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The effect of interband electron-electron scattering (electron-hole scattering, light hole-heavy hole scattering, etc. ) on the electrical transport phenomena is studied with a variational method obtained by a generalization of Kohler's variation principle to a multiband conductor. To this end we make the following assumptions: (1) The electronic structure is given by parabolic conduction and valence bands, separated from each other by k₁T; the valence band may be twofold degenerate; (2) The average occupation numbers of electronic eigenstates are given by Fermi-Dirac statistics; (3) The dynamical interaction between charge carriers is described by a shielded Coulomb potential. Assuming nondegenerate semiconductors, we consider acoustical and optical phonon scattering and ion scattering, besides electron-electron scattering. Quantitative results are obtained for the electrical conductivity, the heat conductivity, and the Seebeck coefficient, including the ambipolar effect. The results can easily be applied to cases of physical interest; we discuss here hole-hole scattering and mobility of p germanium, intercarrier scattering and mobility of intrinsic germanium, transient conductivity of charge carriers in germanium produced by short pulses of high-energy electrons, intercarrier scattering and its influence on the heat conductivity, and the Wiedemann-Franz ratio of intrinsic semiconductors.
Joachim Appel (1962) studied this question.