Relaxation Effects on Donor Spins in Silicon and Germanium

Two problems concerning strain effects on isolated donor states in Si and Ge are treated. One is a modulation of the hyperfine coupling between the donor electronic and nuclear spins which gives rise to a cross relaxation rate T _x ^-1 ( Δ m _s =±1, \(\varDelta m_{I}{=}{\mp}1\)). For Raman process (double-phonon process) T _x ^-1 is shown to depend on the temperature as T ^-7 . For P-donor in Si the calculated value of T _x is approximately 1.5×10 ⁴ second at T =2.16°K, which is in good agreement with the experiments of Honig and Stupp. For single-phonon process the calculation shows that T _x is sensitive to static strains in the crystal, which has been confirmed in the experiments of Wilson and Feher. The other problem treated is the effects of strong external stresses on Ge donor spin-resonance lines. The electronic g -tensor, the single-phonon relaxation rates T _s ^-1 and T _x ^-1 , and an inhomogenous broadening effect are derived for several orientations of the stress and the magnetic field. It is shown that both T _s and T _x can be made longer than 1 second by applying a large compression along the direction within experimentally available conditions.