Scattering by ionization and phonon emission in semiconductors. II. Monte Carlo calculations

Calculations of the pair-creation energy $\epsilon$ and the Fano factor $F$ for semiconductors are done for the assumptions that in each scattering event all possible sets of product particles are equally probable, that the energy bands are those of free particles separated by a band gap $E_g$, and that there is a single phonon energy $\hslash {\omega }_0$. The results from calculations done previously with the use of a recursive method are corroborated and expanded with the use of the Monte Carlo method. The electron-phonon interaction is divided into a deformation-potential interaction and a polar-mode electrostatic interaction, and the $\hslash {\omega }_0$ dependence of these interactions is incorporated into the calculations. New values of $\epsilon$ and $F$ are calculated. For many semiconductors, the accord of these values with experiments is as good as the accord of previous calculations done with the deformation potential alone, indicating the insensitivity of $\epsilon$ to the added interaction.