Theory of phonon drag thermopower

Abstract

The phonon contribution to the thermopower, S/sub p/, was first seen in germanium at low temperatures, and theoretically explained by Herring. Subsequently it was also predicted and identified in metals and alloys. In melts all phonons interact with the electron gas, and the theory is much simpler. In semiconductors only phonons of frequency below /spl omega//sub c/ can interact with electrons, where /spl omega//sub c//spl prop/T/sup 1/2 /. The magnitude of S/sub p/ depends on the relative strength of phonon scattering by electrons compared to either phonon-phonon or phonon-defect interactions. Phonon drag thermopower is important at low temperatures, but it can be appreciable also at higher temperatures, whenever the carrier concentration is large enough for the phonon-electron interaction to be strong below /spl omega//sub c/. This is the case in semiconductors used for energy conversion, where S/sub p/ can be comparable to k/e or 86 V/K, thus making a significant contribution to the figure of merit. To optimize that figure, one reduces the lattice thermal conductivity by point defects, which scatter high frequency phonons, while carrier scattering limits the contribution below /spl omega/c. Attempts have been made to scatter phonons of intermediate frequency by other imperfections. It is necessary to choose such imperfections carefully; if they scatter phonons below /spl omega//sub c/ strongly, the advantage of reducing the lattice thermal conductivity may be offset by a reduction in the thermopower.