Asymptotic Behavior of Hydrodynamic Model; Relaxation Time Limits; Outline of Proofs; Stationary Solutions: Unique Existence of Stationary Solutions; Relaxation Limits of Stationary Solutions; Energy-Transport Model: Uniform Estimate of Local Solution; Semi-Global Existence of Solution; Global Existence of Solution; Energy Relaxation Limit; Additional Regularity; Hydrodynamic Model: Uniform Estimate of Local Solution; Semi-Global Existence of Solution; Global Existence of Solution; Momentum and Energy Relaxation Limits; Appendices: Time Local Solvability of Energy-Transport Model; Time Local Solvability of Hydrodynamic Model.
