DENSITY GRADIENT THEORY ANALYSIS OF ELECTRON DISTRIBUTIONS IN HETEROSTRUCTURES

In recent work we have developed a generalized version of the standard diffusion-drift description of semiconductor transport which includes lowest order quantum effects. This new description, which we refer to as density-gradient theory, is examined in this paper in some detail for the static case. We exhibit a new variational principle and derive a first (energy) integral of the static equations in one-dimension. We then apply these results to the analysis of various equilibrium problems in heterostructures. Detailed comparisons between predictions of density-gradient theory and one-electron quantum mechanics are made and, on this basis, we assess the conditions under which density-gradient theory constitutes a useful tool for device analysis in quantum regimes. In particular, we show it to be of value when effects of quantum confinement/exclusion and tunneling are significant but, as might be expected, less useful (if at all) when interference phenomena are important. © 1990.