February 18, 2015 | Hyun-Sik Kim; Zachary M. Gibbs; Yinglu Tang; Heng Wang; G. Jeffrey Snyder
This paper presents a method to characterize the Lorenz number (L) using the Seebeck coefficient (S) measurement. The Lorenz number is a key parameter in thermoelectric materials, used to estimate the electronic thermal conductivity (κ_E) via the Wiedemann-Franz law: κ_E = LσT, where σ is the electrical conductivity and T is the temperature. Traditionally, L is assumed to be a constant (2.44 × 10⁻⁸ WΩK⁻²) in the degenerate limit, but this can lead to inaccuracies in non-degenerate semiconductors where L converges to 1.5 × 10⁻⁸ WΩK⁻² due to acoustic phonon scattering.
The authors propose a new equation for L: L = 1.5 + exp[-|S|/116], where S is the Seebeck coefficient in μV/K. This equation provides a satisfactory approximation for L, with accuracy within 5% for single parabolic band materials and within 20% for more complex materials like PbSe, PbS, PbTe, and Si₀.₈Ge₀.₂. This equation allows for a first-order correction to the degenerate limit of L based on measured thermopower, independent of temperature or doping.
The proposed equation is validated using experimental data from various thermoelectric materials, including PbTe, Zintl materials, and Half Heusler materials. The results show that the equation provides more accurate estimates of L than the degenerate limit, especially for materials with high thermopower. The equation is also shown to be effective in cases where the band structure and scattering mechanisms differ from the SPB-APS model.
The paper highlights the importance of accurately determining L for improving the estimation of lattice thermal conductivity (κ_L), which is crucial for enhancing the figure of merit (zT) of thermoelectric materials. The proposed equation simplifies the estimation of L without requiring complex numerical solutions, making it a practical tool for thermoelectric material characterization. The study also discusses the limitations of the SPB-APS model and the impact of alternative scattering mechanisms on the Lorenz number. Overall, the proposed equation provides a more accurate and practical approach to estimating the Lorenz number using the Seebeck coefficient measurement.This paper presents a method to characterize the Lorenz number (L) using the Seebeck coefficient (S) measurement. The Lorenz number is a key parameter in thermoelectric materials, used to estimate the electronic thermal conductivity (κ_E) via the Wiedemann-Franz law: κ_E = LσT, where σ is the electrical conductivity and T is the temperature. Traditionally, L is assumed to be a constant (2.44 × 10⁻⁸ WΩK⁻²) in the degenerate limit, but this can lead to inaccuracies in non-degenerate semiconductors where L converges to 1.5 × 10⁻⁸ WΩK⁻² due to acoustic phonon scattering.
The authors propose a new equation for L: L = 1.5 + exp[-|S|/116], where S is the Seebeck coefficient in μV/K. This equation provides a satisfactory approximation for L, with accuracy within 5% for single parabolic band materials and within 20% for more complex materials like PbSe, PbS, PbTe, and Si₀.₈Ge₀.₂. This equation allows for a first-order correction to the degenerate limit of L based on measured thermopower, independent of temperature or doping.
The proposed equation is validated using experimental data from various thermoelectric materials, including PbTe, Zintl materials, and Half Heusler materials. The results show that the equation provides more accurate estimates of L than the degenerate limit, especially for materials with high thermopower. The equation is also shown to be effective in cases where the band structure and scattering mechanisms differ from the SPB-APS model.
The paper highlights the importance of accurately determining L for improving the estimation of lattice thermal conductivity (κ_L), which is crucial for enhancing the figure of merit (zT) of thermoelectric materials. The proposed equation simplifies the estimation of L without requiring complex numerical solutions, making it a practical tool for thermoelectric material characterization. The study also discusses the limitations of the SPB-APS model and the impact of alternative scattering mechanisms on the Lorenz number. Overall, the proposed equation provides a more accurate and practical approach to estimating the Lorenz number using the Seebeck coefficient measurement.