In analyzing zT improvements due to lattice thermal conductivity (κ_L) reduction, electrical conductivity (σ) and total thermal conductivity (κ_Total) are often used to estimate the electronic component of the thermal conductivity (κ_E) and in turn κ_L from κ_L = ∼ κ_Total − LσT. The Wiedemann-Franz law, κ_E = LσT, where L is Lorenz number, is widely used to estimate κ_E from σ measurements. It is a common practice to treat L as a universal factor with 2.44 × 10⁻⁸ WΩK⁻² (degenerate limit). However, significant deviations from the degenerate limit (approximately 40% or more for Kane bands) are known to occur for non-degenerate semiconductors where L converges to 1.5 × 10⁻⁸ WΩK⁻² for acoustic phonon scattering. The decrease in L is correlated with an increase in thermopower (absolute value of Seebeck coefficient (S)). Thus, a first order correction to the degenerate limit of L can be based on the measured thermopower, |S|, independent of temperature or doping. We propose the equation: $L=1.5+exp\left[-\frac{\left|S\right|}{116}\right]$ (where L is in 10⁻⁸ WΩK⁻² and S in μV/K) as a satisfactory approximation for L. This equation is accurate within 5% for single parabolic band/acoustic phonon scattering assumption and within 20% for PbSe, PbS, PbTe, Si_0.8Ge_0.2 where more complexity is introduced, such as non-parabolic Kane bands, multiple bands, and/or alternate scattering mechanisms. The use of this equation for L rather than a constant value (when detailed band structure and scattering mechanism is not known) will significantly improve the estimation of lattice thermal conductivity.

In characterizing thermoelectric materials, electrical and thermal transport measurements are often used to estimate electronic band structure properties such as the effective mass and band gap. The Goldsmid-Sharp band gap, E_g = 2e|S|_maxT_max, is a tool widely employed to estimate the band gap from temperature dependent Seebeck coefficient measurements. However, significant deviations of more than a factor of two are now known to occur. We find that this is when either the majority-to-minority weighted mobility ratio (A) becomes very different from 1.0 or as the band gap (E_g) becomes significantly smaller than 10 k_BT. For narrow gaps (E_g ≲ 6 k_BT), the Maxwell-Boltzmann statistics applied by Goldsmid-Sharp break down and Fermi-Dirac statistics are required. We generate a chart that can be used to quickly estimate the expected correction to the Goldsmid-Sharp band gap depending on A and S_max; however, additional errors can occur for S < 150 μV/K due to degenerate behavior.

Thermal conductivities of polycrystalline thermoelectric materials are satisfactorily calculated by replacing the commonly used Casimir model (freqeuncy-independent) with grain boundary dislocation strain model (frequency-dependent) of Klemens. It is demonstrated that the grain boundaries are better described as a collection of dislocations rather than perfectly scattering interfaces.