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arxiv: 2604.22033 · v1 · submitted 2026-04-23 · ❄️ cond-mat.mtrl-sci · physics.app-ph

Recognition: unknown

Carrier scattering considerations and thermoelectric power factors of half-Heuslers

Rajeev Dutt , Bhawna Sahni , Yao Zhao , Yuji Go , Saff E Awal Akhtar , Ankit Kumar , Sumit Kukreti , Patrizio Graziosi
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Zhen Li Neophytos Neophytou
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Pith reviewed 2026-05-09 20:58 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.app-ph
keywords half-Heusler alloysthermoelectric power factorpolar optical phonon scatteringionized impurity scatteringBoltzmann transportcarrier scatteringab initio calculations
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The pith

Polar optical phonon and ionized impurity scattering together set the thermoelectric power factor of half-Heusler alloys by about 65 percent on average.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper calculates the electronic transport and thermoelectric power factors for 13 n-type and p-type half-Heusler alloys by solving the Boltzmann transport equation with scattering times extracted from first-principles calculations. It accounts for all relevant phonon modes plus ionized impurity scattering and finds that room-temperature peak power factors fall between 5 and 10 mW/mK squared. Across the set of materials, the long-range polar optical phonon scattering combined with ionized impurity scattering controls the power factor to an average of 65 percent, while acoustic and non-polar optical phonon contributions play a smaller role. This result indicates that computationally cheaper models limited to these two Coulombic processes can still give a usable first-order estimate of performance.

Core claim

Using ab initio parameters for scattering rates in the relaxation-time Boltzmann transport framework applied to 13 half-Heusler compounds, the combination of polar optical phonon and ionized impurity scattering determines the thermoelectric power factor on average by about 65 percent, with non-polar phonon interactions contributing far less.

What carries the argument

The relaxation-time Boltzmann transport equation with ab initio scattering times for polar optical phonons, ionized impurities, and non-polar phonons applied to the electronic band structures of the half-Heuslers.

Load-bearing premise

The ab initio scattering parameters for polar optical phonon and ionized impurity processes accurately capture the dominant mechanisms and the relaxation-time Boltzmann transport framework remains valid across the doping and temperature ranges examined.

What would settle it

An experimental measurement of the power factor in any of the 13 alloys at room temperature that deviates strongly from the value obtained when only polar optical phonon and ionized impurity scattering are included.

Figures

Figures reproduced from arXiv: 2604.22033 by Ankit Kumar, Bhawna Sahni, Neophytos Neophytou, Patrizio Graziosi, Rajeev Dutt, Saff E Awal Akhtar, Sumit Kukreti, Yao Zhao, Yuji Go, Zhen Li.

