Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices: Proceedings of a Conference held at the Mathematisches Forschungsinstitut, Oberwolfach, July 5–11, 1992 PDF
Preview Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices: Proceedings of a Conference held at the Mathematisches Forschungsinstitut, Oberwolfach, July 5–11, 1992
ISNM International Series of Numerical Mathematics Vol. 117 Edited by K.-H. Hoffmann, München H. D. Mittelmann, Tempe Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices Proceedings of a Conference held at the Mathematisches Forschungsinstitut, Oberwolfach, July 5-11,1992 Edited by R.E. Bank R. Bulirsch H. Gajewski K. Merten Springer Basel AG Editors R.E. Bank R. Bulirsch Dept. of Mathematics Mathematisches Institut University of California TH München San Diego Postfach 20 24 20 LaJolla, CA 92093 D-80290 München USA Germany H. Gajewski K. Merten Institut für Angewandte ZTIDES2 Analysis und Stochastik Siemens AG Mohrenstr. 39 Otto-Hahn-Ring 6 D-10117 Berlin D-81739 München Germany Germany A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA Deutsche Bibliothek Cataloging-in-Publication Data Mathematical modelling and simulation of electrical circuits and semiconductor devices: proceedings of a conference held at the Mathematisches Forschungsinstitut, Oberwolfach, July 5 - 11,1992 / ed. by R. E. Bank ... - Basel; Boston; Berlin: Birkhäuser, 1994 (International series of numerical mathematics; Vol. 117) ISBN 978-3-0348-9665-8 ISBN 978-3-0348-8528-7 (eBook) DOI 10.1007/978-3-0348-8528-7 NE: Bank, Randolph E. [Hrsg.]; Mathematisches Forschungsinstitut <Oberwolfach>; GT This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use the permission of the copyright owner must be obtained. © 1994 Springer Basel AG Originally published by Birkhäuser Verlag in 1994 Camera-ready copy prepared by the editors Printed on acid-free paper produced from chlorine-free pulp Cover design: Heinz Hiltbrunner, Basel ISBN 978-3-0348-9665-8 987654321 Preface Progress in today's high-technology industries is strongly associated with the develop ment of new mathematical tools. A typical illustration of this partnership is the ma thematical modelling and numerical simulation of electric circuits and semiconductor devices. At the second Oberwolfach conference devoted to this important and timely field, 35 scientists from around the world, mainly applied mathematicians and electrical engineers from industry and universities, presented their new results. The contributions to this conference are presented in this proceedings. They cover electric circuit simulation, device simulation and process simulation, including discussions on experiences with standard software packages and improvements of such packages. In electric circuit simulation three different types of problems can be distinguished de pending on the size of a circuit: small circuits with less than 20 basic elements and an oscillating behaviour; middle-sized circuits up to 500 elements; very large circuits. To day the simulation of middle-sized circuits is well understood. Current focal points for oscillating circuits include new discretization schemes, limit cycle computation and the transient phase. Parallel methods and multirate strategies are suggested and tested for the very large circuits. In the semiconductor area special lectures were given on new modelling approaches, numerical techniques and existence and uniqueness results. Among these, for example, mention is made of mixed finite element methods, an extension of the Baliga-Patankar technique for a three dimensional simulation, and the connection between semiconductor equations and the Boltzmann equations. The editors are grateful to Georg Denk and Peter Rentrop for their effective and efficient help in organizing the conference. The editors Table of Contents Circuit Simulation Denk Go A new efficient numerical integration scheme for highly oscillatory electric circuits 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 Grund Fo Numerische Losung von hierarchisch strukturierten Systemen von Algebro-Differentialgleichungen 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17 Giinther Mo, Rentrop Po Partitioning and multirate strategies in latent electric circuits 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 033 Kiehl Mo Circuit simulation - an application for parallel ODE solvers? 