First-principles analysis of intravalley and intervalley electron-phonon scattering in thermoelectric materials

Intervalley collisions, which scatter electrons from one valley or band to another, can be detrimental to thermoelectric performance in materials with multiple valleys/bands. In this study, density functional theory is used to investigate the electron-phonon scattering characteristics of three lead chalcogenides (PbS, PbSe, PbTe) and three half-Heuslers (ScNiBi, ScPdSb, ZrNiSn), which all possess multiple equivalent conduction valleys, in order to characterize and analyze their intravalley/intervalley components. To elucidate what controls the degree of intravalley and intervalley transitions, the scattering rates are decomposed into the product of the phase space (a measure of how much scattering is possible) and the average electron-phonon coupling. To help guide the search for improved thermoelectric and high-conductivity materials, simple and approximate approaches are demonstrated that can be adopted to identify materials with reduced intervalley scattering, which circumvent the need for computationally demanding electron-phonon scattering calculations. In addition, the benefits of selecting materials with large-energy zone-edge phonons are explored in the limit $\ensuremath{\hbar}\ensuremath{\omega}$ $\ensuremath{\gg}$ ${k}_{B}T$, and found to potentially suppress intervalley processes by up to an order of magnitude, leading to a 70% and 100% increase in conductivity and power factor, respectively.