The intra-collisional field effect in semiconductors. I. Analytic results

TLDR: In this paper, first-order time-dependent perturbation theory is used to derive expression for scattering rates in the presence of high electric fields, and it is suggested that the complicated retarded transport equations recently introduced into hot electron theory are not necessary to treat the intra-collisional field effect in the weak phonon coupling limit.

Abstract: First-order time-dependent perturbation theory is used to derive expression for scattering rates in the presence of high electric fields. Analysis in terms of Houston functions suggests that scattering rates are approximately field independent, but a more accurate treatment in terms of Airy functions shows that at sufficiently high fields, the resonant width of the scattering vertex is limited by the domain of integration, and a field dependent suppression of scattering occurs. This effect occurs first for small-wavevector phonons, and appreciable effects are expected for fields exceeding 104-105 V cm-1. It is also suggested that the complicated retarded transport equations recently introduced into hot electron theory are not necessary to treat the intra-collisional field effect in the weak phonon coupling limit at fields of interest in conventional semiconductor transport. At fields where suppression of scattering is significant, it is found that additional scattering into field-induced band tails is also important.