Impurity scattering of electrons in non-degenerate semiconductors

A unified approach to the theory of impurity scattering in non-degenerate semiconductors is presented using a simple model for the scattering potential, and partial-wave techniques. The theory describes both charged and neutral impurity scattering and distinguishes between sign of charge. It also allows a novel extension to be made to resonance (or Breit-Wigner) scattering. Third-body screening is taken to provide a bridge between the Brooks-Herring and Conwell-Weisskopf formulae, and its effect on neutral impurity scattering is examined for both Erginsoy and Sclar cross sections. The relationship between scattering and the depth of a bound state is exhibited using quantum-defect wavefunctions. Resonance scattering, if the resonance is sharp, has only a weak effect on the mobility, but a large effect on rH, the ratio of Hall and drift mobilities. The latter reaches the magnitude 3.7 for sharp resonance. The ratio rHis therefore a sensitive detector of resonance scattering.