Searching for the best thermoelectrics through the optimization of transport distribution function

The thermoelectric performance of materials is dependent on the interplay or competition among three key components, the electrical conductivity, thermopower, and thermal conductivity, which can be written as integrals of a single function, the transport distribution function (TDF). Mahan and Sofo [Proc. Natl. Acad. Sci. USA 93, 7436 (1996)] found that, mathematically, the thermoelectric properties could be maximized by a delta-shaped transport distribution, which was associated with a narrow distribution of the energy of the electrons participating in the transport process. In this work, we revisited the shape effect of TDF on thermoelectric figure of merit. It is confirmed both heuristically and numerically that among all the normalized TDF the Dirac delta function leads to the largest thermoelectric figure of merit. Whereas, for the case of TDF being bounded, a rectangular-shape distribution is instead found to be the most favorable one, which could be achieved through nanoroute. Our results also indicate that high thermoelectric figure of merit is associated with appropriate violations of the Wiedemann−Franz law.