Field effect on the impact ionization rate in semiconductors

Impact ionization plays a crucial role for electron transport in semiconductors at high electric fields. We derive appropriate quantum kinetic equations for electron transport in semiconductors within linear response theory. The field-dependent collision integral is evaluated for the process of impact ionization. A known, essentially analytical result is reproduced within the parabolic band approximation [W. Quade et al., Phys. Rev. B 50, 7398 (1994)]. Based on the numerical results for zero field strengths but realistic band structures, a fit formula is proposed for the respective field-dependent impact ionization rate. Explicit results are given for GaAs, Si, GaN, ZnS, and SrS.