Sensitivity of Thermoelectric Properties from the EPA Method and Its Variants on Variations in Phonon Frequencies

Abstract

The electron–phonon coupling phenomenon is an important scattering source of charge carriers in thermoelectric materials. As the result, consideration of the scattering mechanism due to electron–phonon coupling is an essential part of the first-principles prediction methods for thermoelectric properties of materials, i.e., the Seebeck coefficient and electrical conductivity. However, a direct, high-resolution treatment of electron–phonon coupling in a realistic situation is too expensive for practical purposes, and approximation methods have been developed for the phenomena at a reasonable level of computational cost. The electron–phonon averaged (EPA) method and its variants have been recently introduced as such approximation methods. These methods comprise two major approximations. First, the electron–phonon coupling matrix elements, which are explicitly dependent on the momentum of charge carriers and that of scattering phonons, are approximated as a function of two energies only, i.e., the energy of the incoming charge carrier before scattering and that of the outgoing charge carrier after scattering. Second, the phonon frequencies in the formula of scattering rate are replaced with their averages in the Brillouin zone. Although these methods have achieved remarkable successes in predicting thermoelectric properties of materials, uncertainty introduced by these approximations and sensitivity of the results to variations of input parameters in these approximations have not been assessed completely. In this study, the uncertainty and sensitivity of thermoelectric properties, predicted with the EPA method and its variants, on variations in phonon frequencies are investigated. A thermoelectric p-type half-Heusler compound, HfCoSb, is used as an example. An empirical bootstrap method is employed to assess the impact of sampled phonon frequencies during the averaging process, whose results show that the impact of variations in phonon frequencies induces a minor but detectable change in predicted thermoelectric properties.