Full-band Monte Carlo simulation of high-energy transport and impact ionization of electrons and holes in Ge, Si, and GaAs

In this work we have computed the rate for impact ionization ab initio and have employed this rate in full-band Monte Carlo simulations in order to determine the high-energy carrier-phonon deformation potentials. We have considered transport and impact ionization of electrons and holes in Ge, Si, and GaAs, the valence bands being treated with nonlocal empirical pseudopotentials and spin-orbit interaction. The impact ionization rates have been computed using three different approximations: (1) the ab initio rate, which accounts for energy and momentum conservation and for the dependence of the Coulomb matrix element on both initial and final states, (2) the constant-matrix-element (CME) approximation, which employee a constant Coulomb matrix element, and (3) the random-k approximation, which relaxes momentum-conservation.