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Hierarchy of Semiconductor Equations: Relaxation Limits with Initial Layers for Large Initial Data (MSJ Memoirs, Mathematical Society of Japan)

Nishibata, Shinya; Masahiro Suzuki

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ISBN 10: 4931469663 / ISBN 13: 9784931469662
Published by Mathematical Society of Japan, Taito, 2011
Used Condition: Near Fine Soft cover
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2011. First edition. Paperback, 109 pp. Near fine. Previous owner's stamp to inside of front wrap. Contents bright, clean and unmarked. Bookseller Inventory # d008053

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Bibliographic Details

Title: Hierarchy of Semiconductor Equations: ...

Publisher: Mathematical Society of Japan, Taito

Publication Date: 2011

Binding: Paperback

Book Condition:Near Fine

Edition: First edition.

About this title


This 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.

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