# 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 »

- 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, 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}

}

*Citation information provided by*

Web of Science

Web of Science