Orbach Spin-Lattice Relaxation of Shallow Donors in Silicon

Abstract

The spin-lattice relaxation rate $\frac{1}{T_1}$ for the exponential temperature-dependent Orbach process has been calculated assuming that the spin-flipping interaction is due to the residual spin-orbit interaction associated with the $1S-T_2$-donor states. The Orbach rate constant is shown to depend principally on two physical parameters, the impurity spin-orbit splitting and the level width of the $1S-T_2$ states. Using the results of the infrared-absorption measurements of Zeiger and Krag on Bi and of Aggarwal and Ramdas on Sb, As, and P, reasonable agreement is found between the calculated results and the experimental measurements of Castner. The simple result found is possible because the level width, assumed due to spontaneous phonon emission, makes it unnecessary to consider the complicated details of the electron-phonon coupling between the $1S-A_1$ and $1S-T_2$ states.