Theory of Transport Effects in Semiconductors: Thermoelectricity

The phenomenological theory of the thermoelectric effects in a cubic or isotropic electronic conductor is developed. It is shown that, as a consequence of the appropriate Onsager relation, the "gauge" adopted here for the thermoelectric coefficients of a single substance is such that the second Kelvin relation takes a specially simple form for a single substance. The general formulas obtained are applied to the theory of thermoelectricity in a two-band semiconductor, and the formulas for the thermoelectric power stated in a previous paper are derived. The Onsager principle leads to a general relation between two phenomenological transport parameters for a single carrier band, one ($\gamma$) measuring the ratio of thermodiffusion coefficient to drift mobility, the other ($\delta$) specifying the thermal energy transported with the current due to an electric field. The modification of these results needed to take account of the variation of band-edge energies with temperature is discussed. The evaluation of thermoelectric data for mixed semiconductors, on the basis of the present results, is discussed: some experimental data for germanium are analyzed from the point of view arrived at. The effect of a strong magnetic field, and the effect of strain, on the thermoelectric power are treated. It is pointed out that shear strain should change the activation energy for an impurity binding a carrier in a "many-valley" band, by decoupling the orbitals associated with different valleys and interacting through the chemical shift effect, and that this change should, among other consequences, appreciably change the thermoelectric power at very low temperatures. Exact formulas for this decoupling effect are obtained for donors in germanium.