Phonon replicas at the M-point in 4H-SiC: A theoretical and experimental study

This paper presents a comprehensive study of the phonons at the M point of the Brillouin zone of $4H\ensuremath{-}\mathrm{SiC},$ i.e., at the position of the conduction-band minimum, from both theoretical and experimental points of view. The phonon energies are derived from the low-temperature photoluminescence (PL) spectrum. The theoretical section contains the classification of phonons by symmetry, the deduction of the polarization selection rules for the photons emitted during recombination of free or nitrogen-bound excitons, and presents a simple lattice dynamics model used to obtain some results on the distribution of the phonon modes with different symmetries above and below the energy gap in the phonon dispersion. The classification of the 24 phonons by symmetry is shown to be ${8M}_{1}{+4M}_{2}{+4M}_{3}{+8M}_{4},$ where ${M}_{i}$ are the irreducible representations of the group of the wave vector at the M point. The polarization selection rules imply that among the 24 phonon replicas (lines) in $4H\ensuremath{-}\mathrm{SiC},$ which can be observed in the PL spectrum, there are 12 with parallel polarization ${(M}_{1}$ and ${M}_{3}$ symmetry), and 12 with polarization perpendicular ${(M}_{2}$ and ${M}_{4}$ symmetry) to the crystal (hexagonal) c axis. Our consideration shows that the phonons of each symmetry are equally distributed above and below the ``phonon'' energy gap. Therefore, there are six replicas of each polarization above and below the gap. In the experimental section an assignment of the phonon replicas based on the similarity of the sets of replicas related to the bound and free excitons is carried out, and the results are compared with the theoretical ones. We have experimentally found 22 of the 24 phonons at the M point in $4H\ensuremath{-}\mathrm{SiC}.$