Free excitons in wurtzite GaN

Abstract

We present a comprehensive study of the free-exciton and exciton-polariton photoluminescence in wurtzite GaN. Using polarization-dependent measurements we were able to resolve the fine-structure energy splittings in the $n=1$ state of the A exciton and to determine the energy separation between the $1S$ and ${2P}_{\ifmmode\pm\else\textpm\fi{}1}$ states as $19.7\ifmmode\pm\else\textpm\fi{}0.2 \mathrm{meV}.$ For the $n=1$ state, the evolution of the emission from two transverse polariton branches ${\ensuremath{\Gamma}}_{5T1}$ and ${\ensuremath{\Gamma}}_{5T2},$ the longitudinal exciton ${\ensuremath{\Gamma}}_{5L},$ and the dipole-forbidden exciton ${\ensuremath{\Gamma}}_{6}$ in magnetic fields up to 15 T have been studied in Faraday configuration. We have estimated the value of the parallel effective g factor of the hole mixed into the $1S$ state of the A exciton as ${g}_{A,1S}^{\ensuremath{\Vert}}=2.25\ifmmode\pm\else\textpm\fi{}0.2.$ To describe these data a theory is developed for the exciton energy structure in hexagonal semiconductors with wurtzite symmetry in zero and in weak external magnetic fields which takes into account the effect of the hexagonal lattice anisotropy and the coupling of all excitonic states belonging to different valence subbands. The effect of the exciton interaction with polar optical phonons is considered. The theory is very successful in describing the free-exciton emission and magnetoluminescence in wurtzite GaN. The effective mass parameters and the magnetic Luttinger constant as well as the effective Rydberg numbers and binding energies of the A, B, and C excitons are determined from a comparison of the theory with experimental data.