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.