High-field transport statistics and impact excitation in semiconductors

The paper is devoted to the statistics of semiclassical charge transport in semiconductors subject to high electric fields. Two main approaches are distinguished: one is mostly analytical and makes use of the notion of a mean free path, and it led to the so-called lucky-drift model; the other one is based upon Monte Carlo computer simulations and has the ability to include a realistic band structure. The present paper aims to show that in spite of the differences in wording and viewpoint, both approaches are fundamentally equivalent. We first review the lucky-drift model in its simplest form, and then present some basic features of the statistical approach used in numerical simulations of transport. On the one hand, statistical concepts are introduced into the lucky-drift model, and the notion of lucky-drift trajectories is criticized and replaced by that of energy autocorrelation. On the other hand, the results obtained in numerical simulations are reproduced in the framework of a generalized lucky-drift model tailored to allow for strong nonparabolicities. The statistical description of transport is applied to the determination of the rate of inelastic collisions undergone by a hot electron in the presence of an impact-excitable impurity. It is argued that such a rate is a better indicator of the fraction of carriers attaining a certain energy than the band-to-band impact-ionization rate. The previous expression of the impact-excitation rate, derived on the basis of the picture of lucky-drift trajectories, is revised, and a comparison with experiment is attempted.