Hydrostatic-pressure coefficient of the indirect gap and fine structure of the valence band of 6H-SiC

Photoluminescence measurements on 6$H$-SiC doped with nitrogen have been performed under hydrostatic pressure up to 50 kbar at low temperature $(T$=29$\ifmmode\pm\else\textpm\fi{}$2 K). The observed emission lines ${S}_{0}$, ${R}_{0}$, ${P}_{0}$, ${S}_{02},$ and ${R}_{02}$ are due to excitons with holes from the $A$ and $B$ valence bands bound to the neutral nitrogen donor. The energy shift of the ${P}_{0}$ line under hydrostatic pressure is used to determine the linear pressure coefficient of the indirect gap of 6$H$-SiC, which yields 0.20 eV/Mbar. The energy difference between the emission lines ${S}_{02}$ ${(R}_{02})$ and ${S}_{0}$ ${(R}_{0})$ of 5.15$\ifmmode\pm\else\textpm\fi{}$0.1 (5.08$\ifmmode\pm\else\textpm\fi{}$0.1) meV gives the splitting ${\ensuremath{\Delta}}_{\mathrm{AB}}$ of the topmost valence bands. We employ nonrelativistic band-structure calculations within the density-functional theory based on the local-density approximation in order to calculate the pressure coefficient of the indirect band gap of 6$H$-SiC (together with those of 4$H$, 2$H$, and 3$C$-SiC as well as those of diamond, Si, and Ge) and the crystal field splitting of the valence band. The latter, together with the experimental splitting ${\ensuremath{\Delta}}_{\mathrm{AB}}$ of the topmost valence bands A and B is used to estimate the spin-orbit splitting of 6$H$-SiC to be about 7.7 meV. The calculated pressure coefficient shows good agreement with the experimental value.