Monte Carlo evaluation of an analytical model for nonequilibrium-phonon-induced electron velocity saturation in GaN

Abstract

The ensemble Monte Carlo method is used to solve the Boltzmann equation for electrons together with the equation for phonons treated in the relaxation-time approximation. The effect of nonequilibrium longitudinal optical phonons on hot-electron energy distribution, mean energy, drift velocity and power dissipation is considered for bulk GaN subjected to electric fields in a range up to 100 kV cm−1. In particular, the suppression of the high-energy tail of the hot-electron distribution due to the phonon accumulation is resolved. The results of the simulation are compared with those obtained within the recently proposed analytical model for the saturation of electron drift velocity at high electric fields. The saturated velocity decreases as the electron gas density increases. Values around 107 cm s−1 are reached at an electric field of 100 kV cm−1 for an electron gas density of 1018 cm−3. The analytically obtained results are in a better agreement with those of Monte Carlo simulation if the electron gas density is higher and the electric field is stronger.