Exciton spectra and spin-orbit splitting in GaN epitaxial films

This paper is concerned with the interpretation of experimental data on free exciton energies in GaN epitaxial films grown on various substrates (sapphire, SiC and GaN). In hexagonal (wurtzite) films the degeneracy in the valence band is completely lifted and three excitons can be observed by reflectivity and photoluminescence excitation spectroscopy. Their energies can be interpreted in terms of the quasi-cubic model of Hopfield which involves two parameters, Delta(so) the spin-orbit splitting and Delta(CR) the axial crystal field energy, which may, in principle, be derived from measurement of the energy differences E(C) - E(A) and E(B) - E(A). In practice, experimental data show considerable variation; this variation is thought to be due to strain in the films introduced as a result of differential thermal expansion during cool-down from the growth temperature to room temperature, and direct calculation of the spin-orbit and crystal field parameters for each sample results in apparently random values. In particular, the values of Delta(so) obtained differ considerably from that measured (unambiguously) on a cubic (zinc blende) film, Delta(so) = 17 meV. We show that it is possible to resolve these dificulties, following an idea introduced by Gil at al (1995), by plotting E(C) and E(B) aginst E(A) for the various samples and obtaining a fit to the data thus displayed. We then find that an excellent fit can be obtained using the quasi-cubic model with Delta(so) = 17 meV and Delta(CR) ranging from 13 meV to 37 meV over the range of samples for which appropriate data have been published.