The relationship between the thermoelectric generator efficiency and the device engineering figure of merit Zd,eng. The maximum efficiency 𝜼max

Thermoelectric materials are used today in thermoelectric devices for heat to electricity(thermoelectric generators-TEG) or electricity to heat(heat pumps) conversion in a large range of applications. In the case of TEGs the final measure of their performance is given by a quantity named the maximum efficiency which shows how much from the heat input is converted into electrical power. Therefore it is of great interest to know correctly how much is the efficiency of a device to can make commercial assessments. The concept of engineering figure of merit, Zeng, and engineering power factor, Peng, were already introduced in the field to quantify the efficiency of a single material under temperature dependent thermoelectric properties, with the mention that the formulas derivation was limited to one leg of the thermoelectric generator. In this paper we propose to extend the concept of engineering figure of merit to a thermoelectric generator by introducing a more general concept of device engineering thermoelectric figure of merit, Zd,eng, which depends on the both TEG materials properties and which shall be the right quantity to be used when we are interested in the evaluation of the efficiency. Also, this work takes into account the electrical contact resistance between the electrodes and thermoelement legs in an attempt to quantify its influence upon the performance of a TEG. Finally, a new formula is proposed for the maximum efficiency of a TEG.