Generation of spin currents in $n$-silicon doped with phosphorus, antimony and bismuth and the influence of spin scattering processes with flip on them

Doping of silicon with bismuth leads to additional spin scattering of the conduction electron by the spin-orbit potential introduced by a heavy donor. In this paper, we discuss spin flip scattering influence on the generation of spin currents in silicon with electronic conductivity. Based on the theory of spin pumping and the diffusion model, the values of spin currents and voltages of the ISHE are calculated with varying the type of donor and its concentration and the spin diffusion lengths. Calculations made it possible to find the dependences of the magnitudes of the effects on the parameters of silicon layers doped with bismuth, and to explain the absence of ISHE signals when the silicon layer is doped only with phosphorus or antimony with a concentration of $N_d>$ 10$^{19}$ cm$^{-3}$.