A generalized analytical model based on multistage scattering phenomena for estimating the impact ionization rate of charge carriers in semiconductors

A generalized analytical model based on multistage scattering phenomena has been developed in this paper for estimating the impact ionization rate of charge carriers in semiconductors. The probabilities of impact ionization initiated by electrons and holes have been calculated separately by taking into account all possible combinations of optical phonon scattering and carrier-carrier collisions prior to the impact ionization. Finally the analytical expressions of impact ionization rate of electrons and holes have been developed by using the aforementioned impact ionization probabilities. The impact ionization rates of electrons and holes in 4H-SiC have been calculated within the field range of \(2.5\times 10^{8}\) – \(6.5\times 10^{8}\hbox { V m}^{-1}\) by using the analytical expressions of those developed in the present paper. Those are also calculated by using the analytical expressions developed by some other researchers earlier without considering the multistage scattering phenomena. Finally the theoretical results obtained from the analytical model proposed in this paper and the analytical model developed by earlier researchers within the field range under consideration have been compared with the ionization rate values calculated by using the empirical relations fitted from the experimentally measured data. Closer agreement with the experimental data has been achieved when the impact ionization rate of charge carriers in 4H-SiC are calculated from the proposed model as compared to the earlier one.