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REVIEW 5 major objections 4 minor 58 references

Ablation of black-Si by (Gauss-)Bessel femtosecond laser beams

T0 review · 5 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Black silicon's antireflective nano-needle surface lets femtosecond lasers modify it at fluences about 50 times below the 0.2 J/cm² single-pulse ablation threshold of flat silicon.

desk verdict The Gaussian-beam half of the paper is a solid, useful measurement; the Gauss-Bessel fluence axis is circularly calibrated, which undermines the quantitative 50x comparison but not the qualitative point. read the letter →

arxiv 2505.05263 v1 pith:OZAJUFRU submitted 2025-05-08 physics.optics physics.app-ph

Nan Zheng , Hsin-Hui Huang , Nguyen Hoai An Le , Tomas Katkus , Haoran Mu , Soon Hock Ng , Thumula Ranaweera , Darius Gailevicius
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Dominyka Stonyte Saulius Juodkazis
This is my paper · ORCID
classification physics.opticsphysics.app-ph
keywords AxiconblacksiliconablationthresholdfemtosecondlaserGauss-Besselbeamanti-reflectivesurfacemicromachininginfraredtransmittance
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

The paper reports that black silicon, whose nano-needle surface reflects less than 1% of visible light, can be laser-modified at pulse fluences roughly 50 times lower than the $0.2~\mathrm{J/cm^2}$ single-pulse ablation threshold of flat silicon. Melting and removal of the nano-needles starts around $4~\mathrm{mJ/cm^2}$, and the modified region stays close to the focal-spot size. With a Gauss-Bessel beam, grooves up to eight times deeper than wide are cut at fluences around $4~\mathrm{J/cm^2}$, twice the aspect ratio of a Gaussian beam at lower energy cost. Two-side nanotextured, plasma-thinned silicon transmits more than 95% of light at $1.7$–$2.1~\mu\mathrm{m}$. A sympathetic reader would care because lower fluence thresholds mean weaker self-focusing, gentler thermal load, and a direct route to controlled surface melting for doping or texturing.

What carries the argument

The mechanism carrying the argument is the black-silicon surface itself: a random array of nano-needles whose reflectance is below 1% in the visible, so the absorbance $A = 1-R-T$ approaches one. Because the ablation-threshold model used in the paper scales the required fluence inversely with absorbance ($F_{\mathrm{th}}\propto 1/A$), reducing reflectance from about 40% to 1% predicts the modification threshold to drop by a factor of roughly 40–50, matching the measured onset near $4~\mathrm{mJ/cm^2}$. A second piece of machinery is the Gauss-Bessel beam made by a diffractive axicon with $10\times$ demagnification, whose long non-diffracting region has a central core of diameter $\sim2.44~\mu\mathrm{m}$ FWHM carrying about 1% of the pulse energy; the Liu method (plotting $W^2$ against $\ln E$) is adapted to this core to define the fluence scale.

What would settle it

Measure the energy passing through a pinhole set to the $2.44~\mu\mathrm{m}$ FWHM of the Gauss-Bessel central core at the sample position; if the transmitted fraction is not 1% of the pulse energy, the computed fluences and the claimed 50× threshold reduction for the Gauss-Bessel beam would need rescaling.

Watch

Extended reading notes

Core claim

The central discovery is that the antireflective texture of black silicon does not just make it black; it makes the surface easier to machine with femtosecond pulses. The paper shows experimentally that modification of black-Si occurs at fluences a factor of about 50 below the single-pulse ablation fluence of $0.2~\mathrm{J/cm^2}$ for flat silicon, and attributes the reduction to the increased absorbance of the nano-needle surface. The width of the molten, re-solidified region is almost independent of pulse energy and is set by the $1/e^2$ intensity profile of the focal spot, implying negligible lateral heat spread. For the Gauss-Bessel beam, the width of modification at threshold matches the FWHM of the central core, and deep grooves with aspect ratio up to 8 are produced at $\sim4~\mathrm{J/cm^2}$, twice the aspect ratio obtainable with a Gaussian beam. The paper also demonstrates that the Liu method for measuring ablation thresholds, originally derived for Gaussian beams, can be applied to the central core of a Gauss-Bessel beam using a thin alumina mask.

