Electron-Electron Scattering and Transport Phenomena in Nonpolar Semiconductors

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 $-e$ 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.