Quasi-classical model of the static electrical conductivity of heavily doped degenerate semiconductors at low temperatures

Germanium, silicon, gallium arsenide, and indium antimonide $n$-type crystals on the metal side of the insulator–metal transition (Mott transition) are considered. In the quasi-classical approximation, the static (direct current) electrical conductivity and the drift mobility of electrons of the $c$ band, and electrostatic fluctuations of their potential energy and the mobility edge are calculated. It is considered that a single event of the elastic Coulomb scattering of a mobile electron occurs only in a spherical region of the crystal matrix with an impurity ion at the center. The results of calculations using the proposed formulas without using fitting parameters are numerically consistent with experimental data in a wide range of concentrations of hydrogenlike donors at their weak and moderate compensation by acceptors.