Fourier-transform photoluminescence spectroscopy of excitons bound to group-III acceptors in silicon: Uniaxial stress

Photoluminescence of excitons bound to Al, Ga, In, and Tl acceptors in Si crystals subjected to 〈001〉, 〈111〉, or 〈110〉 uniaxial stress was studied at liquid-He temperatures with 0.0025-meV spectral resolution. The deformation-potential constants of the group-III acceptors in the ground state are (in eV) $b=-1.01\pm 0.02,$ $d=-3.31\pm 0.06$ for Al, $b=-1.03\pm 0.02,$ $d=-3.10\pm 0.06$ for Ga, $b=-0.43\pm 0.01,$ $d=-2.41\pm 0.05$ for In, and $b=-0.30\pm 0.03,$ $d=-1.95\pm 0.2$ for Tl. The shear deformation-potential constant for electrons in acceptor bound excitons ${\Xi }_u=8.6\mathrm{}\mathrm{eV}$ for all group-III acceptors within an experimental error of $\pm 0.15\mathrm{eV}$ for Al, Ga, and In, and $\pm 0.8\mathrm{eV}$ for Tl. The order of the valley-orbit states in Tl bound excitons is ${\Gamma }_1,$ ${\Gamma }_3,$ ${\Gamma }_5$ with the ${\Gamma }_5$ energy 1.21 meV above ${\Gamma }_1,$ and 0.10 meV above ${\Gamma }_3.$ All details of the spectra including positions, relative amplitudes, and polarizations of the components have been explained on the basis of a simple model of acceptor bound excitons with holes in the $J=0\mathrm{}$ state taking into account the valley-orbit splitting and the spin-orbit coupling of the electron. Significant deviations from the theoretical predictions were observed only for very small strains producing acceptor splittings comparable with the intrinsic zero-stress splitting.