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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIP Publishing LLC
2015-04-01
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| Series: | APL Materials |
| Online Access: | http://dx.doi.org/10.1063/1.4908244 |
| _version_ | 1811289066677731328 |
|---|---|
| author | Hyun-Sik Kim Zachary M. Gibbs Yinglu Tang Heng Wang G. Jeffrey Snyder |
| author_facet | Hyun-Sik Kim Zachary M. Gibbs Yinglu Tang Heng Wang G. Jeffrey Snyder |
| author_sort | Hyun-Sik Kim |
| collection | DOAJ |
| description | 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:
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,
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. |
| first_indexed | 2024-04-13T03:48:23Z |
| format | Article |
| id | doaj.art-d206f2f5acd9498f895aaa79b912a2e3 |
| institution | Directory Open Access Journal |
| issn | 2166-532X |
| language | English |
| last_indexed | 2024-04-13T03:48:23Z |
| publishDate | 2015-04-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | APL Materials |
| spelling | doaj.art-d206f2f5acd9498f895aaa79b912a2e32022-12-22T03:03:55ZengAIP Publishing LLCAPL Materials2166-532X2015-04-0134041506041506-510.1063/1.4908244007591APMCharacterization of Lorenz number with Seebeck coefficient measurementHyun-Sik Kim0Zachary M. Gibbs1Yinglu Tang2Heng Wang3G. Jeffrey Snyder4Department of Materials Science, California Institute of Technology, Pasadena, California 91125, USADivision of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USADepartment of Materials Science, California Institute of Technology, Pasadena, California 91125, USADepartment of Materials Science, California Institute of Technology, Pasadena, California 91125, USADepartment of Materials Science, California Institute of Technology, Pasadena, California 91125, USAIn 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: 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, 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.http://dx.doi.org/10.1063/1.4908244 |
| spellingShingle | Hyun-Sik Kim Zachary M. Gibbs Yinglu Tang Heng Wang G. Jeffrey Snyder Characterization of Lorenz number with Seebeck coefficient measurement APL Materials |
| title | Characterization of Lorenz number with Seebeck coefficient
measurement |
| title_full | Characterization of Lorenz number with Seebeck coefficient
measurement |
| title_fullStr | Characterization of Lorenz number with Seebeck coefficient
measurement |
| title_full_unstemmed | Characterization of Lorenz number with Seebeck coefficient
measurement |
| title_short | Characterization of Lorenz number with Seebeck coefficient
measurement |
| title_sort | characterization of lorenz number with seebeck coefficient measurement |
| url | http://dx.doi.org/10.1063/1.4908244 |
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