Ab initioand molecular dynamics predictions for electron and phonon transport in bismuth telluride

Phonon and electron transport in ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ has been investigated using a multiscale approach, combining the first-principles calculations, molecular dynamics (MD) simulations, and Boltzmann transport equations (BTEs). Good agreements are found with the available experimental results. The MD simulations along with the Green-Kubo autocorrelation decay method are used to calculate the lattice thermal conductivity in both the in-plane and cross-plane directions, where the required classical interatomic potentials for ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ are developed on the basis of first-principles calculations and experimental results. In the decomposition of the lattice thermal conductivity, the contributions from the short-range acoustic and optical phonons are found to be temperature independent and direction independent, while the long-range acoustic phonons dominate the phonon transport with a strong temperature and direction dependence (represented by a modified Slack relation). The sum of the short-range acoustic and optical phonon contribution is about $0.2\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕\mathrm{m}\phantom{\rule{0.2em}{0ex}}\mathrm{K}$ and signifies the limit when the long-range transport is suppressed by nanostructure engineering. The electrical transport is calculated using the full-band structure from the linearized augmented plane-wave method, BTE, and the energy-dependent relaxation-time models with the nonparabolic Kane energy dispersion. Temperature dependence of the energy gap is found to be important for the prediction of electrical transport in the intrinsic regime. Appropriate modeling of relaxation times is also essential for the calculation of electric and thermal transport, especially in the intrinsic regime. The maximum of the Seebeck coefficient appears when the chemical potential approaches the band edge and can be estimated by a simple expression containing the band gap. The scatterings by the acoustic, optical, and polar-optical phonons dominate the electrical conductivity and electric thermal conductivity.