Theoretical study of thermoelectric conversion from the diffusive to ballistic transport regime

Thermoelectric (TE) materials enable the interconversion of electronic and thermal energy, driving applications in power generation and solid-state cooling. The performance of TE devices depends sensitively upon the interplay between the electron and phonon properties. When the size of the TE semiconductor is shrunk to the nanoscale, on a length scale below the mean-free-path, the electron and phonon transport characteristics can deviate significantly from familiar diffusive behavior. In particular, ballistic conduction effects and deviations from classical Joule heating will arise. In this study, we theoretically explore how such non-diffusive phenomena can impact TE conversion efficiency by continuously varying the material length from the diffusive to the near-ballistic transport regime. In our model, the electrons are treated within the McKelvey-Shockley flux method, which captures nonequilibrium and ballistic effects, and the diffusive phonons are described by the heat equation and Fourier's law. This coupled electro-thermal framework is solved iteratively until self-consistency is achieved. Our findings illustrate how TE conversion on the nanoscale can deviate from the traditional bulk TE expressions and potentially lead to higher efficiencies.