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While thermoelectric transport theory is well established and widely applied,there remains some degree of confusion on the proper thermodynamic definitionof the Seebeck coefficient (or thermoelectric power) which is a measure of thestrength of the mutual interaction between electric charge transport and heattransport. Indeed, as one considers a thermoelectric system, it is not alwaysclear whether the Seebeck coefficient is to be related to the gradient of thesystem's chemical potential or to the gradient of its electrochemicalpotential. This pedagogical article aims to shed light on this confusion andclarify the thermodynamic definition of the thermoelectric coupling. First, werecall how the Seebeck coefficient is experimentally determined. We then turnto the analysis of the relationship between the thermoelectric power and therelevant potentials in the thermoelectric system: As the definitions of thechemical and electrochemical potentials are clarified, we show that, with aproper consideration of each potential, one may derive the Seebeck coefficientof a non-degenerate semiconductor without the need to introduce a contactpotential as seen sometimes in the literature. Furthermore, we demonstrate thatthe phenomenological expression of the electrical current resulting fromthermoelectric effects may be directly obtained from the drift-diffusionequation.

A note on the electrochemical nature of the thermoelectric power