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

TL;DR

This study compares the effects of full energy-dependent scattering times versus constant scattering time assumptions on the thermoelectric properties of Co-based half-Heusler alloys, revealing significant differences in power factor predictions and implications for material design.

Contribution

It introduces a full numerical scheme using Fermi's Golden Rule for energy-dependent scattering times, highlighting the importance of detailed scattering physics in thermoelectric property evaluation.

Findings

Full energy-dependent scattering times alter material ranking.

Peak power factor positions shift with scattering assumptions.

Constant relaxation time approximation oversimplifies bandstructure effects.

Abstract

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, versus the commonly employed constant scattering time. For this, we employ DFT bandstructures 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 bandstructure 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.