Maximum thermomagnetic figure of merit of two-band, multivalley semiconductors

Abstract

The general equations are derived for the transport of electrical charge and energy in an anisotropic multiband, multi-energy-extremum semiconductor or semimetal. These are applied to compute the transverse thermomagnetic figure of merit for two-band (one conduction plus one valence band) material. The dimensionless adiabatic thermomagnetic figure of merit, Z t a T, approaches a maximum value of about 10–20β y for an intrinsic semimetal with about a 0–5 kT overlap of the conduction and valence band as the magnetic-field strength increases indefinitely. The quantity β y is a generalized Chasmar and Stratton type of dimensionless material parameter that is a function of the density-of-states masses of electrons and holes, the lattice thermal conductivity, the partial mobilities associated with transport in the principal directions of the constant-energy ellipsoids in the neighborhoods of the various band extrema in wave-number vector space, and the orientations of the principal axes of the various ellipsoids with respect to the rectangular coordinate system corresponding to the case of mutually orthogonal magnetic field, electric current and temperature-gradient directions. Criteria for improved thermomagnetic materials are discussed.