Scattering Mechanism in Heavily Doped Semiconductors. I. Maxima in Resistivity and Hall Coefficient

Resistivities and Hall coefficients of heavily doped semiconductors in the metallic concentration range, especially of Sb-doped Ge and P-doped Si, are investigated by the degenerate electron gas model with impurity scattering. The maxima of resistivity and Hall coefficient are explained by strong temperature variation of the screening length, which is due to the smallness of the Fermi temperature T F in the present systems ( T F ∼100 K). The shapes of the screened impurity potentials and the scattering of electrons by them are investigated in detail by the nonlinear Hartree approximation, the Kohn-Sham density functional formalism and the random phase approximation with valley multiplicity. Including nonlinearity of screening and many-body effect, we obtain the values of resistivity which agree very well with experiments for the higher concentration samples of the metallic range.