Extraction of the k(E) from the E(k)

Approach:

• Extract the k(E,n) states, i.e. each transport state is defined by its position in the Brillouin zone k, its energy E, its band index n, its velocity and DOS.
• Compute the scattering rate for each state as initial charge carrier state and in all available final state, from the same band or from other bands, same energy or other energies.
• The momentum relaxation time is computed for each transport state and then, by through the transport distribution function, the charge transport coefficients are calculated.

The figure at left shows the band structure of TiCoSb in the usual representation. The figure at right displays the constant energy surfaces for two of the TiCoSb valence bands at 0.15 eV below the band edge. Rather than ellipsoids, the surfaces are very warped and spread all over the reciprocal unit cell.

Validation

• Validation of the code concept and scheme using the constant relaxation time approximation to compare with highstreet codes like BoltzTraP for the case of TiCoSb for the density of states (DOS), (a), and the power factor in units of relaxation time, (b) . Excellent agreement is achieved.
• Silicon (c) and GaAs (d) electron mobility at 300 K, considering all the relevant phonon processes (red) and adding the ionized impurities (blue), the black line is for the reference data. The magenta line in (d) shows the mobility neglecting the velocity term in the scattering rate, i.e. using the bare relaxation rate instead of the proper momentum relaxation rate

Role of the scattering physics and materials descriptors

• Transport Distribution Function of 13 half Heuslers under proper treatment of the scattering with phonons, (a) and (d), and the commonly used approximations of constant relaxation time, (b) and (e), constant mean free path, (c) and (f), at 300 K. These approximations smear out the transport details of the Transport Distribution.
• Ranking of some half-Heusler alloys considering their peak Power Factor (PF) for electron (blue) and hole (red) transport, at 300 K in (g) and 900 K in (h), considering bipolar transport and finite energy gap size. The legend reports the Pearson correlation coefficients. The number between parenthesis in (g) is without one outlier. In (h), the descriptor contains the band gap divided by k_BT, the average size of the constant energy surfaces, the relative dielectric constant, the deformation potential of the dominant electron-phonon mechanism (optical phonon in these materials) and the conductivity effective mass.

Open Source Codes

• EMAF - Effective Mass Finder code

  • A code to extract the density-of-states and the conductivity effective masses from arbitrary band structures. These two values can efficiently describe the transport properties of a band structure.

• TransP - semiclassical Transport Properties
  • A code to calculate the charge transport properties of a material considering the full band dependence of the scattering rate upon state momentum, energy and band index.

Publications

• Impact of the scattering physics on the power factor of complex thermoelectric materials - JAP

  • Charge transport in advanced thermoelectric materials, what matters when we aim to calculate the transport coefficients - ArXiv

• Material Descriptors for the Discovery of Efficient Thermoelectrics - ACS Applied Energy Materials - ArXiv

• Ultra-High Thermoelectric Power Factors in Narrow Gap Materials with Asymmetric Bands - J. Phys. Chem. C