Load-bearing premise

All the fluence numbers for the Gauss-Bessel beam depend on the unmeasured assumption that 1% of each pulse's energy lands in the central core and that its FWHM is the deposition area; if the true fraction differs, the reported fluence values and the claimed match to $0.2~\mathrm{J/cm^2}$ shift accordingly.

Editorial extensions

If this is right

  • Black silicon can be patterned and grooved with femtosecond pulses at energies that would barely modify flat silicon, reducing the risk of self-focusing and collateral damage.
  • The modification width on black silicon is controlled by the focal spot size rather than by heat diffusion, so feature size can be set by the optics over a wide fluence range.
  • Gauss-Bessel beams cut grooves in black silicon with aspect ratios up to 8, about twice the aspect ratio of Gaussian-beam cuts, at roughly 50× lower fluence per pulse.
  • The Liu threshold-mapping technique extends to the central core of a Gauss-Bessel beam, giving a practical way to calibrate non-Gaussian machining spots.
  • Double-sided nanotextured silicon thinned to 70 µm transmits more than 95% of near-infrared light at 1.7–2.1 µm, pointing to use in IR windows and filters.

Reading between the lines

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

  • If the 50× threshold reduction is a general property of antireflective textured surfaces, the same machining benefit should appear on other textured semiconductors, not just silicon.
  • The near-constant modification width from the melting onset up to high fluence suggests the nano-needle melting acts like a switch, which could enable single-shot patterning at pulse energies just above the onset with a fixed optical footprint.
  • The paper's fluence calibration for the Gauss-Bessel beam rests on an assumed 1% central-core efficiency; directly measuring that fraction would turn the semi-quantitative comparison into a quantitative one and test the reported match to the silicon threshold.
  • Because molten silicon is denser than the solid, the controlled remelting demonstrated here could support crack-free surface doping or hyperdoping of black silicon without volume-expansion damage.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 4 minor

Summary. The paper reports a comparative study of femtosecond laser modification of black-Si (b-Si) using Gaussian (G) and Gauss-Bessel (GB) beams at 1030 nm with 200 fs pulses. The main claims are: (i) b-Si can be modified at fluences about 50 times below the single-pulse ablation fluence of flat Si (0.2 J/cm2), with modification attributed to melting of nano-needles; (ii) the modification width is nearly independent of pulse energy and approximately equal to the focal spot diameter; (iii) GB-beam machining produces grooves with aspect ratio up to 8 at a quoted fluence of about 4 J/cm2, which is lower than required for comparable G-beam machining; and (iv) double-side nanotextured 70-um-thick Si exhibits IR transmittance above 95% in the 1.7-2.1 um range. The quantitative GB-beam fluence calibration relies on an assumed central-core energy efficiency of 1%, and the paper presents the resulting threshold of 0.2 J/cm2 as an exact match to the known Si ablation threshold.

Significance. The low-fluence modification of nano-textured silicon is a potentially interesting result for laser micromachining and surface engineering, and the G-beam SEM evidence at ~4 mJ/cm2 supports a melting modification threshold well below that of flat Si. However, the central quantitative claim for the GB-beam is not independently established. The 1% central-core efficiency is assumed, not measured, and the subsequent 'exact match' to the 0.2 J/cm2 literature threshold is a consequence of this choice, not a validation. In addition, the paper's Eq. (1) is algebraically inconsistent with the quoted parameters, and the paper conflates melting with ablation in its headline claims. If the GB-beam fluence axis is re-calibrated by direct measurement or the quantitative claims are removed, the study would still document an interesting phenomenon; in its present form, the quantitative conclusions are not reliable.

