Characterization of Lorenz number with Seebeck coefficient measurement
In analyzing zT improvements due to lattice thermal conductivity (κ{sub L}) reduction, electrical conductivity (σ) and total thermal conductivity (κ{sub Total}) are often used to estimate the electronic component of the thermal conductivity (κ{sub E}) and in turn κ{sub L} from κ{sub L} = ∼ κ{sub Total} − LσT. The Wiedemann-Franz law, κ{sub E} = LσT, where L is Lorenz number, is widely used to estimate κ{sub E} from σ measurements. It is a common practice to treat L as a universal factor with 2.44 × 10{sup −8} WΩK{sup −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{sup −8} WΩK{sup −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[−(|S|)/(116) ] (where L is in 10{sup −8} WΩK{sup −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{sub 0.8}Ge{sub 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.