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

Abstract

Reducing lattice thermal conductivity (κL) is one of the most effective ways for improving thermoelectric properties. However, the extraction of κL from the total measured thermal conductivity can be misleading if the Lorenz (L) number is not estimated correctly. κL is obtained using the Wiedemann–Franz law, which estimates the electronic part of thermal conductivity κe = L σT, where σ and T are electrical conductivity and temperature, respectively. κL is then estimated as κL = κT − L σT. For metallic systems, the Lorenz number has a universal value of 2.44 × 10 −8 WΩ K−2 (degenerate limit), but for non-degenerate semiconductors, the value can deviate significantly for acoustic phonon scattering, the most common scattering mechanism for thermoelectric materials above room temperature. Up until now, L is estimated by solving a series of equations derived from Boltzmann transport equations. For the single parabolic band (SPB) model, an equation was proposed to estimate L directly from the experimental Seebeck coefficient. However, using the SPB model will lead to an overestimation of L in the case of low bandgap semiconductors, which results in an underestimation of κL, sometimes even negative κL. In this article, we propose a simpler equation to estimate L for a non-parabolic band. The experimental Seebeck coefficient, bandgap (Eg), and temperature (T) are the main inputs to the equation, which nearly eliminates the need for solving multiple Fermi integrals besides giving accurate values of L.