Semiclassical Carrier Transport Models

Abstract

In this chapter we begin our study of charge and carrier transport through small semiconductor devices. We are confronted with a rich variety of possible transport models. Each of these models makes a different set of simplifying approximations concerning the physics of carrier transport and therefore has its own domain of validity. The overall problem which these various models solve in various ways is the response of a cloud or ensemble of mobile charges, embedded in a media which subjects them to a statistically varied set of scattering events and to a set of externally applied fields. The detail needed in the statistical description of the carrier distribution in phase space generally guides the choice of a transport model. At one extreme, we try to preserve all of the statistical information and solve for a distribution function or use Monte Carlo methods. At the other extreme, we decide that only the mean values are needed and generally solve for the carrier density. (Of particular interest here are a set of models in which hot-carrier phenomena are ignored while nonequilibrium densities are retained.) Lying between these two extremes are a variety of models in which one retains hot-carrier physics in the formulation of carrier current densities as well as nonequilibrium concentrations. If we are interested in noise calculations, we must retain some information concerning statistical fluctuations about the mean value for one or more parameters, and questions then arise as to how one separates the mean motion from the overall motion and how one preserves or represents the fluctuations.