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 electronic component of the thermal conductivity (κE) and in turn κL from κL = ∼ κTotal − LσT. The Wiedemann-Franz law, κE = LσT, where L is Lorenz number, is widely used to estimate κE 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−|S|116 (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, Si0.8Ge0.2 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.

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CoSb3-based filled skutterudite has emerged as one of the most viable candidates for thermoelectric applications in automotive industry. However, the scale-up commercialization of such materials is still a challenge due to the scarcity and cost of constituent elements. Here we study Ce, the most earth abundant and low-cost rare earth element as a single-filling element and demonstrate that, by solubility design using a phase diagram approach, the filling fraction limit (FFL) x in CexCo4Sb12 can be increased more than twice the amount reported previously (x=0.09). This ultra-high FFL (x=0.20) enables the optimization of carrier concentration such that no additional filling elements are needed to produce a state of the art n-type skutterudite material with a zT value of 1.3 at 850 K before nano-structuring. The earth abundance and low cost of Ce would potentially facilitate a widespread application of skutterudites.