An accurate numerical one-dimensional solution of the p- n junction under arbitrary transient conditions

Abstract

A numerical iterative method of solution of the one-dimensional basic two-carrier transport equations describing the behavior of semiconductor junction devices under arbitrary transient conditions is presented. The method is of a very general character: none of the conventional assumptions and restrictions are introduced and freedom is available in the choice of the doping profile, recombination-generation law, mobility dependencies, injection level, and boundary conditions applied solely at the external contacts. For a specified arbitrary input signal of either current or voltage as a function of time, the solution yields terminal properties and all the quantities of interest in the interior of the device (such as mobile carrier and net electric charge densities, electric field, electrostatic potential, particle and displacement currents) as functions of both position and time. Considerable attention is focused on the numerical analysis of the initial-value-boundary-value problem in order to achieve a numerical algorithm sufficiently sound and efficient to cope with the several fundamental difficulties of the problem, such as stability conditions related to the discretization of partial differential equations of the parabolic type, small differences between nearly equal numbers, and the variation of most quantities over extremely wide ranges within short regions. Results for a particular n +- p single-junction structure under typical external excitations are reported. The iterative scheme of solution for a single device is applicable also to ensembles of active and passive circuit elements. As a simple example, resutls for the combination of an n +- p diode and an external resistor, analyzed under switching conditions, are presented. The inductive behavior of the device for high current pulses, and storage and recovery phenomena under forward-to-reverse bias switching, are also illustrated. ‘Exact’ and conventional approximate analytical results are compared and discrepancies are exposed.