An operational method to model carrier degeneracy and band gap narrowing

Abstract

In this paper an operational method of modeling heavily doped silicon to include effects of carrier degeneracy and band gap narrowing is presented. The issue of carier degeneracy on majority carrier flow is discussed together with the question of the ambiguity in the electrostatic potential associated with identifying which band edge is narrowed. Using an exact numerical analysis of a bipolar transistor as an example it is shown that when modeling carrier flow in quasi-neutral regions, classical statistics can be used for the majority carrier and the ambiguity in the electrostatic potential can be ignored. Overall, it is shown that for the same quasi-neutral heavily doped regions the effects of carrier degeneracy and band gap narrowing are accurately modeled within the context of classical statistics by adding the quasi field term to the minority carrier transport equation that is based on the commonly used “band gap narrowing” data available from measurements of minority carrier transport in heavily doped regions. While it is recognized that this is not rigorously correct the result of this paper is to establish the accuracy for the operational method most commonly used to model heavy doping effects.