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Modeling the Seebeck coefficient for organic materials with the Kubo–Greenwood integral and a Gaussian density of states

  • Jerry P. SelvaggiEmail author
Article
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Abstract

The Seebeck coefficient (SC) or thermopower of an organic material may be modeled by using an energy-dependent Gaussian density of states and an energy-dependent diffusivity. Once these have been formulated or parameterized from experimental evidence, the Kubo–Greenwood integral can then be employed in order to analytically evaluate the Seebeck coefficient. The main purpose is to show that a complete analytical formula for the Seebeck coefficient may be obtained for an organic material without recourse to any analytical approximations, asymptotic formulations, or numerical methods. The method developed in this article should not be used to supplant other methods, but to supplement them. In fact, the main advantage for having an analytical formula for the SC is for its use in parametric studies. In order to illustrate the analytical method developed in this article, the author has chosen, for simplicity, a constant diffusivity over the entire density of states energy range. However, it will be shown that this in no way limits the method.

Keywords

Density of states Organic materials Conductivity Diffusivity Seebeck coefficient Fermi-Dirac-type integral Kubo–Greenwood integral 

Notes

Acknowledgements

The author would like to express his thanks to Jerry A. Selvaggi for insightful discussions concerning Fermi–Dirac-type integrals. The author would also like to express his gratitude to Jessica Diaz for helpful comments on various ways to numerically integrate the integrals found in this article.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Rensselaer Polytechnic InstituteTroyUSA
  2. 2.SUNY New PaltzSchenectadyUSA

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