First-principles study of the phonon replicas in the photoluminescence spectrum of 4H -SiC

Abstract

The free-exciton photoluminescence (PL) spectrum of $4H$-SiC exhibits a detailed fine structure due to the different phonons involved in the indirect gap transition. Here a first-principles calculation of these phonons, their symmetry labeling and their contribution to the photoluminescence spectrum is presented. The calculation uses phonons and electron-phonon coupling matrix elements computed via density functional perturbation theory and energy bands and optical phonon matrix elements calculated in density functional theory. The results are in excellent agreement with the experiment for the phonon energies and the polarization dependence of the spectrum. The relative intensities are also in fair agreement if we allow for some phonons within a few meV to be interchanged. There is however a remarkable discrepancy that the experimental spectrum shows a distinct behavior for phonons with energy below $\ensuremath{\sim}55$ meV and above that energy, which is absent in the theory. The experimental PL lines corresponding to phonon energies below 55 meV are about a factor 5--10 smaller in intensity. This is not found in our calculations. The calculations show a similar peak distribution as the experiment in this range but with intensities comparable to those above 55 meV. This indicates that another mechanism outside the scope of the electron-phonon mediated transitions is operative for photon energies of the PL lines closer to the indirect exciton gap than this 55 meV cutoff, which reduces the overall intensity of these lines. We propose that this may result from competition between the phonon-assisted PL and trapping of the electron in the available unoccupied hexagonal site N-donor shallow level at 53-meV binding energy. As part of this study, we also present the phonon dispersions and density of states in $4H$-SiC and the electronic band structure including quasiparticle corrections.