Improved Calculation of Acoustic Deformation Potentials from First Principles

Angela Dyson; Patrick Williams

REVIEW 4 major objections 5 minor 67 references

Improved Calculation of Acoustic Deformation Potentials from First Principles

T0 review · 4 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read Acoustic deformation potentials can now be computed purely from first principles, giving scattering parameters for semiconductors without experimental data.

desk verdict A useful, honest incremental method paper with a real reproducibility gap: the finite-q extraction is never checked for convergence in the long-wavelength limit. read the letter →

arxiv 2502.08538 v2 pith:62XA67E7 submitted 2025-02-12 cond-mat.mtrl-sci

Patrick Williams , Angela Dyson This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords acousticdeformationpotentialelectron-phononcouplingdensityfunctionalperturbationtheoryfirstprinciplessilicondiamondcubicboronnitridechargetransportsimulation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that the acoustic deformation potential—the material parameter controlling how electrons scatter off lattice vibrations—can be obtained from first-principles calculations instead of by fitting to experimental transport data. The authors compute the electron-phonon coupling matrix with density-functional theory and density-functional perturbation theory, evaluate the deformation potential at twenty polar angles between electron and phonon wavevectors, and fit the standard angular expressions to get angle-averaged values. For silicon the result (8.56–9.52 eV) matches the accepted range; for diamond it is larger than prior empirical values (20.0–21.4 eV versus 8.7–17.7 eV); for cubic boron nitride it falls near the estimate used in earlier simulations (10.2–12.2 eV). If the claim is right, transport simulations no longer need experimental scattering parameters for every new material.

What carries the argument

The central object is the ratio $\sqrt{2m_0\omega/\hbar}\, g^\nu_{m,n}(k,q)/|q|$, whose $|q|\to 0$ limit is the acoustic deformation potential. That ratio is computed from DFT/DFPT electron-phonon matrix elements via Wannier-Fourier interpolation. The angle-dependent fits of $\Xi_{\mathrm{LA}}(\theta)$ and $\Xi_{\mathrm{TA}}(\theta)$ to the computed points separate $\Xi_d$ and $\Xi_u$, and Eqs. (11)–(12) average them into the scalar $\Xi_{\mathrm{ADP}}$ that enters the acoustic scattering rate.

What would settle it

Recompute the silicon, diamond, or cBN deformation potentials using phonon wavevectors whose magnitudes are repeatedly halved while keeping all other settings fixed; if the fitted $\Xi_{\mathrm{ADP}}$ from Eqs. (11) and (12) changes by more than a few percent as $|q|\to 0$, the reported values are not converged and the comparison with literature is not yet settled.

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Extended reading notes

Core claim

In the paper's own terms, the acoustic deformation potential at a band edge is the small-$|q|$ gradient of the electron-phonon coupling matrix element, so it can be read directly out of DFT/DFPT outputs. The authors calculate $\Xi_{\mathrm{adp}}$ from Eq. (8) at twenty polar angles with azimuthal averaging, fit the longitudinal and transverse angular dependences $\Xi_{\mathrm{LA}}(\theta)=\Xi_d+\Xi_u\cos^2\theta$ and $\Xi_{\mathrm{TA}}(\theta)=\Xi_u\sin\theta\cos\theta$, and combine the fitted $\Xi_d$ and $\Xi_u$ via Eqs. (11) and (12) into a single $\Xi_{\mathrm{ADP}}$. The silicon numbers reproduce the literature, the cBN numbers support the estimate used by earlier workers, and the diamond numbers come out higher than the empirical range, which the paper attributes to the use of deformation potentials as free parameters in prior fits.

Load-bearing premise

The load-bearing assumption is that the finite phonon wavevectors used in the calculation are already small enough that $g/|q|$ is in its linear regime; the paper does not report the q magnitudes or a convergence test for this regime.

