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 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: (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. L = 1.5 + exp [-|S|116]
- Research Organization:
- California Institute of Technology (CalTech), Pasadena, CA (United States); USDOE Energy Frontier Research Center, Solid-State Solar-Thermal Energy Conversion Center (S3TEC), Washington, DC (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- Grant/Contract Number:
- AC02-05CH11231; SC0001299
- OSTI ID:
- 1179639
- Alternate ID(s):
- OSTI ID: 1188807; OSTI ID: 1421206
- Journal Information:
- APL Materials, Journal Name: APL Materials Vol. 3 Journal Issue: 4; ISSN 2166-532X
- Publisher:
- American Institute of PhysicsCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
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