Grading studies for efficient thermoelectric devices using combined 1D material and device modeling

Abstract

The efficiency at which thermoelectric generators (TEGs) can convert heat into electrical energy is governed by the properties of the employed functional materials. For a given thermoelectric (TE) material, efficiency needs to be maximized by adjusting, e.g., the carrier concentration n. Usually, chemically homogeneous materials with a constant n along the leg are employed to fabricate TEG. However, for most TE materials, the optimum n has a pronounced temperature dependence, typically increasing toward the hot side of the leg. A local variation of n, either continuously (grading) or discontinuously (segmenting), thus has the potential to increase the efficiency of TEGs substantially. Predictions on efficiency gain are challenging, and an adequate physical model for the thermoelectric transport properties in the material as well as the device is required here. To address this challenge, we have combined a two-band model to describe the material properties with a device model based on the solution of the one-dimensional heat equation. Using Mg2Sn as an example, we have adjusted the n profile to maximize the thermoelectric figure of merit locally. We show that this would result in an increase in conversion efficiency by more than 7% for cold and hot side temperatures of 300 and 700 K, respectively. Using a thermoelectric self-compatibility criterion, we verify that the calculated n profile is indeed close to the best possible one. The presented methodology can be transferred to other material systems, and we show that it can also be used to calculate the effect of other, practically more feasible n profiles.