Figure 1
Figure 1. Figure 1: (a, b) Square of the wavefunction overlaps be [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) The bandstructure of HfNiSn. b(i) and b(ii) show the Fermi surface of the conduction and valence bands, [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Thermoelectric coefficients for HfNiSn for n-type [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The power factor versus density for all 13 HHs considered, for n-type (first row, a-c) and p-type (second row, [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Scattering relaxation times for different mechanisms and their effect on transport for all the 13 HHs considered. (a, [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) The averaged screening length for all 13 HHs [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a, d) The momentum relaxation scattering times for POP (purple lines) and IIS (green lines) for n-type and p-type [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The average values of the PF across p-type materi [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The averaged power factor of all 13 HHs considered for multiple scattering case considerations as labelled in the [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Acoustic (a,c,e) and optical (b,d,e) matrix elements of the VB of HfNiSn in the Γ-X direction for intra-band [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Acoustic (a,c,e) and optical (b,d,e) matrix elements or the VB of HfNiSn in the Γ-L direction for intra-band [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Acoustic (a,c,e) and optical (b,d,e) matrix elements for the VB of HfNiSn in the Γ-K direction for intra-band [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of the relaxation time due to ADP (red color) and ODP (blue color) for HfNiSn for n-type (left column) [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: The effect of screening in POP scattering rates for HfNiSn for n-type (left column) and p-type (right column). [PITH_FULL_IMAGE:figures/full_fig_p021_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Comparison of the power factor (σS2 ) of the half-Heusler alloys considered for transport conditions limited by ADP+ODP scattering (blue circles), POP scattering (green triangles), and all phonon scattering, ADP+ODP+POP (black stars). The PF values show are computed at reduced Fermi-level ηF = 0 eV. (a) n-type materials. (b) p-type materials. The dashed lines indicate the average values for each scatterin… view at source ↗
Figure 16
Figure 16. Figure 16: The bandstructures of the HHs considered, calculated using PBE-GGA exchange correlation. Materials shown [PITH_FULL_IMAGE:figures/full_fig_p023_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Density of states of (a) conduction band (n-type) and (b) valence band (p-type) for all 13 HHs considered. [PITH_FULL_IMAGE:figures/full_fig_p023_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: The screening length versus reduced Fermi level for n-type carriers (a, b - first row) and for p-type carriers (c, d - [PITH_FULL_IMAGE:figures/full_fig_p024_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: The electrical conductivity (first column) and Seebeck coefficients (second column) of the 13 HHs under consideration [PITH_FULL_IMAGE:figures/full_fig_p025_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: The Seebeck coefficients of the HHs under consideration versus reduced Fermi level for n-type (a) and p-type (b) [PITH_FULL_IMAGE:figures/full_fig_p026_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Comparison of the calculated power factor ( [PITH_FULL_IMAGE:figures/full_fig_p027_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: (a, b) The conductivity effective mass, mcond, and density of states effective mass, mdos, respectively, for the HHs considered. Values for n-type (green circles) and p-type (red circles) are shown. The dashed horizontal lines indicate the average value of each category. The values are as extracted from the EMAF code85 [PITH_FULL_IMAGE:figures/full_fig_p028_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: The power factors (σS2 ) versus reduced Fermi level for all 13 p-type HHs considered, grouped, and averaged by the degree of degeneracy of their valence band maxima (VBM). The groups of materials have the valence band maxima at different high-symmetry points Γ, L, Γ+L, and L+W, as indicated in the legend of (a). The specific groups of materials are also indicated in the legend of (b). Various scattering m… view at source ↗
read the original abstract

The electronic and thermoelectric (TE) transport properties of 13 n-type and p-type half-Heusler alloys are computationally examined using Boltzmann transport. The electronic scattering times resulting from all relevant phonon interactions and ionized impurity scattering (IIS) are fully accounted for using ab initio extracted parameters. We find that at room temperature the average peak TE power factors (PF) of all materials we examine reside between 5 and 10 mW/mK$^2$. We also find that IIS in combination with the long range polar optical phonon (POP) scattering are more influential in determining the electronic transport and PF over all other non-polar phonon interactions (acoustic and optical phonon transport). In fact, the combination of POP and IIS determines the thermoelectric power factor of the half-Heuslers examined on average by about 65\%. The results highlight the crucial impact of Coulombic scattering process (POP and IIS) on the TE properties of half-Heusler alloys and provide profound insight for understanding transport, which can be applied widely in other complex bandstructure materials. In terms of computation expense, the computationally cheaper POP and IIS provide an acceptable first-order estimate of the power factor of these materials, while the non-polar contributions, which require more expensive ab initio calculations, could be of secondary importance.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript computationally examines the electronic and thermoelectric transport properties of 13 n-type and p-type half-Heusler alloys using Boltzmann transport theory. Scattering times from all relevant phonon interactions and ionized impurity scattering (IIS) are incorporated via ab initio extracted parameters. The authors report that average peak power factors at room temperature lie between 5 and 10 mW/mK² and that the combination of polar optical phonon (POP) scattering and IIS determines the power factor on average by about 65%, with the remaining contribution from non-polar acoustic and optical phonons; they conclude that the computationally cheaper POP+IIS processes provide an acceptable first-order estimate.

Significance. If the central quantitative attribution holds, the work provides concrete evidence that long-range Coulombic scattering mechanisms dominate thermoelectric power factors in half-Heuslers, offering a practical route to reduce computational cost in screening complex-bandstructure materials while highlighting the limited role of short-range phonon scattering.

