Characterization of Lorenz number with Seebeck coefficient measurement

In analyzing zT improvements due to lattice thermal conductivity(κL) reduction, electrical conductivity(σ) and total thermal conductivity(κTotal) are often used to estimate the electroniccomponent of the thermalconductivity (κE) and in turnκL from κL = ∼κTotal − LσT. The Wiedemann-Franzlaw, κE = LσT, where Lis Lorenz number, is widely used to estimate κE fromσ measurements. It is a common practice to treatL as a universal factor with 2.44 × 10−8WΩK−2 (degenerate limit). However, significant deviations from thedegenerate limit (approximately 40% or more for Kane bands) are known to occur fornon-degenerate semiconductors where L converges to 1.5 ×10−8 WΩK−2 for acoustic phononscattering. The decrease in L is correlated withan increase in thermopower (absolute value of Seebeck coefficient(S)). Thus, a first order correction to the degenerate limit ofL can be based on the measured thermopower, |S|,independent of temperature or doping. We propose the equation:L=1.5+exp−|S|116(where L is in 10−8WΩK−2 and S in μV/K) as a satisfactory approximationfor L. This equation is accurate within 5% for single parabolic band/acousticphononscattering assumption and within 20% for PbSe, PbS, PbTe,Si0.8Ge0.2 where more complexity is introduced, such asnon-parabolic Kane bands, multiple bands, and/or alternate scatteringmechanisms. The use of this equation for L rather than a constant value(when detailed bandstructure and scattering mechanism is not known) willsignificantly improve the estimation of lattice thermal conductivity