The Theory of Electronic Conduction in Polar Semi-Conductors

The Boltzmann equation is set up for the conduction electrons in a crystal in which the scattering is due to the polarization waves of the lattice, and it is pointed out that at low temperatures it is impossible to define a unique time of relaxation for the scattering process. The Boltzmann equation is solved by means of a variational method, and exact expressions for the electrical conductivity and the thermo-electric power are obtained in the form of ratios of infinite determinants. By approximating to the exact solutions, relatively simple expressions are derived which are used to discuss the dependence of the conduction phenomena upon the temperature and upon the degree of degeneracy of the electron gas.