Band-to-band impact ionization by hot electrons and holes is an important process in high-field transport in semiconductors, leading to carrier multiplication and avalanche breakdown. Here we perform first principles calculations for the respective microscopic scattering rates of both electrons and holes in various wide band gap semiconductors. The impact ionization rates themselves are calculated directly from the electronic band structure derived from empirical pseudopotential calculations for cubic GaN, ZnS, and SrS. In comparison with the electron rates, a cutoff in the hole rate is found due to the relatively narrow valence bandwidths in these wide band gap semiconductors, which correspondingly reduces hole initiated carrier multiplication.

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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 ͑1994͔͒. 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.

We have performed extensive ab initio band structure calculations within density functional theory using an exact exchange formalism with a local density approximation for correlations. The wave-vector-dependent impact ionization rate is determined for GaAs, GaN, and ZnS. A strong asymmetry of the microscopic scattering rate as well as a pronounced influence of the band structure is found. We present also energy-averaged impact ionization rates which can be used in ensemble Monte Carlo simulations of high-field electron transport in these materials.

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