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Title: Characterization of Lorenz number with Seebeck coefficient measurement

Abstract

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: (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 assumptionmore » 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]« less

Authors:
ORCiD logo [1];  [2];  [2];  [2];  [2]
  1. California Institute of Technology, Pasadena, CA (United States); Samsung Advanced Institute of Technology, Samsung Electronics, Suwon (South Korea)
  2. California Institute of Technology, Pasadena, CA (United States)
Publication Date:
Research Org.:
USDOE Energy Frontier Research Center, Solid-State Solar-Thermal Energy Conversion Center (S3TEC), Washington, DC (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1179639
Alternate Identifier(s):
OSTI ID: 1188807; OSTI ID: 1421206
Grant/Contract Number:
SC0001299; AC02-05CH11231
Resource Type:
Journal Article: Published Article
Journal Name:
APL Materials
Additional Journal Information:
Journal Volume: 3; Journal Issue: 4; Journal ID: ISSN 2166-532X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE

Citation Formats

Kim, Hyun -Sik, Gibbs, Zachary M., Tang, Yinglu, Wang, Heng, and Snyder, G. Jeffrey. Characterization of Lorenz number with Seebeck coefficient measurement. United States: N. p., 2015. Web. doi:10.1063/1.4908244.
Kim, Hyun -Sik, Gibbs, Zachary M., Tang, Yinglu, Wang, Heng, & Snyder, G. Jeffrey. Characterization of Lorenz number with Seebeck coefficient measurement. United States. doi:10.1063/1.4908244.
Kim, Hyun -Sik, Gibbs, Zachary M., Tang, Yinglu, Wang, Heng, and Snyder, G. Jeffrey. Wed . "Characterization of Lorenz number with Seebeck coefficient measurement". United States. doi:10.1063/1.4908244.
@article{osti_1179639,
title = {Characterization of Lorenz number with Seebeck coefficient measurement},
author = {Kim, Hyun -Sik and Gibbs, Zachary M. and Tang, Yinglu and Wang, Heng and Snyder, G. Jeffrey},
abstractNote = {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]},
doi = {10.1063/1.4908244},
journal = {APL Materials},
number = 4,
volume = 3,
place = {United States},
year = {Wed Apr 01 00:00:00 EDT 2015},
month = {Wed Apr 01 00:00:00 EDT 2015}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1063/1.4908244

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Cited by: 149 works
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