gFactor and Donor Spin-Lattice Relaxation for Electrons in Germanium and Silicon

The $g$ factors of electrons in Ge and Si are calculated on the basis of the effective mass approximation. The results are consistent with experimental spin resonance data. The effect is predicted to be anisotropic, with $g_{\mathrm{II}}$ less than $g_{\perp }$. This anisotropy introduces a strong interaction between the electron spin and shear waves, for the singlet donor ground state. This interaction can account in order of magnitude for the observed spin-lattice time ${\tau }_s$ for donor electrons in Si at low temperatures, including both a one-phonon process and a two-phonon Raman-type process. The temperature and magnetic-field dependence for the two processes are predicted to be ${{\tau }_s}^{-1\mathrm{}}\propto T{H}^4$ and ${{\tau }_s}^{-1\mathrm{}}\propto T^7{H}^2$, respectively. The temperature dependence agrees with experiment; however there are discrepancies in the magnetic-field dependence. ${\tau }_s$ is predicted to be anisotropic.