Magnetic moment relaxation of a shallow acceptor center in heavily doped silicon

Results of studying the temperature dependence of the residual polarization of negative muons in crystalline silicon with germanium ($9\times 10^{19}\,$cm$^{-3}$) and boron ($4.1\times 10^{18}, 1.34\times 10^{19}$, and $4.9\times 10^{19}\,$cm$^{-3}$) impurities are presented. It is found that, similarly to $n$-and $p$-type silicon samples with impurity concentrations up to $\sim 10^{17}\,$cm$^{-3}$ , the relaxation rate $\nu$ of the magnetic moment of a $\mu$Al acceptor in silicon with a high impurity concentration of germanium ($9\times 10^{19}\,$cm$^{-3}$ ) depends on temperature as $\nu\sim T^q , q\approx 3$ at $T=(5{-}30)\,$ K. An increase in the absolute value of the relaxation rate and a weakening of its temperature dependence are observed in samples of degenerate silicon in the given temperature range. Based on the experimental data obtained, the conclusion is made that the spin-exchange scattering of free charge carriers makes a significant contribution to the magnetic moment relaxation of a shallow acceptor center in degenerate silicon at $T\lesssim 30$ K. Estimates are obtained for the effective cross section of the spin-exchange scattering of holes ($\sigma_h$) and electrons ($\sigma_e$) from an Al acceptor center in Si: $\sigma_h\sim 10^{-13}\,$cm$^2$ and $\sigma_e\sim 8\times 10^{-15}\,$cm$^2$ at the acceptor (donor) impurity concentration $n_a (n_d )\sim 4\times 10^{18}\,$cm$^{-3}$.