%A R. E. Bank
%A W. M. Coughran\ Jr.
%A W. Fichtner
%A D. J. Rose
%A R. K. Smith
%T Computational Aspects of Semiconductor Device Simulation
%R Technical Report NAMs 85-3
%I AT&T - Bell Labratories
%D 1985
%X In this chapter, we present an overview of the numerical
techniques used to solve the coupled system of nonlinear
partial differential equations that model the behavior of
semiconductor devices.  These methods have been incorporated
into our device simulation package which has been success-
fully used to model complex device structures in two and
three space dimensions for both steady-state and transient
conditions.

%A R. E. Bank
%A W. M. Coughran\ Jr.
%A W. Fichtner
%A E. H. Grosse
%A D. J. Rose
%A R. K. Smith
%T Transient Simulation of Silicon Devices and Circuits
%R Technical Report NAMs 85-8
%I AT&T - Bell Labratories
%D 1985
%X In this paper, we present an overview of the physical prin-
ciples and numerical methods used to solve the coupled sys-
tem of nonlinear 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.