Theoretical current gain of a cylindrical mesa transistor

Abstract

For the cylindrical mesa transistor, computation of base-region transport efficiency is considered a boundary-value problem; solution of this problem yields mathematical equations applicable to the design and development of practical semiconductor devices. This analytical method is applied to the problem of minority-carrier transport across a solid-cylinder type structure which approximates the transistor base region. Minority-carrier losses—representing a fundamental limitation upon transistor-current gain—are introduced through an assumption of bulk and surface-recombination mechanisms. Applications of this analysis are illustrated by establishing the common-emitter current gain for typical junction transistors. Assuming, in such computations, physical parameters approximating germanium and silicon diffused devices, the silicon transistor is shown to be less sensitive to surface recombination mechanisms. Further, the existence of an optimum emitter radius is demonstrated for a semiconductor structure similar to the cylindrical hook collector.