On the intracenter relaxation of shallow arsenic donors in stressed germanium. Population inversion under optical excitation

The relaxation rates of lower excited states $1s(T)$, $2p_{0}$, $2s$, $3p_{0}$, and $2p_{\pm}$ of arsenic donors in a germanium crystal are calculated upon the interaction with long-wavelength acoustic phonons depending on the uniaxial stress in the crystallographic direction [111]. The populations of states under optical excitation are estimated for calculated times. It is shown theoretically that optical excitation of the medium forms an inverse population of arsenic donor levels and leads to the possibility of the implementation of a four-level laser scheme with the radiative transition between $2p$ states and the $1s$ triplet state at zero strain. The estimated value of the expected gain in the medium under optical excitation conditions by CO$_2$ laser radiation in the medium at a donor concentration of 2 $\times$ 10$^{15}$ cm$^{-3}$ is $\sim$0.35 cm$^{-1}$ at a frequency of 1.98 THz if the laser transition is 2$p_{\pm}\to1s(T)$ and 1.25 THz if the laser transition is 2$p_{0}\to1s(T)$.