Criteria for Erroneous Substrate Contribution to the Thermoelectric Performance of Thin Films

Abstract

Thermoelectric materials have attracted considerable interest for energy applications such as waste-heat recovery and energy harvesting to power Internet-of-things sensors. In recent decades, an increasing number of different strategies to increase performance have been invented and tested, including the synthesis of thin films and other high-performance multilayered structures. Although it has already been shown that the pure combination of the properties of each layer without interactions will yield worse performance compared to the best layer, a critical estimation of the size of the deviation to trace back individual properties is still missing. In this paper we derive a set of formulas to describe the total Seebeck coefficient, electrical and thermal conductivity, power factor, and $zT$ value of a two-layer system from a simple model and elucidate the origin and size of the contribution of each layer to the total thermoelectric performance. We further show that the influence of the substrate can lead to large deviation between the measured and the film's properties, advising caution when analyzing such systems. Moreover, this model allows one to ensure that the contribution of the substrate is below a desired threshold by introducing material-related quantities ${\ensuremath{\epsilon}}_{\ensuremath{\sigma}}$ and ${\ensuremath{\epsilon}}_{\ensuremath{\lambda}}$.