A system of three quasi-linear partial differential equations is considered, as a simplified model of the transport of mobile carriers in a semiconductor device. Assuming a convenient form of the boundary conditions, it is shown that the initial value problem is well-posed, and that the steady state solution is unique and stable. A finite difference approximation preserving reasonable bounds on the numerical solutions is also described.

An Initial Value Problem from Semiconductor Device Theory

The most effective way to design VLSI device structures is to use sophisticated, complex two-dimensional (2D) and three-dimensional (3D) models. This paper and its companion [1] discusses the numerical simulation of such device models. Here we describe the basic semiconductor equations including several choices of variables. Our examples illustrate results obtained from finite-difference and finite-element implementations. We stress the necessary 3D calculations for small-size MOSFET's. Numerical results on inter-electrode capacitive coupling are included.

Semiconductor Device Simulation

A study of heavy doping effects on the current gain of diffused bipolar silicon transistors is continued, with emphasis on the variation of the current gain with injection level. The sensitivity of the calculations to some assumptions and approximations made previously is appraised. Numerical solutions of the heavy doping model simultaneously with the carrier transport equations are included.

On heavy doping effects and the injection efficiency of silicon transistors

Direct evaluation of branching points for equations arising in the theory of explosions of solid explosives

Time discretization of a nonlinear initial value problem

An analysis is presented of the error in numerical approximations to a system of elliptic equations describing the steady-state distribution of mobile carriers in a semiconductor device. Although this system has been extensively studied by finite difference methods, the accuracy of the numerical methods employed has not been previously established. Computation schemes are presented for which suitable error estimates are obtained, without assuming an unreasonably small mesh size. In addition, for the one-dimensional problem, the effect of the inexact solution of the discrete equations is estimated.

On the computation of semiconductor device current characteristics by finite difference methods

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On the computation of semiconductor device current characteristics by finite difference methods