Editorial extensions

If this is right

Monte Carlo and Boltzmann-transport simulations can obtain acoustic scattering parameters from DFT/DFPT alone, removing the need to fit to time-of-flight or mobility measurements.
The method gives concrete first-principles $\Xi_{\mathrm{ADP}}$ values for diamond ($\approx$20–21 eV) and cBN ($\approx$10–12 eV) that can be tested in transport simulations.
Because the same pipeline works for silicon, diamond, and cBN, the approach should transfer to other diamond-structure and zinc-blende semiconductors with sparse experimental data.
The silicon and cBN agreement supports the paper's conclusion that the wide spread of diamond deformation potentials in the literature comes largely from empirical free-parameter fitting.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper leaves the q-convergence question open: checking $g/|q|$ at successively smaller phonon wavevectors would confirm or overturn the reported values.
The large azimuthal variation seen for cBN hints that the angle-averaged $\Xi_{\mathrm{ADP}}$ may depend on how many azimuthal directions are sampled, so a finer azimuthal grid is a natural robustness test.
If the diamond value near 20–21 eV is used in a mobility simulation, the predicted mobility will be lower than simulations using the empirical 8.7–17.7 eV range, making the discrepancy directly testable.
The same extraction could be applied to hole bands and to additional conduction valleys, where the deformation potential may differ, to build complete first-principles scattering tables.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper does one thing and does it cleanly: it extracts acoustic deformation potentials for Si, diamond, and cBN from EPW electron-phonon matrix elements, fitting the full angular dependence rather than picking special points as Li et al. and Yang et al. did. The Si benchmark lands close to literature values, which lends the workflow initial credibility. The diamond and cBN numbers are new and directly useful for anyone running Monte Carlo transport simulations on ultra-wide-bandgap materials. Credit where due: the data is deposited, the figures are readable, and the text is refreshingly plain about what is assumed and what is uncertain. No circularity—no experimental mobility is fed into the fits.

The soft spots are real but not fatal. The most important is the one the stress-test highlights: equation 9 defines the ADP as a |q|→0 limit, but the paper never reports the actual q magnitudes, the number of q points, or any test that g/|q| is flat in the range used. That is not a nitpick. The entire output rests on that ratio being in the linear regime, and a single arbitrary q could shift every reported Ξ_d, Ξ_u, and Ξ_ADP. The Si agreement is reassuring, but it is not a substitute for a convergence test. There are also no error bars on any fitted parameter, and the cBN polar correction is described in one sentence. The cBN comparison to Siddiqua et al. is against a "reasonable estimate," so saying "excellent agreement" overstates the validation. The diamond value sits well above all prior reports; the authors' explanation about free parameters in empirical fits is plausible, but they do not demonstrate it quantitatively.

Even with these gaps, the central method is sensible and the paper does not overclaim. The data release and the Si benchmark show good faith, and the cBN result is explicitly flagged as an estimate support rather than a measurement. The likely fix is a short convergence study plus error bars and a bit more detail on the polar subtraction—none of that is conceptually hard.

Who is this for? Anyone doing transport simulations of diamond, cBN, or other sparse-data UWBG materials who needs a defensible ADP input. A serious referee should see this; it is a legitimate incremental contribution, not a desk reject. My recommendation is to send it to peer review with the expectation of a revision that addresses the q-convergence issue and reports uncertainties.

Referee Report

4 major / 5 minor

Summary. This manuscript develops a first-principles procedure for extracting acoustic deformation potentials (ADPs) for the conduction band minima of silicon, diamond, and cubic boron nitride. Using DFT and DFPT via Quantum Espresso and EPW, the authors compute electron-phonon coupling matrix elements at fixed polar and azimuthal angles and convert them to angle-dependent deformation potentials through Eq. 8 (with the definition in Eq. 9), fit the results to the Herring–Vogt angular forms in Eqs. 10a and 10b, average over polar angle via Eqs. 11a and 11b, and combine longitudinal and transverse contributions via Eq. 12. For Si, the fitted Ξ_ADP values (9.52 and 8.56 eV) agree with literature values; for diamond they obtain larger values (21.42 and 20.04 eV) than most empirical reports; for cBN they obtain 12.21 and 10.23 eV, which bracket the estimate used by Siddiqua et al. The central claim is that this approach provides ADP scattering parameters without requiring empirical mobility or time-of-flight fits.

