Electron Transport at High Temperatures in the Presence of Impurities

We investigate the linear transport properties of electrons in a solid when both phonon and impurity scattering are important. The problem is treated for the case where Maxwellian statistics apply and the electrons are described by a classical distribution function in position and velocity, $f(\mathrm{r},\mathrm{v})$. This function satisfies a space-dependent equation in which the interaction with the impurities is treated as part of the Hamiltonian and the phonon scattering is described by a linear Boltzmann-type collision term. This equation is solved formally in the presence of a weak external electric field in a form convenient for perturbation expansions in the relative strength of the different scattering mechanisms, some of which are carried out explicitly. We also show rigorously that the change in conductivity due to the presence of impurities is negative.