# An Analytic Study of the Wiedemann-Franz Law and the Thermoelectric Figure of Merit

## TL;DR

This paper generalizes the Wiedemann-Franz law to optimize thermoelectric efficiency by calculating exact Fermi-Dirac integrals, considering both electronic and phononic thermal conductivities, and analyzing parameter dependencies.

## Contribution

It introduces a method to optimize the thermoelectric figure of merit ZT by generalizing the Wiedemann-Franz law using exact Fermi-Dirac integrals and includes comprehensive thermal conductivity analysis.

## Key findings

- Generalized Wiedemann-Franz law for ZT optimization
- Insight into parameter space and complex solutions
- Impact of scattering parameter r and chemical potential

## Abstract

Advances in optimizing thermoelectric material efficiency have seen a parallel activity in theoretical and computational advances. In the current work, it is shown that the calculation of exact Fermi-Dirac integrals enables the generalization of the Wiedemann-Franz law (WF) to optimize the dimensionless thermoelectric figure of merit ZT. This is done by optimizing the Seebeck coefficient, the electrical conductivity and the thermal conductivity. In the calculation of the thermal conductivity, both electronic and phononic contributions are included. The solutions provide insight into the relevant parameter space including the physical significance of complex solutions and their dependence on the scattering parameter r and the reduced chemical potential.