Impact of the scattering physics on the power factor of complex thermoelectric materials

We assess the impact of the scattering physics assumptions on the thermoelectric properties of five Co-based p-type half-Heusler alloys by considering full energy-dependent scattering times vs the commonly employed constant scattering time. For this, we employ density functional theory band structures and a full numerical scheme that uses Fermi's golden rule to extract the momentum relaxation times of each state at every energy, momentum, and band. We consider electron-phonon scattering (acoustic and optical), as well as ionized impurity scattering, and evaluate the qualitative and quantitative differences in the power factors of the materials compared to the case where the constant scattering time is employed. We show that the thermoelectric power factors extracted from the two different methods differ in terms of (i) their ranking between materials, (ii) the carrier density where the peak power factor appears, and (iii) their trends with temperature. We further show that the constant relaxation time approximation smoothens out the richness in the band structure features, thus limiting the possibilities of exploring this richness for material design and optimization. These details are more properly captured under full energy/momentum-dependent scattering time considerations. Finally, by mapping the conductivities extracted within the two schemes, we provide appropriate density-dependent constant relaxation times that could be employed as a fast first-order approximation for extracting charge transport properties in the half-Heuslers we consider.