Limits of thermoelectric performance with a bounded transport distribution

Band engineering is an important strategy that seeks to tailor a material’s electronic and scattering properties to improve its thermoelectric (TE) performance. This effectively alters the material’s transport distribution (TD), which is the central quantity that determines the electronic conductivity, Seebeck coefficient and electronic thermal conductivity. This work theoretically derives what is the optimal bounded TD and its implications on the limits of TE performance. To maximize the figure-of-merit ZT and the power factor the ideal transport distributions are boxcar and Heaviside functions, respectively – the edges of which must be located at specific energies. The optimal power factor is simply limited by the magnitude of the Heaviside TD, and reaches ZT values between 4-5. The optimal figure-of-merit, which can approach the Carnot limit, is uniquely determined by a key quantity that is proportional to the TD magnitude and temperature, and inversely proportional to the lattice thermal conductivity. These results suggest two general approaches to enhance TE performance: identify or design materials with TDs that have large magnitude and that possess the ideal boxcar or Heaviside shape. This study can help guide the search for improved TEs by establishing practical upper limits on performance, and by providing target TDs to guide band and scattering engineering strategies.



Acknowledgements: this research was supported by NSERC and the Digital Research Alliance of Canada.