major comments (2)
  1. [Results / Computational Methods] The 65% attribution (abstract and results section) is obtained by comparing power factors computed with the full set of ab initio scattering rates versus the POP+IIS subset, all within the relaxation-time approximation. Because POP scattering is inelastic and the half-Heusler bands are multi-valley and non-parabolic, the RTA does not solve the linearized Boltzmann transport equation exactly; the resulting error in the transport integrals could be comparable in magnitude to the 35% attributed to non-polar phonons, undermining both the numerical claim and the statement that POP+IIS furnish an “acceptable first-order estimate.”
  2. [Results] No error bars, sensitivity analysis with respect to doping level or temperature, or direct comparison to experimental power-factor data are provided for the reported 5–10 mW/mK² range or the 65% figure, making it impossible to assess whether the quantitative conclusions are robust within the examined parameter space.
minor comments (2)
  1. [Abstract] The abstract states that “the average peak TE power factors … reside between 5 and 10 mW/mK²” without specifying the precise definition of “peak” (maximum versus value at a fixed carrier concentration) or the temperature at which the average is taken.
  2. [Methods] Notation for the scattering rates (e.g., symbols for POP, IIS, and non-polar contributions) should be introduced once in the methods section and used consistently in all figures and tables.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review of our manuscript. We address the major comments point by point below and outline the revisions we plan to make.

read point-by-point responses

  1. Referee: [Results / Computational Methods] The 65% attribution (abstract and results section) is obtained by comparing power factors computed with the full set of ab initio scattering rates versus the POP+IIS subset, all within the relaxation-time approximation. Because POP scattering is inelastic and the half-Heusler bands are multi-valley and non-parabolic, the RTA does not solve the linearized Boltzmann transport equation exactly; the resulting error in the transport integrals could be comparable in magnitude to the 35% attributed to non-polar phonons, undermining both the numerical claim and the statement that POP+IIS furnish an “acceptable first-order estimate.”

    Authors: We appreciate this important observation regarding the limitations of the relaxation-time approximation (RTA). It is true that for inelastic scattering mechanisms such as polar optical phonon (POP) scattering, the RTA provides an approximate solution to the Boltzmann transport equation, and the multi-valley, non-parabolic nature of the bands in half-Heuslers can introduce additional complexities. However, since both the full scattering model and the reduced POP+IIS model are evaluated using the identical RTA implementation, the relative 65% contribution is a consistent measure of the impact of those specific scattering channels within the same methodological framework. We do not claim that RTA is exact, but rather that it is a practical and commonly employed approach for such comparative studies. To address the concern, we will revise the manuscript to include a more explicit discussion of the RTA limitations and note that the percentage is within this approximation. We believe this does not undermine the practical utility for first-order estimates, as the computational savings remain significant. revision: partial

  2. Referee: [Results] No error bars, sensitivity analysis with respect to doping level or temperature, or direct comparison to experimental power-factor data are provided for the reported 5–10 mW/mK² range or the 65% figure, making it impossible to assess whether the quantitative conclusions are robust within the examined parameter space.

    Authors: We agree that additional analyses would help demonstrate the robustness of our findings. In the revised manuscript, we will include sensitivity analyses showing how the power factor and the relative contribution of POP+IIS vary with carrier concentration (doping level) and temperature for selected representative materials from our set of 13 alloys. This will provide a better assessment of the stability of the 65% figure and the 5-10 mW/mK² range. Regarding direct comparison to experimental data, while our primary focus is on computational trends and the role of scattering mechanisms across multiple compounds, we will add a discussion section comparing our computed power factors to available experimental values reported in the literature for a subset of well-characterized half-Heusler materials (e.g., NbFeSb, ZrNiSn). This will help contextualize the results, although we note that experimental samples often include additional scattering from defects and grain boundaries not fully captured in our ideal crystal calculations. revision: yes

Circularity Check

0 steps flagged

No circularity: 65% PF attribution is direct output of ab initio BTE comparison

full rationale

The paper extracts scattering parameters ab initio for all mechanisms, computes power factors via Boltzmann transport under the full set versus the POP+IIS subset, and reports the average ratio as ~65%. This comparison is a post-processing step on independently computed rates; no parameter is fitted to the target PF value, no self-citation supplies the uniqueness or the numerical result, and no ansatz is imported. The derivation chain therefore remains self-contained against external benchmarks and does not reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the standard Boltzmann transport framework and the assumption that ab initio scattering rates are transferable; no explicit free parameters or new entities are introduced.

axioms (1)
  • domain assumption The relaxation-time approximation to the Boltzmann transport equation is sufficient to describe thermoelectric transport in these half-Heusler alloys.
    Invoked implicitly when scattering times are used to compute conductivity and Seebeck coefficient.

pith-pipeline@v0.9.0 · 5570 in / 1278 out tokens · 38382 ms · 2026-05-09T20:58:15.205385+00:00 · methodology

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Reference graph

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