On the best bandstructure for thermoelectric performance: A Landauer perspective

The question of what bandstructure produces the best thermoelectric device performance is revisited from a Landauer perspective. We find that a delta-function transport distribution function (TDF) results in operation at the Mahan-Sofo upper limit for the thermoelectric figure-of-merit, ZT. We show, however, the Mahan-Sofo upper limit itself depends on the bandwidth (BW) of the dispersion, and therefore, a finite BW dispersion produces a higher ZT when the lattice thermal conductivity is finite. Including a realistic model for scattering profoundly changes the results. Instead of a narrow band, we find that a broad BW is best. The prospects of increasing ZT through high valley degeneracy or by distorting the density-of-states are discussed from a Landauer perspective. We conclude that while there is no simple answer to the question of what bandstructure produces the best thermoelectric performance, the important considerations can be expressed in terms of three parameters derived from the bandstructure—the density-of-states, $D(E)$⁠, the number of channels, $M(E)$⁠, and the mean-free-path, $λ(E)$⁠.