Thermoelectric transport and the role of different scattering processes in the half-Heusler NbFeSb

TL;DR

This study delivers an ab initio Boltzmann transport analysis of NbFeSb, a leading half-Heusler thermoelectric, by resolving full energy/momentum/band–dependent scattering from ADP, ODP, POP, and IIS using a deformation-potential framework. The ElecTra solver enables accurate transport predictions with substantial cost savings over full DFPT+Wannier approaches, enabling comprehensive bipolar transport and screening treatments. The results identify POP and IIS as the dominant scattering channels, especially for n-type, with intra-valley processes prevailing; the p-type PF peaks at $11.45\ \mathrm{mW\,m^{-1}\,K^{-2}}$ around $T=500\ \mathrm{K}$, while the n-type peak is $5.92\ \mathrm{mW\,m^{-1}\,K^{-2}}$ near $T=900\ \mathrm{K}$, closely matching experiments for PF and revealing notable overestimation of conductivity likely due to defects in real samples. The method provides mechanistic insight into scattering hierarchies and is generalizable to other polar thermoelectrics, offering a scalable, accurate route for performance optimization across material families.

Abstract

We perform an ab initio computational investigation of the electronic and thermoelectric transport properties of one of the best performance half-Heusler (HH) alloys, NbFeSb. We use Boltzmann Transport equation while taking into account the full energy/momentum/band dependence of all relevant electronic scattering rates, i.e. with acoustic phonons, non-polar optical phonons (intra- and inter-valley), polar optical phonons (POP), and ionized impurity scattering (IIS). We use a highly efficient and accurate computational approach, where the scattering rates are derived using only a few ab initio extracted matrix elements, while we account fully for intra-/inter valley/band transitions, screening from both electrons and holes, and bipolar transport effects. Our computed thermoelectric power-factor (PF) values show good agreement with experiments across densities and temperatures, while they indicate the upper limit of PF performance for this material. We show that the polar optical phonon and ionized impurity scattering (importantly including screening), influence significantly the transport properties, whereas the computationally expensive non-polar phonon scattering part (acoustic and non-polar optical) is somewhat weaker, especially for electrons, and at lower to intermediate temperatures. This insight is relevant in the study of half-Heusler and other polar thermoelectric materials in general. Although we use NbFeSb as an example, the method we employ is material agnostic and can be broadly applied efficiently for electronic and thermoelectric materials in general, with more than 10x reduction in computational cost compared to fully ab initio methods, while retaining ab-initio accuracy.

Figures (23)

• Figure 1: Crystal structure: (a) Primitive unit cell for NbFeSb. (b) Electronic band structure. (c) Phonon band structure. (d),(e) Intervalley scattering within conduction band minima valleys at the X- high symmetry point and valence band maxima valleys at the L-high symmetry point respectively. (f),(g) 2D cross-section view of the Brillouin zone for electrons (transparent) and phonons (cyan) with conduction band valleys shown by blue ellipsoids and valence band valleys in grey circles, respectively, showing the path of the phonon q-vector along the $\Gamma$-X direction for the intervalley processes.
• Figure 2: Scattering matrix elements for intravalley deformation potential extraction for holes: (a) For all phonons (two modes show polar behaviour) along the $\Gamma$ - X direction. (b) Short range part of the matrix elements for optical and (c) acoustic phonons for scattering from the valence band maxima (VBM to VBM). The insets in (a) and (b) show the frequencies corresponding to the polar optical and non-polar optical modes, respectively.
• Figure 3: Scattering matrix elements for intervalley deformation potential extraction for holes. The data correspond to transitions from an initial VBM valley (on the L-point) to any other equivalent VBM valley (on the L-point), as shown by solid black arrow in BZ. The other equivalent transitions are shown by the dashed arrows. The contributions of the different modes are shown by different colors. The brown square shows the overall value of intervalley deformation potential for these transitions.
• Figure 4: Scattering matrix elements for intravalley deformation potential exaction for electrons: (a) For all phonons (two modes show polar behaviour) along the $\Gamma$-X direction. (b) Short range part of matrix elements for optical and (c) acoustic phonons for scattering from the conduction band minima (CBM to CBM). The insets in (a) and (b) show the frequencies corresponding to the polar optical and non-polar optical modes, respectively.
• Figure 5: Scattering matrix elements for intervalley deformation potential for electrons: The data show transitions from an initial CBM valley (on the X-point) to any other equivalent CBM valley (on the X-point) by the solid black arrow in the BZ. The other equivalent transitions are shown by the dashed arrows. The contributions of the different modes are shown by different colors. The brown square shows the overall value of intervalley deformation potential for these transitions.