Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices: Proceedings of a Conference held at the Mathematisches Forschungsinstitut, Oberwolfach, October 30 – November 5, 1988

298 Pages·1990·10.518 MB·English

by  K. Merten (auth.), R. E. Bank, K. Merten, R. Bulirsch (eds.)

ISNM93:
International Series of Numerical Mathematics
Intemationale Schriftenreihe zur Numerischen Mathematik
Serie intemationale numerique
d~nalyse
Vol. 93
Edited by
K.-H. Hoffmann, Augsburg; H. D. Mittelmann, Tempe;
J. Todd, Pasadena
Springer Basel AG
Mathematical Modelling
and Simulation of
Electrical Circuits and
Semiconductor Devices
Proceedings of a Conference held at the
Mathematisches Forschungsinstitut, Oberwolfach,
October 30 - November 5,1988
Edited by
R. E. Bank
R. Bulirsch
K. Merten
1990
Springer Basel AG
Editors
R. E. Bank R. Bulirsch
Dept. of Mathematics Mathematisches Institut
University of California TU München
San Diego Arcisstrasse 21
LaJolla, CA 92093 D-8000 München 2
USA
K. Merten
ZTI DES 2
Siemens AG
Otto-Hahn-Ring 6
D-8000 München 83
CIP-Titelaufnahme der Deutschen Bibliothek
Mathematical modelling and simulation of electrical circuits and semiconductor devices:
proceedings of a conference held at the Math. Forschungsinst, Oberwolf ach, October 30 -
November 5,1988 / ed. by R. E. Bank ... - Basel ; Boston ; Berlin :
Birkhäuser, 1990
(International series of numerical mathematics; Vol. 93)
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 those of translation, reprinting, re-use of
illustrations, broadcasting, reproduction by photocopying machine or similar means,
and storage in data banks. Under § 54 of the German Copyright Law where copies are
made for other than private use a fee is payable to »Verwertungsgesellschaft Wort«,
Munich.
© Springer Basel AG 1990
Originally published by Birkhäuser Verlag Basel in 1990
Softcover reprint of the hardcover 1st edition 1990
ISBN 978-3-0348-5700-0 ISBN 978-3-0348-5698-0 (eBook)
DOI 10.1007/978-3-0348-5698-0
v
Preface
Numerical simulation and modelling of electric circuits and semiconductor devices are
of primal interest in today's high technology industries.
At the Oberwolfach Conference more than forty scientists from around the world, in
cluding applied mathematicians and electrical engineers from industry and universities,
presented new results in this area of growing importance.
The contributions to this conference are presented in these proceedings. They include
contributions on special topics of current interest in circuit and device simulation, as
well as contributions that present an overview of the field.
In the semiconductor area special lectures were given on mixed finite element methods
and iterative procedures for the solution of large linear systems. For three dimensional
models new discretization procedures including software packages were presented. Con
nections between semiconductor equations and the Boltzmann equation were shown as
well as relations to the quantum transport equation. Other issues discussed in this
area include the design of simulation programs for semiconductors, vectorcomputers,
and interface problems in several dimensions.
Topics discussed in the area of circuit simulation include the index classification of
differential-algebraic systems, connections with ill-posed problems, and regularization
techniques. Split discretization procedures were given for the efficient calculation of
periodic solutions of circuits taking into acount the latency. Homotopy methods and
new numerical techniques for differential-algebraic systems were presented, and im
provements of special numerical methods for standard software packages were sug
gested.
The editors
VII
Table of Contents
Circuit Simulation
Merten K.
Circuit Simulation in the Semiconductor Industry -
State of the Art, Requirements and Future Development
Griepentrog E.
The Index of Differential-Algebraic Equations and
its Significance for the Circuit Simulation ..................................... 11
MarzR.
Analysis and Numerical Treatment of
Differential-Algebraic Systems ................................................ 27
Zheng Q.
Hopf Bifurcation in Differential Algebraic Equations
and Applications to Circuit Simulation ....................................... 45
Rentrop P.
ROW-Type Methods for the Integration of
Electric Circuits .............................................................. 59
Schultz R.
Local Timestep Control for Simulating Electrical Circuits 73
Denk G.
An Improved Numerical Integration Method
in the Circuit Simulator SPICE2-S ........................................... 85
Kiehl M.
Increasing the Vector Length for Matrix Multiplication
with Reduced Memory Access ................................................ 101
VIII
Device Simulation
Hansch W., Jacobs H.
Semiconductor Equations and Analytical Models for MOSFETs ............... 111
Bank R. E., Biirgler J., Coughran W. M., Fichtner W., Smith R. K.
Recent Progress in Algorithms for
Semiconductor Device Simulation............................... ... .... .. . .... 125
Seidman T. I.
A New Algorithmic Model for the
Transient Semiconductor Problem 141
Degond P., Guyot-Delaurens F., Mustieles F. J., Nier F.
Semiconductor Modelling Via
the Boltzmann Equation..................................................... 153
Ringhofer Ch.
A Numerical Method for the Simulation of Quantum Tunneling
Phenomena in Solid State Semiconductors .................................... 173
Kerkhoven T.
Modelling of Semiconductors Subject to Prescribed Currents.. ... .... . .... ... . 185
Ascher U.
Differential-Algebraic Problems and
Semiconductor Device Simulation.. ....... ...................... ...... . . . ... . . 201
Jerome J. W.
Algorithmic Aspects of the
Hydrodynamic and Drift-Diffusion Device Models............................. 217
Sawatzki R.
About the Dependence of the Convergence of Gummel's algorithm
and its linear variants on the device geometry ................................. 237
IX
Polak S. J.
=
Mixed FEM for 6.u au ..................................................... 247
Miller J. J. H., Wang S.
A Mixed Finite Element Method with Tetrahedral Elements
for the Semiconductor Continuity Equations .................................. 257
Rank E.
Local Oxidation of Silicon - A Finite Element Approach ..................... 267
Steger K.
Corner Singularities of Solutions of the
Potential Equation in three Dimensions ....................................... 283
XI
List of Participants
Prof. Dr. K. Antreich Prof. Dr. U. M. Ascher
Lehrstuhl fur Rechnergestutztes Department of Computer
Entwerfen Science
Technische Universitat Miinchen University of British Columbia
Arcisstr. 21
Vancouver, B. C. V6T 1W5
8000 Miinchen 2 CANADA
Prof. Dr. R. E. Bank J. Burgler
Dept. of Mathematics Institut fUr Integrierte Systeme
University of California, ETH-Zentrum
San Diego Gloriastr. 35
La Jolla, CA 92093 CH-8092 Zurich
USA
Prof. Dr. R. BuIirsch Prof. Dr. W. M. Coughram Jr.
Mathematisches Institut AT&T
cler TU Munchen Bell Laboratories
PF 20 24 20, Arcisstr. 21 600 Mountain Avenue
8000 M iinchen 2 Murray Hill, NJ 07974-2070
USA
Prof. Dr. P. Degoncl G. Denk
Centre cle Mathematiques Mathematisches Institut
Appliquees cler TU Munchen
Ecole Poly technique PF 20 24 20, Arcisstr. 21
E. R. A. - C. N. R. S. 747
8000-Miinchen 2
F -91128 Palaiseau Ceclex