101. An analytic study of the Wiedemann–Franz law and the thermoelectric figure of merit
- Author
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Sree Ram Valluri, Pranawa C. Deshmukh, Aakash Yadav, Ken Roberts, and Najeh Jisrawi
- Subjects
Physics ,Work (thermodynamics) ,Condensed matter physics ,General Physics and Astronomy ,02 engineering and technology ,Parameter space ,010402 general chemistry ,021001 nanoscience & nanotechnology ,Thermoelectric materials ,01 natural sciences ,0104 chemical sciences ,symbols.namesake ,Thermal conductivity ,Lambert W function ,Seebeck coefficient ,symbols ,0210 nano-technology ,Wiedemann–Franz law ,Dimensionless quantity - Abstract
Advances in optimizing thermoelectric material efficiency have seen parallel activities in theoretical and computational studies. In the current work, we calculate the exact Fermi–Dirac integrals to enable the generalization of the Wiedemann–Franz law (WF) in order to enhance the dimensionless thermoelectric figure of merit ZT = α 2 σ / κ . This is done by optimizing the Seebeck coefficient α, the electrical conductivity σ, and the thermal conductivity κ in terms of the Lambert W, and the generalized Lambert W functions (offset log). In the calculation of the thermal conductivity κ, we include both electronic and phononic contributions. The solutions provide insight into the relevant parameter space including the physical significance of complex solutions and their dependance on the scattering parameter r and the reduced chemical potential μ*.
- Published
- 2019
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