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.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets

The International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 'HYP2008', was held at the University of Maryland from June 9-13, 2008. This book, the first in a two-part volume, contains nineteen papers based on plenary and invited talks presented at the conference.

This book offers, from both a theoretical and a computational perspective, an analysis of macroscopic mathematical models for description of charge transport in electronic devices, in particular in the presence of confining effects, such as in the double gate MOSFET. The models are derived from the semiclassical Boltzmann equation by means of the moment method and are closed by resorting to the maximum entropy principle. In the case of confinement, electrons are treated as waves in the confining direction by solving a one-dimensional Schrödinger equation obtaining subbands, while the longitudinal transport of subband electrons is described semiclassically. Limiting energy-transport and drift-diffusion models are also obtained by using suitable scaling procedures. An entire chapter in the book is dedicated to a promising new material like graphene. The models appear to be sound and sufficiently accurate for systematic use in computer-aided design simulators for complex electron devices. The book is addressed to applied mathematicians, physicists, and electronic engineers. It is written for graduate or PhD readers but the opening chapter contains a modicum of semiconductor physics, making it self-consistent and useful also for undergraduate students.

'The International Conference on Hyperbolic Problems: Theory, Numerics and Applications', 'HYP2008', was held at the University of Maryland from June 9-14, 2008. This title contains articles that cover a range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of 'hyperbolic PDEs'.

Professor Ziman's classic textbook on the theory of solids was first pulished in 1964. This paperback edition is a reprint of the second edition, which was substantially revised and enlarged in 1972. The value and popularity of this textbook is well attested by reviewers' opinions and by the existence of several foreign language editions, including German, Italian, Spanish, Japanese, Polish and Russian. The book gives a clear exposition of the elements of the physics of perfect crystalline solids. In discussing the principles, the author aims to give students an appreciation of the conditions which are necessary for the appearance of the various phenomena. A self-contained mathematical account is given of the simplest model that will demonstrate each principle. A grounding in quantum mechanics and knowledge of elementary facts about solids is assumed. This is therefore a textbook for advanced undergraduates and is also appropriate for graduate courses.

This book presents a hierarchy of macroscopic models for semiconductor devices, studying three classes of models in detail: isentropic drift-diffusion equations, energy-transport models, and quantum hydrodynamic equations. The derivation of each, including physical discussions, is shown. Numerical simulations for modern semiconductor devices are performed, showing the particular features of each. The author develops modern analytical techniques, such as positive solution methods, local energy methods for free-boundary problems and entropy methods.

Provides a critical history of Western architecture theory from the ancient world to the present day. It looks at how the architect generates architectural form in order to explain a number of issues, including the origins of style, the persistence of tradition and the role of genius.