Eur. Phys. J. Plus (2016) 131: 76
https://doi.org/10.1140/epjp/i2016-16076-8

Regular Article

A note on the electrochemical nature of the thermoelectric power

¹ Lycée Jacques Prévert, F-27500, Pont-Audemer, France
² Russian Quantum Center, 100 Novaya Street, Skolkovo, 143025, Moscow region, Russian Federation
³ UFR Langues Vivantes Etrangères, Université de Caen Normandie, Esplanade de la Paix, 14032, Caen, France
⁴ Laboratoire Interdisciplinaire des Energies de Demain (LIED), UMR 8236 Université Paris Diderot, CNRS, 5 Rue Thomas Mann, 75013, Paris, France
⁵ Institut d’Electronique Fondamentale, Université Paris-Sud, CNRS, UMR 8622, F-91405, Orsay, France

Received: 16 November 2015
Accepted: 5 March 2016
Published online: 4 April 2016

Abstract

While thermoelectric transport theory is well established and widely applied, it is not always clear in the literature whether the Seebeck coefficient, which is a measure of the strength of the mutual interaction between electric charge transport and heat transport, is to be related to the gradient of the system’s chemical potential or to the gradient of its electrochemical potential. The present article aims to clarify the thermodynamic definition of the thermoelectric coupling. First, we recall how the Seebeck coefficient is experimentally determined. We then turn to the analysis of the relationship between the thermoelectric power and the relevant potentials in the thermoelectric system: As the definitions of the chemical and electrochemical potentials are clarified, we show that, with a proper consideration of each potential, one may derive the Seebeck coefficient of a non-degenerate semiconductor without the need to introduce a contact potential as seen sometimes in the literature. Furthermore, we demonstrate that the phenomenological expression of the electrical current resulting from thermoelectric effects may be directly obtained from the drift-diffusion equation.