major comments (5)
  1. [Sec. II C, 'The estimate of an average fluence per central core...'] The central-core efficiency epsilon_op = 1% is assumed, not measured. The text states that 1% is used instead of 2% because of circular polarization and the splitting of intensity maxima, and then the resulting FWHM-scaled threshold of 0.2 J/cm2 is presented as an exact match to the known Si ablation threshold. This is circular: the value of epsilon_op was selected so that the computed threshold matches the literature value. If epsilon_op were 2%, the threshold would be approximately 0.4 J/cm2. All GB-beam fluence values in Figs. 9 and 10 and the claimed 50x reduction in the abstract scale with this unverified efficiency. Please provide a direct measurement of the central-core energy fraction (e.g., via a calibrated pinhole or beam profile) or present all GB fluence values with an explicit, quantified uncertainty and remove the claim of exact validation.
  2. [Sec. II B, Eq. (1) and the numerical example following it] The quoted efficiency of 2% for the central spot is inconsistent with the stated parameters. With D = 3.5 mm, gamma = 1 deg, lambda = 1030 nm, one has N = D sin(gamma)/lambda approx 59, and w0 = D/2. Equation (1) gives epsilon_op = 2 sqrt(e) lambda/(w0 sin(gamma)) = 4 sqrt(e)/N approx 11%, not 2%. If one instead uses the stated equivalence to 2 sqrt(e)/N, the value is about 5.6%. Neither value supports the factor-of-two reduction to 1% for circular polarization. This algebraic discrepancy is load-bearing because it feeds directly into the fluence calibration and the claimed threshold match. The authors should correct the formula and recalculate the efficiency, or explain the origin of the 2% figure in detail.
  3. [Abstract and Conclusions (also Sec. III A, Fig. 6)] The headline claim of a 'factor ~50x reduction' below the single-pulse ablation fluence of 0.2 J/cm2 conflates two different processes. The low-fluence events are identified in the text and in Fig. 6(b) as melting of the nano-needles, while ablation (material removal) is stated to occur above 0.2 J/cm2. The 50x reduction is therefore a reduction in the melting/modification threshold, not in the ablation threshold. Please rephrase the abstract and the conclusions to distinguish these endpoints clearly; otherwise the claim is misleading.
  4. [Sec. II C / Sec. III B (fluence diameter definition)] There is an inconsistency in the diameter used for fluence normalization. In Sec. II C, the threshold match is obtained after rescaling the central-core fluence by 2.13^2, i.e., using the FWHM diameter d_FWHM = 2.44 um. In Sec. III B and Fig. 10, however, the fluence is calculated from the observed diameter d0 = 2.6 um (the first-zero diameter) with the 1% efficiency. The paper should state clearly which diameter defines the fluence axis in Figs. 9 and 10, and quantify the resulting uncertainty (which is at least a factor of (2.6/2.44)^2 = 1.14 in fluence).
  5. [Sec. III B, 'Counterintuitively...'; Sec. IV] The Liu method is applied to measure the central-core parameters on a 40-nm AlOx mask, but the text explicitly says that Eq. (3) cannot be applied to the b-Si surface because of redeposition and oxidation effects. Nevertheless, the mask-derived d0 = 2.6 um and the threshold energy are used to compute fluence values for all b-Si GB-beam irradiations. The applicability of the calibration to the actual b-Si surface should be justified, or the GB fluence values should be presented with a caveat that they rely on a mask-based calibration that may not transfer to the structured surface.
minor comments (4)
  1. [Fig. 2] The transmittance axis is unlabeled; please specify the units (e.g., %) and clarify the relation between the wavelength and wavenumber scales.
  2. [Sec. II C] The sentence '1% is considered instead of 2% due to circularly polarised beam and separation of the intensity maxima into two peaks' would benefit from a quantitative justification or a reference; as written, the halving is not obvious.
  3. [Sec. III A] The paper uses the Airy disk diameter 2.8 um for the fluence area of the Gaussian beam; please clarify whether this is the diameter between first zeros or the 1/e^2 diameter, and whether the same convention is used throughout.
  4. [Abstract] The phrase 'at a lower fluence of ~4 J/cm2 (50x reduction)' is confusing, as 4 J/cm2 is not 50 times below 0.2 J/cm2; please clarify what the factor 50 is referenced against.

Circularity Check

2 steps flagged · score 6.0 of 10

The GB-beam fluence scale is calibrated by an assumed 1% central-core efficiency; the 'exact match' to the 0.2 J/cm2 Si threshold is recovered by construction, not by independent validation.

