Phonon-assisted optical transitions in GaN with impurities and defects

Abstract

We have classified all the possible types of phonon-assisted optical processes involving bound or extended initial, final, and virtual (intermediate) electron states and formulated, for the first time, in terms of site symmetry, the selection rules for corresponding transitions. We apply this theory to phonon-assisted transitions in hexagonal GaN involving substitutional impurities and vacancies with C 3v site-symmetry as well as interstitial impurities and molecular point defects (paired impurities, double vacancies, and vacancy-impurity complexes) occupying sites with C 3v, C s, and C 1 ones. We show that phonon-assisted optical recombination is allowed in any polarization for free and bound carriers and excitons whatever is the number of involved phonons. Just, the nature of virtual state(s) and phonon(s) can depend on the polarization of the emitted light. We discuss, in particular, the case of excitons bound to neutral donors or acceptors. Our predictions are in good agreement with experimental optical spectra published in the literature which exhibit numerous lines assigned to one- and multi-phonon-assisted transitions.