Theory of materials for thermoelectric and thermomagnetic devices

The relation between the thermoelectric figure of merit Z and the basic properties of the material such as carrier mobilities, band structure, thermal conductivity and minority carrier lifetime is discussed. For isotropic materials with parabolic bands it is shown that the figure of merit based on the Seebeck coefficient will increase when a magnetic field is applied, if acoustic-mode scattering is predominant. If optical-mode scattering is predominant, the figure of merit will increase if ZT>0.77. Materials for devices based upon the Nernst or Ettingshausen effects will have large figures of merit only if 1) (m^*)^3/2µ/κL is large, 2) the energy gap is less than kT, and 3) the electron and hole mobilities are similar. Materials requirements for Nernst- and Seebeck-type devices are compared.