A semiclassical approach to Coulomb scattering of conduction electrons on ionized impurities in nondegenerate semiconductors

Abstract

In the proposed model of mobility, the time of electron–ion interaction equals the time taken by the conduction electron to pass a spherical region, corresponding to one impurity ion in crystal, and the minimum scattering angle is determined after Conwell–Weisskopf. We consider the acts of electron scattering on ions as independent and incompatible events. It is shown in the approximation of quasimomentum relaxation time, that for nondegenerate semiconductors, the mobility μ_i, limited by the elastic scattering by impurity ions with the concentration N_i, is proportional to T/N_i^2/3; the Hall factor equals 1.4. The calculated dependences of the mobility of the majority charge carriers upon their concentration for different temperatures T agree well with known experimental data. It is shown, that the Brooks–Herring formula μ_BH ∝ T^3/2/N_i gives overestimated values of mobility. Comparison of the calculations of mobility in degenerate semiconductors with experimental data also yields μ_i < μ_BH.