Calculation of the electron and hole impact ionization rate for wurtzite AlN and GaN

Abstract

The interband impact ionization transition rate (IIR) of electrons and holes in wurtzite GaN and AlN is calculated using full local density approximation (LDA) band structures under the scissor approximation. The IIR of AlN is first calculated and the results show a large difference between the IIR of electrons and holes. The IIR of electrons grows from zero to 1014 at energies of ∼6.6–10 eV, while the IIR of holes is zero below 12.2 eV. The difference is interpreted by the energy gap between the sixth and the seventh valence bands. Analysis shows that it is hard for holes in AlN to tunnel through the large energy gap between the sixth and the seventh valence bands; as a result, holes can hardly get enough energy for impact ionization in the electrical field of several MV cm−1. This indicates that AlN is a good material for avalanche photodetectors of controllable gain, low noise and wide bandwidth with a cutoff wavelength of 210 nm. To further facilitate Monte Carlo simulation, the AlN and GaN IIR are fitted to the Keldysh formula.