THEORY OF THE THERMOELECTRIC-POWER OR SEEBECK COEFFICIENT - THE CASE OF PHONON-SCATTERING FOR A DEGENERATE FREE-ELECTRON GAS

In order to illustrate the flexibility of the variational solution of the Boltzmann equation for transport coefficients, and in particular f or the thermoelectric power of solids, we use a simple model of free e lectrons and consider their scattering from a spherical Fermi surface by acoustic phonons alone, without any mass enhancement effect or umkl app process. We recall the variational method, pointing out that forma l constraints exist; we take two trial functions only, and we calculat e the Seebeck effect in such a framework. The low-temperature behavior of this effect is known to be very complicated. Sign reversals occur which cannot be explained by a model based upon free or nearly free el ectrons. As shown hereby, when the inelasticity of the scattering of q uasifree electrons by phonons is taken into account, nontrivial behavi or in the intermediate (but still low) temperature range can be found. The Appendixes contain analytical expressions.