Transient Simulation of Silicon Devices and Circuits

TLDR

The paper provides an overview of the physical principles and numerical methods for transient simulation of silicon VLSI devices and shows how these techniques extend to circuit simulation. It introduces a composite linear multistep time‑integration scheme, employs Newton‑iterative solvers for the resulting nonlinear equations, and presents an efficient data structure for nonsymmetric matrices with symmetric nonzero patterns. Computational examples, such as a CMOS latchup scenario, illustrate the effectiveness of the proposed methods.

Abstract

In this paper, we present an overview of the physical principles and numerical methods used to solve the coupled system 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.