Analysis of phonon-induced spin relaxation processes in silicon

We study all of the leading-order contributions to spin relaxation of conduction electrons in silicon due to the electron-phonon interaction. Using group theory, the k·p perturbation method, and the rigid-ion model, we derive an extensive set of matrix element expressions for all of the important spin-flip transitions in the multivalley conduction band. The scattering angle has an explicit dependence on the electron wave vectors, phonon polarization, valley position, and spin orientation of the electron. Comparison of the derived analytical expressions with results of empirical pseudopotential and adiabatic band charge models shows excellent agreement.