  1. self definitional [Section II C, 'Laser micro-machining setup' (fluence estimate following the Liu fit).]
    "The estimate of an average fluence per central core (per pulse) for the used efficiency ϵop = 1% of GB-beam (1% is considered instead of 2% due to circularly polarised beam and separation of the intensity maxima into two peaks for two perpendicular polarisations). One finds F(th)p = ϵop E(th)p / π(d0/2)2 = 0.043 J/cm2. ... Then the energy in the central core per dFWHM0 for the ablation threshold corresponds to the threshold fluence F(th)p × 2.132 = 0.2 J/cm2, which exactly matches that for Si."

    The 1% central-core efficiency is assumed, not measured; the only numerical justification given is a halving of the ideal-axicon 2% value. Using E(th)p = 900 nJ and d0/2 = 2.6 µm from the AlOx Liu fit, this assumption gives 0.043 J/cm2, and multiplying by (d0/dFWHM0)^2 = 2.13^2 converts it to 0.2 J/cm2. The paper presents the exact match to the literature Si threshold as validation of the Liu-method adaptation. But 0.2 J/cm2 is recovered by construction: any assumed core efficiency scales the reported fluence linearly, and d0/dFWHM0 is a fixed geometrical ratio of the assumed Bessel profile. Had 2% been used, the result would be 0.4 J/cm2, removing the agreement. The agreement is therefore not independent evidence; it is a consequence of the chosen calibration constant.

  2. self citation load bearing [Section II B, discussion of Eq. (2) and ref. [46]; invoked again in Sec. II C.]
    "The axial intensity (Eqn. 2) maximum for the diffractive axicon has two axially-shifted positions for two perpendicular polarisations. This results in two distinct peaks when a circularly polarised incident beam is used 46. It is caused by the form birefringence with two distinct refractive indices."

    Ref. 46 (Anand et al., J. Phys. Photonics 3, 024002 (2021)) shares several authors with the present paper (Katkus, Ng, Juodkazis, et al.). The load-bearing factor of 1/2 that converts the ideal axicon efficiency from 2% to 1% is justified solely by this self-cited prior result; the present paper provides no independent measurement of the actual central-core energy fraction in its own setup. That 1% is then the pivot for the 'exact match' to 0.2 J/cm2 and for every GB fluence value reported later. Thus a central quantitative premise rests on a self-citation chain rather than on a measurement or on an externally verified value presented in this paper.

full rationale

The paper has a genuinely independent component: the Gaussian-beam data use measured pulse energy and a measured 2.8-µm focal spot, and the observation that b-Si is modified at ~4 mJ/cm2, about 50x below the 0.2 J/cm2 flat-Si ablation threshold, does not depend on the 1% GB-core assumption. The qualitative finding of very-low-fluence melting of nano-needles therefore survives. However, the GB-beam quantitative fluence axis is circular in an important sense: the central-core efficiency is assumed to be 1% (halved from the ideal-axicon 2% on the strength of a self-cited prior result), and the resulting F(th)p = 0.043 J/cm2 is multiplied by the FWHM/first-zero area factor 2.13^2 to obtain exactly 0.2 J/cm2, the literature threshold that is then used as confirmation that the calibration is valid. Because the efficiency is an unreported input rather than a measured quantity, the 'exact match' is a consequence of the chosen normalization, not an independent check. The GB-specific claims of '4 J/cm2 (50x reduction)' and the aspect-ratio comparisons built on that fluence scale are proportionally affected. The G-beam results, the SEM observations of modification width, and the qualitative threshold reduction are independent of this calibration step, so the circularity is partial rather than total. Score 6 reflects one constructionally recovered 'validation' plus a load-bearing self-citation for the 1% efficiency, while the central qualitative scientific observation retains independent support.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central quantitative claims rest on one hand-set efficiency parameter, the fitted central-core radius, the applicability of the Liu method to a non-Gaussian beam, and the assumption that the low-fluence modification is governed mainly by the antireflection of black-Si. No new physical entities are introduced.

