A new approach to the modeling of pnpn structures

Abstract

An approach for the derivation of stationary voltage-current characteristics of pnpn-structures is presented. In contrast to the classical method of the two-transistor analog, the van Roosbroeck system is considered throughout the device. The problem is simplified by using the methods of asymptotic analysis: a suitable normalisation leads to the identification of small dimensionless parameters which are used in a formal perturbation procedure. Neglecting these small parameters is equivalent to making certain simplifying assumptions such as charge neutrality, depletion or low injection. The approximate problems are in general much easier to solve than the full van Roosbroeck system. The main results are explicit formulae for the stationary voltage-current characteristic for moderate currents, expressions for the holding current and the statement that, in the absence of impact ionisation, the breakover voltage can be explained by finite domain effects. © 1991.