Significance. If the method is sound, it offers a practical route to transport parameters for materials with sparse experimental data, supporting Monte Carlo and Boltzmann transport simulations. The work has several strengths: it does not use experimental mobilities to fix the deformation potentials, so the central extraction is not circular; it benchmarks against Si, a well-characterized material; the fits shown in Figs. 2, 4, and 6 capture the dominant angular trends; and the authors have deposited the data underlying the figures in a public repository. The main significance, however, is conditional on the method's operational validity, particularly whether the finite-q evaluation used in Eq. 8 is demonstrably in the linear regime and whether the polar correction for cBN is adequately specified. The large spread in literature values for diamond and the absence of experimental data for cBN make the predictive claim rest heavily on these technical details.

major comments (4)

[§II.B, Eq. 9, and §III.A–C] The manuscript never reports the magnitude of the phonon wavevectors |q| used in evaluating the ratio g/|q| in Eq. 8, nor does it present a convergence study showing that the computed values are in the small-q linear regime where Eq. 9 applies. Since every fitted value of Ξ_d and Ξ_u and hence every reported Ξ_ADP depends on this finite-q ratio, the extraction procedure is operationally underdefined without such a test. A single q point per polar angle could accidentally match literature values (as in Si), but this does not establish that the method yields a unique material parameter. I request a convergence test over a range of |q| values, or a plot showing g behaves linearly in |q| for the q values used, for at least one material.
[§III.C] For cBN, the only statement about the polar correction is that "the long range effects were subtracted before the deformation potential was calculated." No details are given about the subtraction scheme, the Fröhlich parameters, how the q→0 limit was handled, or the sensitivity of the resulting acoustic matrix elements to the subtraction. This is load-bearing because the longitudinal acoustic deformation potential is extracted from the same matrix elements that require the polar correction, and the cBN result is used as evidence of predictive power. Please specify the polar-correction method used in the EPW calculations and quantify its effect on the reported Ξ_ADP.
[§III.B, §III.C, Tables II and III, Eqs. 11–12] No uncertainties are reported for the fitted deformation potentials, despite the visible scatter in the angular data and the two fitting procedures yielding substantially different results (Fit 1 vs Fit 2: 21.42 vs 20.04 eV for diamond; 12.21 vs 10.23 eV for cBN). The azimuthal bars in Figs. 4 and 6 and the differences between fitting protocols should be propagated into the final Ξ_ADP values. Without error estimates, the claimed agreement for cBN with the Siddiqua et al. estimate (which the authors themselves note may be coincidental) cannot be quantitatively assessed, and the diamond discrepancy with literature remains only qualitatively interpreted.
[§II.A, Eqs. 10–12] The angular averaging leading to Eqs. 11a and 11b assumes a uniform distribution of polar angles and an isotropic combination via Eq. 12, but the manuscript does not justify this averaging scheme as the physically appropriate one for scattering in these valleys. This is an assumption of the method rather than a derived result; showing that Eq. 12 reproduces the full first-principles scattering rate in a model test, or at least discussing the sensitivity of Ξ_ADP to the averaging choice, would strengthen the central claim.

minor comments (5)

[§III.B, text before Fig. 3] The text states that the diamond conduction band minimum is located at "roughly 73%" of the distance between Γ and X, but the caption of Fig. 3(a) states the minimum is at "82% along the Δ direction." Please reconcile this inconsistency.
[§III.C, §II.A, Fig. 6] The phrase "The black dashed line is then the plot of equation 10b for Ξ_u = 16.4 eV" is unexplained: neither Fit 1 (19.12 eV) nor Fit 2 (15.89 eV) gives 16.4 eV. Please correct this value or clarify which fit it corresponds to.
[§II.B] The sentence describing the q-point grid says it was used "in conjuncture with" a 10×10×10 grid; this should be "in conjunction with." There are also several typographical errors in the introduction (e.g., "ab inito," "catagorising") that should be corrected.
[§III, Table I and Table II] The table headings "Fit 1" and "Fit 2" are not self-explanatory without reading the text; please add a footnote defining the two fitting procedures in each table caption.
[§II.A, Eq. 9] Equation 9 defines the deformation potential as a derivative with respect to |q|, but the absolute value notation is applied only to the matrix-element prefactor and not to the matrix element itself. For clarity, specify whether the derivative is taken on the magnitude of the complex matrix element or on its real part.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the deformation potentials are extracted from DFT/DFPT electron-phonon matrix elements via Eq. 8, with empirical values used only as post-hoc comparison.

