Benchmarking ab initio calculation of thermoelectric coefficients

The Seebeck coefficient and the thermoelectric figure of merit ZT are key design parameters in the study of thermoelectric materials. In this work, we test the accuracy of the ab initio Boltzmann transport equation for calculations of the Seebeck coefficient and ZT; we use silicon as a test case given the abundance of experimental data for high-purity samples. To obtain the Seebeck coefficient, we include spin-orbit couplings and GW quasiparticle corrections for the bands structures, density-functional perturbation theory and Wannier-Fourier interpolation for electron-phonon couplings, long-range quadrupole corrections, and ionized impurity scattering. To calculate thermal conductivity, we consider three-phonon, four-phonon, and phonon-isotope scattering, as well as the electronic contribution. We find that our calculated values are in good agreement with experiments across all experimentally-relevant temperatures, and especially at low carrier density. We discuss possible avenues for future improvement.