Monte Carlo calculation of electron initiated impact ionization in bulk zinc-blende and wurtzite GaN

Calculations of the high-field electronic transport properties of bulk zinc-blende and wurtzite phase gallium nitride are presented focusing particularly on the electron initiated impact ionization rate. The calculations are performed using ensemble Monte Carlo simulations, which include the full details of the band structure derived from an empirical pseudopotential method. The model also includes the numerically generated electron impact ionization transition rate, calculated based on the pseudopotential band structures for both crystallographic phases. The electron initiated impact ionization coefficients are calculated as a function of the applied electric field. The electron distribution is found to be cooler and the ionization coefficients are calculated to be lower in the wurtzite phase as compared to zinc-blende gallium nitride at compatable electric-field strengths. The higher electron energies and the resulting larger impact ionization coefficients in zinc-blende gallium nitride are believed to result from the combined effects of a lower density of states and phonon scattering rate for energies near and below 3 eV above the conduction-band minimum, and a somewhat higher ionization transition rate compared to the wurtzite phase. The nature of the impact ionization threshold in both phases of gallium nitride is predicted to be soft. Although there is considerable uncertainty in the knowledge of the scattering rates and the band structure at high energies which lead to uncertainty in the Monte Carlo calculations, the results presented provide a first estimate of what the electron initiated impact ionization rate in GaN can be expected to be.