Calculation of the electron mobility for the $\Delta_1$ model of the conduction band of germanium single crystals

The concentration dependences of the charge-carrier mobility are obtained for the $\Delta_1$ model of the conduction band of $n$-Ge crystals on the basis of anisotropic scattering at 77 K. It is shown that the absolute-minimum inversion of the $L_1$–$\Delta_1$ type caused by single-axis pressure on $n$-Ge crystals along the [100] crystallographic direction substantially decreases the charge-carrier mobility. This is explained by a decrease in the relaxation time because the effective electron masses differ only slightly in terms of different minima. For the other two cases of inversion of the $L_1$–$\Delta_1$ absolute minimum under hydrostatic and single-axis pressure along the [110] crystallographic direction, a decrease in the electron mobility is caused mainly by an increase in the effective mass. It is shown also that it is the degree of effective-mass anisotropy that substantially affects the efficiency of charge-carrier scattering in anisotropic semiconductors in this case.