00000000000000000000061 MarzR. Numerical stability criteria for differential-algebraic systems 00000000000000000000000 73 Mathis Wo Analysis of linear time-invariant networks in the frequency domain 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 083 Schmidt Wo Limit cycle computation of oscillating electric circuits 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 91 Sieber Eo-R, Feldmann Do, Schultz R., Wriedt Ho Timestep control for charge conserving integration in circuit simulation 0 0 0 0 0 0 0 0 0 0 0 103 Taubert K. Ein Zusammenhang zwischen Waveformrelaxation und Iterationsverfahren fur nichtlinear gestorte Gleichungen 115 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 VIII Wiedl W. Multilevel-Newton-Verfahren in der Transientenanalyse elektrischer Netzwerke ........................................ 127 Wriedt H. Transientensimulation elektrischer Netwerke mit TRBDF ......................... 133 Zheng Q. The transient behavior of an oscillator ........................................... 143 Device Simulation Albinus G. Numerical simulation of the carrier transport in semiconductor devices on the base of an energy model ......................... 157 Gajewski H. On uniqueness of solutions to the drift-diffusion-model of semiconductor devices ......................................................... 171 Gartner K. On restrictions for discretizations of the simplified linearized van Roosbroeck's equations .................................. 185 Hiptmair R., Hoppe R. H. W. Mixed finite element discretization of continuity equations arising in semiconductor device simulation ....................................... 197 Kerkhoven T. A piecewise linear Petrov-Galerkin analysis of the box-method .................... 219 Mittelmann H. D., Chang K.-T., Jankowski D. F., Neitzel G. P. Stability analysis of thermocapillary convection in semiconductor crystal growth ................................................. 237 IX Montrone F. The method of Baliga-Patankar and 3-D device simulation ........................ 251 Paffrath M. A mass conserving moving grid method for dopant simulation .................... 267 Wick J. Numerical approaches to the kinetic semiconductor equations ..................... 281 Wrzosek D. The non-stationary semiconductor model with bounded convective velocity and generation/recombination term .................. 293 List of Participants Dr. G. Albinus Prof. Dr. R. E. Bank Institut fUr Angewandte Analysis Dept. of Mathematics, C-012 und Stochastik University of California, San Diego Mohrenstr.39 La Jolla, CA 92093 10117 Berlin USA Dr. R. P. Brinkmann Prof. Dr. R. Bulirsch ZFE BT ACM 31 Mathematisches Institut Siemens AG der TU Miinchen Otto-Hahn-Ring 6 80290 Miinchen 81739 Miinchen J.-F. Chabilan Dr. G. Denk Fachbereich Mathematik Mathematisches Institut AG 8 Numerische Mathematik der TU Miinchen Technische Hochschule 80290 Miinchen Darmstadt Schlo6gartenstr. 7 64289 Darmstadt Prof. Dr. P. Deuflhard Dr. U. Feldmann Konrad-Zuse-Zentrum fiir ZFE BT SE 43 Informationstechnik Berlin SIEMENS AG Heilbronner Str. 10 Otto-Hahn-Ring 6 10711 Berlin 81739 Mi inchen XII Prof. Dr. H. Gajewski Dr. K. Gartner Institut fiir Angewandte Analysis IPS und Stochastik ETH-Zentrum Mohrenstr. 39 CH-8092 Ziirich 10 117 Berlin Dr. J. Gawriljuk Dr. Albert Gilg Warschauer Str. 14/1602 ZFE SPT 3 SIEMENS AG 99089 Erfurt Otto-Hahn-Ring 6 81739 Munchen Prof. Dr. F. Grund R. Hiptmair Institut fiir Angewandte Analysis Mathematisches Institut und Stochastik der TU Mu nchen Mohrenstr. 39 80290 Munchen 10117 Berlin Prof. Dr. Karl-Heinz Hoffmann Prof. Dr. R. Hoppe Institut fiir angewandte Mathematik Mathematisches Institut und Statistik der TU Mu nchen der TU Mu nchen 80290 Munchen 80290 Munchen Prof. Dr. T. Kerkhoven Dr. M. Kiehl Department of Computer Science Mathematisches Institut University of Illinois at der TU Munchen Urbana-Champaign 80290 Munchen 1304 W. Springfield Av. Urbana, IL 61801 USA
The list of books you might like
