Thermoelectric coefficients ofn-doped silicon from first principles via the solution of the Boltzmann transport equation

Abstract

We present a first-principles computational approach to calculate thermoelectric transport coefficients via the exact solution of the linearised Boltzmann transport equation, also including the effect of non-equilibrium phonon populations induced by a temperature gradient. We use density functional theory and density functional perturbation theory for an accurate description of the electronic and vibrational properties of a system, including electron-phonon interactions; carriers' scattering rates are computed using standard perturbation theory. We exploit Wannier interpolation (both for electronic bands and electron-phonon matrix elements) for an efficient sampling of the Brillouin zone, and the solution of the Boltzmann equation is achieved via a fast and stable conjugate gradient scheme. We discuss the application of this approach to n-doped silicon. In particular, we discuss a number of thermoelectric properties such as thermal and electrical conductivities of electrons, Lorenz number and Seebeck coefficient, including the phonon drag effect, in a range of temperatures and carrier concentrations. This approach gives results in good agreement with experimental data and provides a detailed characterization of the nature and the relative importance of the individual scattering mechanisms. Moreover, the access to the exact solution of the Boltzmann equation for a realistic system provides a direct way to assess the accuracy of different flavours of relaxation time approximation, as well as of models that are popular in the thermoelectric community to estimate transport coefficients.

Acoustic deformation potentials of n -type PbTe from first principles

“…To be consistent with the standard definition of deformation potentials [46], we also remove the wavefunction overlap integral from the resulting electron-phonon matrix element, see Eq. (7). The impact of the wavefunction overlap on our calculated deformation potentials is small since its values become close to 1 as q → 0.…”

Dominant electron-phonon scattering mechanisms inn-type PbTe from first principles

“…(3) using a Lorentzian or Gaussian with an empirical parameter for energy broadening, or using the linear tetrahedron method 43 . Our parametrization and the exact energy conservation enable us to use a very fine k point sampling in those parts of the BZ which contribute most to mobility, and thus substantially reduce the computational cost compared to the standard first-principles methods 23,32,42 .…”

“…In recent years, it has become possible to calculate the strength of e-ph scattering of semiconductors in the entire Brillouin zone (BZ) purely from first principles [20][21][22][23][24] . Methods for solving the linearized Boltzmann transport equation (BTE) and calculating the electronic transport coefficients from first principles have also been developed [25][26][27][28] . However, these methods suffer from a large computational cost.…”

Thermally induced band gap increase and high thermoelectric figure of merit of n-type PbTe

“…First-principles calculations of thermoelectric transport quantities are typically carried out using the electronic band structure obtained from density functional or higher level theories, where the band shifts due to temperature are not accounted for [12,13,14,15,16,17,18,19,20]. For example, recent abinitio calculations of TE transport in PbTe used a fixed band gap value at all temperatures [17].…”