full rationale

The derivation chain is self-contained against ab initio data. Equation 8 expresses the acoustic deformation potential as sqrt(2m0*omega/hbar) * g/|q|, where g is the EPW-computed electron-phonon matrix element obtained from DFPT. The uniaxial and dilatation constants Xi_d and Xi_u are obtained by fitting Eqs. 10a and 10b to the angular dependence of these ab initio values; they are not fitted to mobilities, time-of-flight data, or any experimental scattering observable. Literature values for Si and diamond are used for comparison and discussion only, not as inputs to the fit. For cBN, the authors explicitly state that agreement with Siddiqua et al. is against an estimate and that the similarity 'could be coincidental,' so no fitted experimental target is built into the calculation. No load-bearing self-citations are present; the cited formalisms (Bardeen-Shockley, Herring-Vogt) are external and standard. The paper's under-reporting of the actual q magnitudes and the absence of an explicit small-q convergence test is a legitimate robustness and correctness concern, but it is not circularity: no quantity is made equal to its own input by construction. Under the rule that circularity must be exhibited as a specific reduction, no such step can be identified in this manuscript.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central quantitative results rest on standard DFT/DFPT assumptions and on unquantified choices in the extraction procedure, chiefly the finite-q evaluation of Eq. 9 and the angular averaging convention. No new physical entities are introduced, and no experimental data are used to set the deformation potentials. The main risk is that the reported Xi_ADP values inherit errors from q convergence, the PBE functional, and the phenomenological angular model.

free parameters (3)

Xi_d and Xi_u per material (fitted from DFT/EPW angular data) = Si: 1.47/10.03 eV (fit 1), 2.47/8.03 eV (fit 2); diamond: -10.81/33.69 eV (fit 1), -9.63/31.33 eV (fit 2); cBN…
These are the parameters of Eqs. 10a and 10b fitted to the computed angular dependence. They are the paper's headline outputs rather than hidden inputs, but the final Xi_ADP depends on them through Eqs. 11 and 12.
Effective-mass polynomial coefficients m_l and m_t = Si: 0.958/0.204 m0; diamond: 1.64/0.29 m0; cBN: 0.92/0.30 m0
Fitted by a second-order polynomial to the DFT band edge near the conduction-band minimum. They are used for comparisons and for discussing the DOS effective mass, but they are not required to compute the deformation potential itself.
Sound velocities v_l and v_t used in Eq. 12 = Si: 9.04e3 / 5.34e3 m/s; diamond: 18.038e3 / 12.834e3 m/s; cBN: 15.4e3 / 11.8e3 m/s
Taken from literature references [38,40,41,49,55]. They are inputs rather than fitted here, but the final combined Xi_ADP scales with the ratio (v_l/v_t)^2, so the result depends on their accuracy.

assumptions (6)

domain assumption Density functional theory with the PBE functional gives electron-phonon coupling matrix elements accurate enough for deformation-potential extraction
The band gaps are underestimated by 24-25% in diamond and cBN, and the paper asserts this should not affect the ADP without presenting a test (Section III).
domain assumption The electron-phonon matrix elements from EPW satisfy the relation in Eqs. 6-9, and the small-q limit can be accessed by the finite q values used
Equation 9 defines the ADP as a q-gradient, but the paper does not report the q magnitudes or show that the computed g/|q| values are in the linear regime.
domain assumption The overlap between initial and final electronic states is approximately unity for small q
Used to move from Eq. 6 to Eq. 7. It is standard for small q, but no quantitative justification is given.
domain assumption The Herring-Vogt angular forms Eqs. 10a/10b fully describe the angular dependence of the acoustic deformation potentials in the first conduction valley
These forms are used as the fitting model. The large azimuthal spread reported for cBN suggests the model may not capture all anisotropy.
ad hoc to paper The uniform average over polar angle in Eqs. 11a/11b is the appropriate physical average for scattering
The paper averages (d + u cos^2(theta))^2 with a uniform theta distribution. A spherical average with sin(theta) weighting would give different coefficients, and the physical averaging choice is not derived.
domain assumption The polar long-range effects in cBN have been correctly subtracted before extracting the deformation potential
Section III C states only that 'long range effects were subtracted before the deformation potential was calculated' with no detail on the correction or its validation.

