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 WiedemannFranz 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 nondegenerate 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 »
 Authors:
 California Institute of Technology, Pasadena, CA (United States); Samsung Advanced Institute of Technology, Samsung Electronics, Suwon (South Korea)
 California Institute of Technology, Pasadena, CA (United States)
 Publication Date:
 Research Org.:
 USDOE Energy Frontier Research Center, SolidState SolarThermal Energy Conversion Center (S3TEC), Washington, DC (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 OSTI Identifier:
 1179639
 Alternate Identifier(s):
 OSTI ID: 1188807; OSTI ID: 1421206
 Grant/Contract Number:
 SC0001299; AC0205CH11231
 Resource Type:
 Journal Article: Published Article
 Journal Name:
 APL Materials
 Additional Journal Information:
 Journal Volume: 3; Journal Issue: 4; Journal ID: ISSN 2166532X
 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. 2015.
"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 WiedemannFranz 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 nondegenerate 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 nonparabolic 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 [S116]},
doi = {10.1063/1.4908244},
journal = {APL Materials},
number = 4,
volume = 3,
place = {United States},
year = 2015,
month = 4
}
Web of Science

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 WiedemannFranz 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 (approximatelymore » 
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 WiedemannFranz 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 limitmore »Cited by 149