Diffusion and Drift of Minority Carriers in Semiconductors for Comparable Capture and Scattering Mean Free Paths

Abstract

A method of treating transport of injected minority carriers is developed applicable to cases in which the physical dimension and the mean free path for capture may be less than the mean free path for scattering. The basic differential equations of scattering and capture are those of the conservation of flux method of McKelvey, Longini, and Brody, and the results agree with theirs, the new feature being a demonstration that the basic equations are equivalent to a continuity equation of the conventional form but with a diffusion constant reduced by including the effect of capture in shortening the mean free path. This method of treatment reduces the problems to a familiar form when suitable boundary conditions are introduced. The basic differential equations of scattering and capture are shown to correspond to certain simplifying and restricting assumptions about the carrier velocity distributions. The treatment is extended from the case of one dimension with zero electric field to three dimensions with electric fields.