Globally Optimal Band Structure for Thermoelectrics in Realistic Systems

Observation is made that a linear dispersion in any dimension under acoustic-phonon-deformation-potential scattering theoretically prescribes a constant charge transport distribution, required for the boxcar profile known to maximize the thermoelectric figure of merit. A linear dispersion squeezed by two transport gaps under scattering by phonon deformation then theoretically constitutes a globally optimal qualitative band structure that may arise in realistic materials. Optimum bandwidth and electron velocity are also determined under deformation-potential scattering in three dimensions. The prescriptions lead to constant zT for all temperatures for a given value of lattice thermal conductivity, in agreement with purely analytic results from a boxcar transport distribution. This indicates that for a truly optimal band structure, the electronic part of the performance is temperature-independent, and the temperature-dependence of zT owes solely to that of lattice thermal conductivity.