free parameters (2)
  • Central-core energy efficiency epsilon_op = 1% (assumed; ideal is 2%)
    Sec. II C: '1% is considered instead of 2% due to circularly polarised beam and separation of the intensity maxima into two peaks'. This value is not directly measured and is used to convert measured pulse energy into fluence.
  • Effective central-core radius of GB-beam = 2.6 micrometers (d0/2 from Liu fit on AlOx mask)
    Sec. II C and Fig. 4: the central-core radius is obtained from a linear fit of W^2 versus ln(Ep). It is a measured fit but still a fitted parameter used to compute all GB-beam fluence values.
assumptions (3)
  • domain assumption The Liu method for ablation-threshold determination is applicable to the central core of a Gauss-Bessel beam.
    Sec. II C and IV: the paper adapts Liu's Gaussian-beam method to the GB central core; the validation relies on matching the known 0.2 J/cm2 Si threshold, which is affected by the assumed efficiency.
  • ad hoc to paper The 50x reduction in modification threshold is caused primarily by the increased absorbance (reduced reflectance) of black-Si.
    Sec. V: the estimate is called 'only qualitative' and assumes dynamic energy deposition is governed by reflectance ratios; field enhancement and defect accumulation are also mentioned as possible contributors.
  • domain assumption The central-core fluence can be computed from ideal Bessel-beam properties with a fixed energy fraction, ignoring clipping, aberrations, and the actual demagnified intensity profile.
    Sec. IV: 'Exact Bessel-like beam geometry and properties are affected by focusing, filling/clipping...' The quantitative comparisons rely on this idealization.

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Pith. "Pith review of Ablation of black-Si by (Gauss-)Bessel femtosecond laser beams." pith.science (2026). https://pith.science/paper/OZAJUFRU

@misc{pith2026250505263,
  author       = {Pith},
  title        = {Pith review of: Ablation of black-Si by (Gauss-)Bessel femtosecond laser beams},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OZAJUFRU}},
  note         = {Machine review of arXiv:2505.05263}
}
read the original abstract

Laser machining and modification of black-Si (b-Si) by femtosecond laser Gaussian (G-) and Gauss-Bessel (GB-) beams are compared at a wavelength of 1030 nm. The GB-beam was generated using a diffractive axicon lens and 10x demagnification optics. It was found that modification of b-Si well below (a factor 50x) the single pulse ablation fluence of 0.2 J/cm2 was possible, corresponding to ablation/melting of nano-needles. The width of modification was almost independent of pulse energy/fluence and had a width of 1/e2-intensity profile at the melting regime. For the GB-beam, the smallest width of laser modification at 0.2 J/cm2 threshold (at the center core) was close to the FWHM of the core of the GB-beam. The aspect ratio of the ablated groove on the surface of b-Si made by GB-beam was twice as large - up to 8 - compared to that achievable with G-beam, and it was at a lower fluence of 4 J/cm2 (50x reduction). Reflectivity of two-side nanotextured b-Si on plasma-thinned 70-micrometers thick Si was strongly reduced in the near-IR range, reaching transmittance >95% at 1.7-2.1 micrometres wavelengths.

Figures

Figures reproduced from arXiv: 2505.05263 by the authors.

Figure 1
Figure 1. shows the angular dependence of the absorbance of b-Si with different heights of nano-needles, corresponding to 40 min and 20 min plasma etch. For a broad spectral range of 450-1000 nm, low reflectance R < 1% (large absorbance A > 99%) was observed even up to angles of incidence θi ∼ 30◦ [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) IR transmittance of one and two-sided b-Si (70- [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Laser micro-machining setup (WOP, Lithuania) based on Carbide-40W fs-laser (Light [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Determination of the central core diameter of the GB-beam from the width (diameter), [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Black-Si ablation by Gaussian fs-laser beam. (a) Photo of fs-laser machined regions [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) The width vs. single pulse fluence [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Depth vs. fluence per pulse. The top inset shows a SEM image of high-fluence, small [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Black-Si ablation by Gauss-Bessel beam. (a) Dark-field image (with [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. SEM image of b-Si ablated by Gauss-Bessel beam at lowest pulse energy. It was used to [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. The depth [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

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    + commands may be crafted by hand or, preferably, generated by using Bib . The AIP styles for REV 4 include Bib \ style files +aipnum.bst+ and +aipauth.bst+, appropriate for numbered and author-year bibliographies, respectively. REV 4 will automatically choose the style approp...

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Reviewed August 15, 2026 · model on record in the stance chip above.