Generalized Drude model: unification of ballistic and diffusive electron transport

Abstract

For electron transport in parallel-plane semiconducting structures, a model\nis developed that unifies ballistic and diffusive transport and thus\ngeneralizes the Drude model. The unified model is valid for arbitrary magnitude\nof the mean free path and arbitrary shape of the conduction band edge profile.\nUniversal formulas are obtained for the current-voltage characteristic in the\nnondegenerate case and for the zero-bias conductance in the degenerate case,\nwhich describe in a transparent manner the interplay of ballistic and diffusive\ntransport. The semiclassical approach is adopted, but quantum corrections\nallowing for tunneling are included. Examples are considered, in particular the\ncase of chains of grains in polycrystalline or microcrystalline semiconductors\nwith grain size comparable to, or smaller than, the mean free path. Substantial\ndeviations of the results of the unified model from those of the ballistic\nthermionic-emission model and of the drift-diffusion model are found. The\nformulation of the model is one-dimensional, but it is argued that its results\nshould not differ substantially from those of a fully three-dimensional\ntreatment.\n