Hot photoluminescence in GaN: Carrier energy relaxation and hot phonon effects

Abstract

A theoretical study of carrier energy relaxation in wurzite GaN is presented. The analysis is focused on describing phenomena which occur when very energetic electrons and holes are optically injected into the material, as is the case during a hot photoluminescence experiment. Due to the wurtzite symmetry, transverse optical-like phonon modes become active for carrier scattering. Their contribution is analyzed and quantitatively compared to the longitudinal optical (LO) phonon contribution. A pseudoisotropic model of optical phonons in GaN is proposed and is shown to give similar results as the more rigorous anisotropic model. The electron and hole energy relaxation rates are calculated. It is predicted that very energetic carriers should form a discrete distribution, only slightly broadened by carrier–carrier scattering. The conditions for having the electron and hole gases thermalized at the bottom or top of their band are given. Their actual temperature is calculated with or without taking into account hot phonon effects. The LO phonon temperature is calculated and found to be significantly higher than the lattice temperature. Hot phonon effects are important and contribute to equalizing the electron and hole temperatures. The resulting photoluminescence temperature is calculated and compared with experimental data. The agreement with experimental results is improved if hot phonons are included in the calculation.