Characterization of Lorenz number with Seebeck coefficient measurement
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[−_(|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, Si_(0.8) Ge _(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.
© 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. Received 31 December 2014; accepted 1 February 2015; published online 18 February 2015. The authors would like to acknowledge funding from The Materials Project: supported by Department of Energy's Basic Energy Sciences program under Grant No. EDCBEE, DOE Contract No. DE-AC02-05CH11231 and as part of the Solid-State Solar-Thermal Energy Conversion Center (S3TEC), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, and Basic Energy Sciences under Award No. DE-SC0001299.
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