Simplified approach to estimate Lorenz number using experimental Seebeck coefficient for non parabolic band

TL;DR

This paper introduces a simplified method to estimate the Lorenz number from the Seebeck coefficient for non-parabolic bands, improving accuracy over traditional models and aiding in better thermal conductivity analysis in thermoelectric materials.

Contribution

A new, simpler equation is proposed to estimate the Lorenz number directly from experimental data for non-parabolic bands, reducing computational complexity and increasing accuracy.

Findings

The new equation provides accurate Lorenz number estimates.

It nearly eliminates the need for complex Fermi integral calculations.

The method improves thermal conductivity analysis in thermoelectric research.

Abstract

Reduction of lattice thermal conductivity ($\kappa_L$) is one of the most effective ways of improving thermoelectric properties. However extraction of $\kappa_L$ from the total measured thermal conductivity can be misleading if Lorenz ($L$) number is not estimated correctly. The $\kappa_L$ is obtained using Wiedemann-Franz law which estimates electronic part of thermal conductivity $\kappa_e$ = $L$$\sigma$T where, $\sigma$ and T are electrical conductivity and temperature. The $\kappa_L$ is then estimated as $\kappa_L$ = $\kappa_T$ - $L$$\sigma$T. For the metallic system the Lorenz number has universal value of 2.44 $\times$ 10$^{-8}$ W$\Omega$K$^{-2}$ (degenerate limit), but for no-degenerate semiconductors, the value can deviate significantly for acoustic phonon scattering, the most common scattering mechanism for thermoelectric above room temperatures. Up till now, $L$ is estimated by solving a series of equation derived form Boltzmann transport equations. For the single parabolic band (SPB) an equation was proposed to estimate $L$ directly from the experimental Seebeck coefficient. However using SPB model will lead to overestimation of $L$ in case of low band gap semiconductors which result in underestimation of $\kappa_L$ sometimes even negative $\kappa_L$. In this letter we propose a simpler equation to estimate $L$ for a non parabolic band. Experimental Seebeck coefficient, band gap($E_g$), and Temperature ($T$) are the main inputs in the equation which nearly eliminates the need of solving multiple Fermi integrals besides giving accurate values of $L$.