Speaker
Description
Achieving high thermoelectric performance requires reconciling the competing dependences of the Seebeck coefficient, electrical conductivity, and thermal conductivity that together determine the figure of merit ZT. Our work develops a unified analytical framework that combines polylogarithmic representations of Fermi–Dirac statistics with multibranch formulations of the Lambert W function to model these interdependent transport coefficients more rigorously. By extending classical transport theory to include energy-dependent scattering and realistic quantum-statistical carrier distributions, we obtain closed-form expressions for electrical conductivity, Seebeck coefficient, Lorenz number, and electronic thermal conductivity. A key result is an analytic inversion of the reduced chemical potential ϕ, enabling direct extraction of carrier concentration and degeneracy regime from experimentally measurable quantities. This analytic structure avoids the iterative numerical inversion typically required in transport modelling, allowing transparent parameter dependence and clearer physical interpretation.
Our framework facilitates extremum analyses for power factor and ZT, identifying the carrier densities, scattering parameters, and temperature windows that optimize thermoelectric performance across different material classes. The resulting equations highlight how quantum effects, band curvature, and scattering asymmetry shape the interplay between transport coefficients, and provide scalable criteria for materials design beyond numerical fitting alone. In particular, the derived extremum relations reveal universal behaviours that persist across semiconductor families, offering guidance for both bulk and nanostructured thermoelectrics.
By integrating polylogarithmic methods with the multivalued structure of the Lambert W function, this work establishes a generalizable modelling approach for evaluating and optimizing thermoelectric behaviour in emerging quantum and low-dimensional materials. The resulting closed-form relations offer a pathway toward predictive transport modelling and inform strategies for enhancing sustainable energy harvesting and waste-heat recovery technologies.
| Keyword-1 | Thermoelectric Figure of Merit |
|---|---|
| Keyword-2 | Lambert W Function |
| Keyword-3 | Analytical Modelling |