Ionized Impurity Scattering in n-Type Germanium and n-Type Silicon

The relaxation time tensor components for ionized impurity scattering in semiconductors with ellipsoidal energy surfaces are derived on the basis of the Herring-Vogt formalism. Numerical evaluation is performed for n -type germanium and n -type silicon. It is found that the anisotropy of ionized impurity scattering is dependent on energy. The mobility and the effective anisotropy parameter K =µ ⊥ /µ || for n -Ge are evaluated by using the calculated relaxation times for ionized impurity scattering and the experimentally determined lattice scattering mobility. Fair agreement between theory and experiment is obtained at liquid nitrogen temperature for carrier concentrations smaller than 10 17 /cm 3 .