Modelling of band tails and their effects on minority carrier transport in heavily doped silicon

Abstract

The purpose of this paper is to clarify a long standing controversy as to whether or not band tail effects are important in minority carrier transport. It is shown that minority carrier transport in heavily-doped quasi-neutral regions can be well-modelled by two coupled differential equations of the first order including the effects of density of states distortion. The energy-dependent mobility and lifetime are incorporated into the transport equations for the first time. A simple empirical exponential tail model is proposed based on quantum mechanical theories of band tails. This simple tail model is verified by comparing the measured and calculated photoluminescence spectra. At room temperature, the presence of band tails in both bands increases the equilbrium minority carrier concentration by a factor of two. 30% of the minority carriers are located in the tails, which do not contribute to the d.c. current because of low mobility. However, the transient or a.c. transport is expected to be modified due to band tail effects.