The Compatibility of Thin Films and Nanostructures in Thermoelectric Cooling Systems

The compatibility of low-dimensional thermoelectric materials in forms such as thin films and nanowires for use in thermoelectric coolers is examined. First-order thermoelectric theory predicts that the cold and hot junction temperatures of a thermoelectric circuit are governed solely by the nondimensional figure of merit, $ZT$⁠. Performance predictions based on this traditional theory have been more broadly applied to the performance of thermoelectric cooler systems, thereby implying that these coolers may be miniaturized without loss of performance and that system performance is dictated principally by $ZT$⁠. A nondimensional thermoelectric system model for a cooler is developed and typical performance metrics for thermoelectric coolers are presented along with predictions from traditional theory. Performance is examined as a function of thermoelectric element length for representative system conditions. This system study shows that cooler performance may drop significantly when miniaturized, particularly if the cooling elements are realized at the scale of many recently proposed thermoelectric thin films and nanostructured materials. The system theory illustrates that performance is governed by three nondimensional parameters: an effective thermoelectric figure of merit, $ZeTa$⁠, the relative ability for heat to be drawn into the cooler, and the relative ability for heat to be rejected from the cooler to the ambient environment. As cooler performance depends both on material properties $(ZeTa)$ as well as the relative scale of the materials with respect to system thermal conductances, the applicability of some low-dimensional forms of materials such as thermoelectric elements may require reevaluation. The realization of high performance coolers based on thermoelectric effects must rely on developing high quality materials realized at an appropriate, application-dependent scale.