Relaxation times and population inversion of excited states of arsenic donors in germanium

The relaxation times of excited states of arsenic dopant in germanium at cryogenic temperatures $T< 15$ K have been experimentally studied by the optical pump-probe method using radiation of a free-electron laser. Two variants of the excitation of impurity centers have been used in the experiment: (i) from the $1s(A_1)$ ground state of the dopant and (ii) from the $1s(T_2)$ first excited state having a finite thermal population. In the former variant, it has been shown that the decay times of the $2p_0$ and $3p_\pm$ states are about $0.8$ and $0.6$ ns, respectively. In the latter variant, a single measurement can simultaneously provide the relaxation times of two $2p_\pm$ and $1s(T_2)$ states about $0.6$ and no more than $0.16$ ns, respectively. The data obtained have indicated the possibility of forming population inversion and the gain of terahertz radiation at the $2p_\pm\to 1s(T_2)$ and $2p_0\to 1s(T_2)$ transitions at the optical excitation of the mentioned impurity centers.