Efficiency as a performance metric for material optimization in thermoelectric generators

The optimization of thermoelectric (TE) materials with respect to carrier concentration, chemical composition, microstructure, etc. is inevitable for maximizing the performance of thermoelectric devices. Theoretical performance prediction can speed up this process dramatically as the synthesis and experimental characterization of all relevant combinations is practically impossible. Conventionally, the dimensionless figure of merit (zT) is considered as a measure of TE energy conversion capability. However, zT could mislead the search for optimized materials as it is only an intermediate parameter. To resolve this issue, we combined a device performance calculation routine (one-dimensional continuum theory-based, with fully temperature dependent TE properties) with a band structure-based material model. As an example, a study was conducted on p-type Mg2Si1-xSnx solid solutions for which optimization of carrier concentration (n) and composition (x) is required. Here, according to previous findings, a single parabolic band (SPB) model was assumed, with an effective mass linearly dependent on composition and carrier concentration. It was found that for a cold-side temperature of 300 K and a hot-side temperature of 500 K (which is well within the validity limits of a SPB model), the optimum n for Mg2Si1-xSnx based on efficiency was found to be at 4.5 ×1019 cm-3, while based on zTmax it was found to be about 20% higher. Additionally, the usage of the temperature average of zT (zTTAv) for finding the optimum parameters is also analyzed. For p-Mg2(Si,Sn) zTTAv predicts the optimum composition and carrier concentration close to the exact efficiency calculation, despite the fact that the efficiency predicted by zTTAv can be quite off from exact efficiency. The usage of zTTAv was further tested for common TE material examples such as n-type Mg2Si1-xSnx and PbTe and a similar conclusion is obtained. Finally, the reason for this closeness and the importance of using exact efficiency plots is discusse