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Cite this review

Pith. "Pith review of Improved Calculation of Acoustic Deformation Potentials from First Principles." pith.science (2026). https://pith.science/paper/62XA67E7

@misc{pith2026250208538,
  author       = {Pith},
  title        = {Pith review of: Improved Calculation of Acoustic Deformation Potentials from First Principles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/62XA67E7}},
  note         = {Machine review of arXiv:2502.08538}
}

read the original abstract

Using density functional theory (DFT) and density functional perturbation theory (DFPT), the band structure, phonon dispersion and electron phonon coupling matrix were calculated for silicon (Si), diamond and cubic boron nitride (cBN). From these, the acoustic deformation potential was calculated for multiple angles between the electron and phonon wave vectors and analytic expressions for the longitudinal and acoustic modes were fit to find an average deformation potential. The ability to calculate the deformation potential from first principles allows for the scattering rates to be determined without the use of lengthy empirical methods. For Si, the numerically calculated deformation potentials are in excellent agreement with what is seen in the literature. On the other hand, the deformation potentials calculated for diamond were found to be larger than what has been seen previously, however previous calculations of transport parameters in diamond report a large range of values for scattering parameters which may be due to assumptions made in each model. Excellent agreement was also seen between the value calculated for cBN and the literature, however there are no experimental results for cBN and so this value is compared against an estimate. This shows that scattering parameters can be calculated via first principles for materials with sparse experimental data, which in turn allows for increased confidence in the output of charge transport simulations of new and emerging materials.

Figures

Figures reproduced from arXiv: 2502.08538 by the authors.

**Figure 2.** FIG. 2. Polar dependence of the longitudinal (red) and trans [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** FIG. 4. Polar dependence of the longitudinal (red) and [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

Figures from the paper (3 more)

**Figure 3.** Figure 3: FIG. 3. (a) The electronic band structure of diamond as cal [PITH_FULL_IMAGE:figures/full_fig_p005_3.png]

**Figure 5.** Figure 5: FIG. 5. (a) The electronic band structure of cBN as calculate [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: FIG. 6. Polar dependence of the longitudinal (red) and trans [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

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B. K. Bose, Global energy scenario and impact of power electronics in 21st century, IEEE Transactions on Indus- trial Electronics 60, 2638 (2013)

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13% from the ex- perimental value [43, 44]

57 ˚ A, a percentage diﬀerence of 0 . 13% from the ex- perimental value [43, 44]. The bulk modulus and the cohesive energy per atom were also found to have a per- centage error of 2 . 4% [45] and 2 . 2% [34], respectively, when compared to experimental results. -20 -15 -10 -5 0 5 10 15 20 25 X Γ L (a) Energy (eV) k Path 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14...

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47 eV [47, 48]. The phonon dispersion shows good agreement between the numerically calculated phonon energies and those collected experimentally [46], of par- ticular note is the agreement between the experimentally and numerically calculated acoustic phonon modes. As with Si, the longitudinal and transverse acoustic deformation potentials were found usin...

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57% from the exper- imental value [32]

461 ˚ A, a percentage diﬀerence of 0 . 57% from the exper- imental value [32]. The bulk modulus and the cohesive energy per atom were also found to have a percentage -10 -5 0 5 10 X Γ L (a) Energy (eV) k Path 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 ΓX LA TA TO LO q Path (b) Energy (eV) L LA TA TO LOFIG. 1. (a) The electronic band structure of silicon as calc...

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1 eV [55, 58]. The phonon dispersion shows good agree- ment with what is seen in other numerical calculations for cBN [59, 60] The longitudinal and transverse acoustic deformation potentials were found using equation 9 with the polar angle between the phonon vector and the longitudinal axis of the kz conduction band minimum valley found at twenty evenly s...

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