  We theoretically investigate the thermoelectric properties of semiconducting (gapped) materials by varying the degrees of polynomials in their energy dispersion relations, in which either the valence or conduction energy dispersion depends on the wave vector raised to the power of two, four, and six. The thermoelectric transport coefficients such as the Seebeck coefficient, electrical conductivity, and thermal conductivity are calculated within the linearized Boltzmann transport theory combined with the relaxation time approximation. We consider various effects such as band gaps, dimensionalities, and dispersion powers to understand the conditions that can give the optimal thermoelectric efficiency or figure of merit ($ZT$). Our calculations show that the so-called pudding-mold band structure produces larger electrical and thermal conductivities than the parabolic band, but no significant difference is found in the Seebeck coefficients of the pudding-mold and parabolic bands. Furthermore, we find that a high $ZT$ can be obtained by tuning the band gap of the material to an optimum value simultaneously with breaking the band symmetry. The largest $ZT$ is found in a combination of two-contrasting polynomial powers in the dispersion relations of valence and conduction bands. This band asymmetry also shifts the charge neutrality away from the undoped level and allows optimal $ZT$ to be located at a smaller chemical potential. With some reasonable values of thermal conductivity parameters, the maximum $ZT$ for the bulk systems can be larger than 1, while for one-dimensional systems it can even reach almost 4. We expect this work to trigger high-throughput calculations for screening of potential thermoelectric materials combining various polynomial powers in the energy dispersion relations of semiconductors. 
Thermoelectric properties of semiconducting materials with parabolic and   pudding-mold band structures