Electron-Electron Scattering and Transport Phenomena in Nonpolar Semiconductors

Abstract

The effect of electron-electron scattering processes due to Coulomb forces on the transport phenomena in nonpolar isotropic solids is treated in the framework of Kohler's variation principle. By considering the conduction electrons as a Fermi-Dirac gas of noninteracting free quasi-particles, each with charge $\ensuremath{-}e$ and mass ${m}^{*}$, electron-electron scattering is taken into account as a small perturbation, as is electron-phonon scattering in nonpolar solids. A shielded Coulomb potential which depends on two parameters---the effective dielectric constant and the shielding constant---is used as the interaction potential. These two parameters, for small concentrations of electrons, may be assumed to be independent of the distance between two electrons during a scattering process.A general qualitative result is that electron-electron scattering causes the electrical conductivity to be reduced less than the electronic heat conductivity. The conductivities and the Wiedemann-Franz ratio will be reduced by an amount determined by the energy dependence of that perturbation of the electron distribution which is induced by primary scattering sources such as electron-phonon scattering or electron-impurity scattering. Quantitative results for nondegenerate semiconductors are obtained in terms of the variational method. With electron-phonon and electron-ion scattering assumed in turn as the primary scattering mechanism, the influence of electron-electron scattering on the electrical conductivity, the heat conductivity, and the Seebeck coefficient is calculated as function of temperature. The results are discussed with respect to the experimental situation.The effect of electron-electron scattering on transport phenomena in metals is briefly considered. The applicability of the results obtained for isotropic semiconductors to an important class of anisotropic semiconductors is shown.