Theory of Spin-Dependent Phonon-Assisted Optical Transitions in Silicon

A theory for the relation between the spin polarization and luminescence in silicon is presented. The theory provides intuitive relations for phonon-assisted optical transitions between the conduction and valence band edges. It is shown that an opposite behavior of longitudinal and transverse optical phonon-assisted transitions is responsible to recent experimental results of spin injection into silicon. The effects of spin-orbit coupling and doping are studied in detail.