Seebeck Coefficient in Nonparabolic Bulk Materials

We address a simplified formulation of the Seebeck coefficient (S) in degenerate bulk III–V and skutterudite materials within the framework of the k·p formalism, the conduction-band electrons of which obey Kane’s second-order energy dispersion relation. Incorporation of longitudinal acoustic phonon, screened ionized impurity, and polar optical phonon scatterings explains the origin of the experimentally determined change of sign of S in a skutterudite material such as CoSb3. The use of an overlap function due to band nonparabolicity significantly affects the carrier relaxation time when compared with the corresponding parabolic energy dispersion relation. The well-known expression of S for nondegenerate wide-band-gap materials is obtained as a special case, and this compatibility is an indirect test of the generalized theoretical analysis. The present model of S also agrees well with the available experimental data on such materials over a wide range of temperatures and can be carried forward for accurate analysis of the thermoelectric figure of merit.