Estimating carrier relaxation times in the Ba₈Ga₁₆Ge₃₀ clathrate in the extrinsic regime

We used a semi-empirical method to extract carrier relaxation times at different temperatures (τ(T)) in thermoelectric materials from a combination of experimental results and first-principles calculations. The methodology is based on the Boltzmann transport equation formalism within the relaxation time approximation. It can be applied to single crystals and polycrystalline materials. We applied the method to investigate the electronic transport properties of the clathrate compound Ba₈Ga₁₆Ge₃₀ type-I. The calculations indicate that the carrier relaxation process in single crystals is dominated by electron-phonon scattering (τ ∝ T^-3/2), while in polycrystalline materials scattering at grain boundaries dominates (τ ∼ cte). The Seebeck coefficient, electrical conductivity, and electron heat conduction are in consistent agreement with experiment. Furthermore, the Slack relation for lattice heat conductivity was successfully applied to the material. The calculated figure of merit is in good agreement with experimental results.