An analytic study of the Wiedemann–Franz law and the thermoelectric figure of merit

Abstract

Advances in optimizing thermoelectric material efficiency have seen parallel activities in theoretical and computational studies. In the current work, we calculate the exact Fermi–Dirac integrals to enable the generalization of the Wiedemann–Franz law (WF) in order to enhance the dimensionless thermoelectric figure of merit ZT = α2σ/k. This is done by optimizing the Seebeck coefficient α, the electrical conductivity σ, and the thermal conductivity κ in terms of the Lambert W, and the generalized Lambert W functions (offset log). In the calculation of the thermal conductivity κ, we include both electronic and phononic contributions. The solutions provide insight into the relevant parameter space including the physical significance of complex solutions and their dependance on the scattering parameter r and the reduced chemical potential μ*.