Raman Spin-Lattice Relaxation of Shallow Donors in Silicon

This work reports both experimental measurements and calculations of two-phonon Raman spin-lattice relaxation times for shallow donors in silicon. Saturation, line broadening, and adiabatic fast passage techniques were used to measure $T_s (\Delta M_s=\pm 1,\Delta M_I=0)$ between 2 and 30°K for P, As, Sb, and Bi at 3300 G. $T_x (\Delta M_s=\pm 1,\Delta M_I=\mp 1)$ was measured in the liquid He range for As, Sb, and Bi at 3300 G. The calculations of the spin-lattice relaxation rates $\frac{1}{T_s}$ and $\frac{1}{T_x}$ for Raman processes were made using only the $1S$ doublet and triplet valley-orbit excited states. The calculations were made for both the power-law temperature-dependent region and the exponential temperature-dependent region.