Impact ionization threshold energy of trigonal selenium: An ab initio study

Impact ionization coefficient is a critical parameter that determines the multiplication gain in avalanche photodiodes. The impact ionization coefficient is closely related to the ionization threshold, Eth, which is determined by the band dispersion of the semiconducting material used in detectors. The ionization threshold energy is commonly calculated based on a parabolic band assumption, which provides only a crude approximation. Here we present a first principle study of the ionization threshold energy through an analysis of the electronic structure of trigonal selenium. It is shown that the excess energy of primary charge carriers required to initiate the impact ionization in trigonal selenium can be as low as the band gap, E-g, which is a sharp contrast to the parabolic band approximation that implies Eth = 3/2E(g). Such a low Eth value is a favourable factor for impact ionization.