Spin-dependent optical properties in strained silicon and germanium

We present a comprehensive theory of the circularly polarized luminescence and its dependence on strain in spin-polarized Si and Ge. Symmetries of wavefunctions and interactions are used to derive concise ratios between intensities of the right and left circularly polarized luminescence for each of the dominant phonon-assisted optical transitions. These ratios are then used to explain the circular polarization degrees of the luminescence peaks in the spectra of biaxially-strained Si and Ge, and of relaxed ${\rm{Si}}_{1-x}{\rm{Ge}}_{x}$ alloys. The spectra are numerically calculated by a combination of an empirical pseudopotential method, an adiabatic bond-charge model and a rigid-ion model.