Analysis of simple scattering models on the thermoelectric performance of analytical electron dispersions

Abstract

Recent first-principles electron-phonon scattering calculations of heavily doped semiconductors suggest that a simple DOS scattering model, wherein the electronic scattering rates are assumed to be proportional to the density-of-states, better approximates the rigorous scattering characteristics compared to the commonly used constant relaxation-time and constant mean-free-path approximations. This work investigates how the thermoelectric properties predicted with the DOS model compare to the other two scattering models, using three analytical electron dispersions (parabolic band in 3D/2D/1D, Kane band in 3D/2D/1D, and ring-shaped quartic band in 2D). Our findings show that the scattering models can lead to significant differences and can disagree about whether certain band structures can provide benefits. A constant relaxation-time is found to be always optimistic compared to a constant mean-free-path, while the DOS scattering model shows no such clear trend. Notably, the 1D parabolic band and 2D quartic band exhibit the highest power factors with the DOS model, resulting from a rapid decrease in density-of-states, and thus scattering - suggesting a possible strategy for improved thermoelectrics based on engineering band structures with sharp/discontinuous drops in density-of-states. The DOS scattering approximation also suggests that searches for materials with a delta function-like DOS (as a proxy to the transport distribution) or converged bands may yield limited benefits, due to the increase in scattering. This work highlights the importance of simple and accurate scattering models when rigorous ab initio scattering calculations are not feasible.