Transient simulation of silicon devices and circuits
- 1 October 1985
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Electron Devices
- Vol. 32 (10), 1992-2007
- https://doi.org/10.1109/t-ed.1985.22232
Abstract
In this paper, we present an overview of the physical principles and numerical methods used to solve the coupled system of non-linear partial differential equations that model the transient behavior of silicon VLSI device structures. We also describe how the same techniques are applicable to circuit simulation. A composite linear multistep formula is introduced as the time-integration scheme. Newton-iterative methods are exploited to solve the nonlinear equations that arise at each time step. We also present a simple data structure for nonsymmetric matrices with symmetric nonzero structures that facilitates iterative or direct methods with substantial efficiency gains over other storage schemes. Several computational examples, including a CMOS latchup problem, are presented and discussed.Keywords
This publication has 26 references indexed in Scilit:
- Variation Diminishing Splines in SimulationSIAM Journal on Scientific and Statistical Computing, 1986
- ODE Methods for the Solution of Differential/Algebraic SystemsSIAM Journal on Numerical Analysis, 1984
- A New Class of Cyclic Multistep Formulae for Stiff SystemsSIAM Journal on Scientific and Statistical Computing, 1983
- Differential/Algebraic Equations are not ODE’sSIAM Journal on Scientific and Statistical Computing, 1982
- Yale sparse matrix package I: The symmetric codesInternational Journal for Numerical Methods in Engineering, 1982
- Global approximate Newton methodsNumerische Mathematik, 1981
- On the physics and modeling of small semiconductor devices—ISolid-State Electronics, 1980
- A stiffly stable integration process using cyclic composite methodsACM Transactions on Mathematical Software, 1978
- Calculation of the turn-on behavior of mostSolid-State Electronics, 1974
- An accurate numerical one-dimensional solution of the p-n junction under arbitrary transient conditionsSolid-State Electronics, 1968