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Deterministic simulation of the particle transport in semiconductor devices is an interesting alternative to the common Monte Carlo approach. In this book, a state-of-the-art technique called the multigroup approach is presented and applied to a variety of transport problems in bulk semiconductors and semiconductor devices. High-field effects as well as hot-phonon phenomena in polar semiconductors are studied in detail. The mathematical properties of the presented numerical method are studied, and the method is applied to simulating the transport of a two-dimensional electron gas formed at a semiconductor heterostructure. Concerning semiconductor device simulation, several diodes and transistors fabricated of silicon and gallium arsenide are investigated. For all of these simulations, the numerical techniques employed are discussed in detail. This unique study of the application of direct methods for semiconductor device simulation provides the interested reader with an indispensable reference on this growing research area.
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MULTIGROUP EQUATIONS FOR THE DESCRIPTION OF THE PARTICLE TRANSPORT IN SEMICONDUCTORS
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Series on Advances in Mathematics for Applied Sciences - Vol. 70
MULTIGROUP EQUATIONS FOR THE DESCRIPTION OF THE PARTICLE TRANSPORT IN SEMICONDUCTORS Martin Galler Graz University of Technology, Austria
N E W JERSEY
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Library of Congress Cataloging-in-PublicationData Galler, Martin, 1977Multigroup equations for the description of the particle transport in semiconductors/ Martin Galler. p. cm. -- (Series on advances in mathematics for applied sciences ; v. 70) ISBN 981-256-355-5 (alk.paper) 1.Transport theory--Mathematics. 2. Semiconductors--Mathematics. I. Title. 11. Series. QC793.3.V G35 2005 530.13’8-dc22 200504943I
British Library Cataloguing-in-PublicationData A catalogue record for this book is available from the British Library.
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Preface
Accurate semiconductor device simulation is mainly based on Monte Carlo methods. However, there are essential advantages gained by directly solving the Bloch-Boltzmann-Peierls equations, which govern the dynamics of carriers and phonons in semiconductors. In this book, an attempt is made to introduce such deterministic solution techniques, called multigroup model equations, especially for describing the particle transport in 111-V compound semiconductors. First, we present a multigroup model to the Boltzmann equations governing the transient transport regime in polar semiconductors. Special effort is invested in an accurate description of the coupled hot-electron hotphonon system. The related conservation laws for the electron density and the total en