Inelastic-phonon-scattering effect on the behavior of the thermoelectric power of metals

The thermoelectric power (TEP) or Seebeck coefficient is calculated along the lines of Ziman variational method taking into account explicitly the inelastic scattering of electrons or holes (occupying a single parabolic band) by the (acoustic) phonon spectrum. The metallic limit is used to show the relative signs of terms appearing in the TEP expression. It is undoubtedly and quantitatively indicated that inelastic scattering can account for the usual bump seen in TEP vs temperature data at moderate temperatures. Also, TEP does not have a uniform sign even for electronic conduction in a single band. The low-temperature expansion is also given.