Theoretical study of hole initiated impact ionization in bulk silicon and GaAs using a wave-vector-dependent numerical transition rate formulation within an ensemble Monte Carlo calculation

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Abstract
In this paper, calculations of the hole initiated interband impact ionization rate in bulk silicon and GaAs are presented based on an ensemble Monte Carlo simulation with the inclusion of a wave-vector-dependent numerical transition rate formulation. The ionization transition rate is determined for each of the three valence bands, heavy, light, and split-off, using Fermi’s golden rule with a two-body, screened Coulomb interaction. The dielectric function used within the calculation is assumed to be wave-vector-dependent. Calculations of the field-dependent impact ionization rate as well as the quantum yield are presented. It is found from both the quantum yield results and examination of the hole distribution function that the effective threshold energy for hole initiated impact ionization is relatively soft, similar to that predicted for the corresponding electron initiated ionization rate threshold in both GaAs and silicon. It is further found that light-hole initiated ionization events occur more frequently than either heavy or split-off initiated ionization events in bulk silicon over the applied electric field strengths examined here, 250–500 kV/cm. Conversely, in GaAs, the vast majority of hole initiated ionization events originate from holes within the split-off band.