Electron energy filtering by a nonplanar potential to enhance the thermoelectric power factor in bulk materials

Abstract

We present a detailed theory on electron energy filtering by the nonplanar potential introduced by dispersed nanoparticles or impurities in bulk materials for enhancement of the thermoelectric power factor. When electrons with energies below a certain cut-off energy are prevented from participating in conduction through the material, the Seebeck coefficient and thus the thermoelectric power factor can be drastically enhanced. Instead of using planar heterostructures which require elaborate epitaxial techniques, we study embedded nanoparticles or impurities so that the conservation of lateral momentum limiting electron transport at heterointerfaces is no longer a limiting factor. Based on the Boltzmann transport equations under the relaxation time approximation, the optimal cut-off energy level that maximizes the power factor is calculated to be a few ${k}_{B}T$ above the Fermi level, and is a function of the scattering parameter, Fermi level, and temperature. The maximized power factor enhancement is quantified as a function of those parameters. The electronic thermal conductivity and Lorenz number are also shown to be suppressed by the electron filtering to further enhance the thermoelectric figure of merit. We find that the power factor of PbTe at 300 K could be enhanced by more than 120$%$ when the cut-off energy level is 0.2 eV or higher and the carrier density higher than $5\ifmmode\times\else\texttimes\fi{}{10}^{19}$ cm${}^{\ensuremath{-}3}$. Finally we propose the use of distributed resonant scatterings to partially realize the nonplanar electron filtering in bulk materials.