Sticking behavior and transformation of tin droplets on silicon wafers and multilayer-coated mirrors

Christian Meier; Norbert B\"owering

REVIEW 4 major objections 4 minor 40 references

Sticking behavior and transformation of tin droplets on silicon wafers and multilayer-coated mirrors

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Substrate temperature controls whether molten tin droplets adhere to silicon and multilayer mirror surfaces, with cooling to about -50 °C making them self-peel, while any adhering deposit can be removed by inducing the tin-pest phase…

desk verdict Useful experimental addition on tin drop adhesion and tin-pest cleaning, but the collector super-cooling recommendation goes beyond the measured temperature range. read the letter →

arxiv 1908.03881 v1 pith:MTGC2EOV submitted 2019-08-11 physics.app-ph

Norbert Böwering , Christian Meier This is my paper · ORCID

classification physics.app-ph

keywords dropletimpactphasetransformationopticscleaningmultilayercoatingextremeultravioletlighttinpestself-peelingthermaleffusivity

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 tries to establish that the sticking of molten tin droplets onto silicon and multilayer-coated mirror surfaces is controlled mainly by substrate temperature: at roughly 90 °C droplets adhere strongly, while at -50 °C they do not stick on any tested surface except glass. This matters for extreme ultraviolet lithography, where tin debris from the plasma source contaminates collector mirrors and shortens their life. The paper also shows that tin deposits that do stick can be removed in-situ by seeding them with gray tin powder and cooling, triggering the tin-pest phase transformation that embrittles and detaches the deposit within hours without damaging the mirror coating. A sympathetic reader would take away a practical recipe: run the collector cold to avoid sticking, and use tin pest as a cleaning step.

What carries the argument

The load-bearing theoretical object is the interfacial contact temperature $T_c = T_s + (T_d - T_s)(1+e_s/e_d)^{-1}$ from Eq. (1), where $e_i=(k\rho c_p)^{1/2}$ is thermal effusivity, plus the per-area thermal resistance $R_t/A$ of the coating stack listed in Table 2. This pair of quantities converts a materials list into a predicted sticking ranking: low effusivity or high coating resistance keeps the interface hot and promotes adhesion, while high effusivity and thin coatings cool the interface and promote self-peeling. The second mechanism is the allotropic $\beta$-tin to $\alpha$-tin tin-pest transformation, induced by seeding with gray tin powder at low temperature, which expands the deposit by about 25 percent, embrittles it, and drives detachment.

What would settle it

Measure the sticking outcome of identical tin drops on two Mo/Si multilayer samples with the same ZrO2 cap and the same surface chemistry but coating thicknesses differing by, say, a factor of two: if the thicker coating does not stick more often at the same substrate temperature, the thermal-resistance mechanism is wrong. Alternatively, embed a thin-film thermocouple or use high-speed thermal imaging to check whether the interfacial contact temperature under the splat actually changes with coating thickness as Eq. (1) plus Table 2 predicts.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central experimental discovery is a temperature-controlled adhesion switch. Tin drops at about 250 °C falling 41 cm onto smooth horizontal samples stick strongly when the surface is held near 90 °C, peel off or contract and detach at 23 °C on low-adhesion coatings, and do not stick at all at -50 °C except on soda-lime glass, which still holds drops even at -100 °C. The order of sticking tendency across coatings follows the one-dimensional thermal resistance of the coating stack: thicker or more insulating layers (thick oxide, Mo/Si multilayers with ZrO2 cap) keep the interfacial contact temperature higher and favor sticking, while bare silicon with its thin native oxide cools the interface fastest and favors self-peeling. For every case where a splat did stick, infection with alpha-tin powder followed by cooling to -30 to -40 °C converted the beta-tin to gray alpha-tin, with roughly 25 percent volume expansion and embrittlement, cracking and detaching the deposit; full conversion occurred within 24 hours, usually in less than 12 hours, with no visible damage to the multilayer coating.

Load-bearing premise

The argument that cooling prevents sticking and that coating ranking predicts sticking rests on a contact-temperature formula that assumes two homogeneous semi-infinite bodies with no contact resistance; the authors themselves note that coated samples are not homogeneous semi-infinite, so if layered heat flow or interfacial contact resistance behaves differently, the proposed mechanism and the collector-mirror recommendation could fail.

Editorial extensions

If this is right

Cooling an EUV collector mirror surface to roughly -50 °C should make most incident molten tin drops self-peel or contract instead of adhering, reducing contamination buildup during source operation.
Any tin splat that nevertheless sticks can be removed in situ within about a day by sprinkling gray tin seed powder on it and cooling to -30 to -40 °C, because the tin-pest transformation embrittles and lifts the deposit without damaging the Mo/Si multilayer.
The cleaning step works on every substrate tested, including bare Si, oxidized Si, uncapped Mo/Si, ZrN-capped and ZrO2-capped Mo/Si, and glass, so it does not depend on the cap-layer chemistry.
Coating stacks with higher thermal resistance, such as thick oxide or Mo/Si with a ZrO2 cap, tend to hold tin splats even at room temperature, while bare silicon and thin-oxide surfaces spontaneously shed them.
The observed self-contraction in vacuum shows that recoil of spread tin splats is not caused by trapped air; surface tension alone can pull the splat back into a ball.

Reading between the lines

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

If the thermal-resistance picture transfers to smaller droplets, super-cooling should also suppress adhesion of tin microdroplets and vapor-condensed tin, which would make the EUV debris problem much smaller; this is a testable extension the authors only hint at.
A direct falsification of the model would be to compare two coatings with identical top-layer chemistry but very different layer thickness: if sticking does not track $R_t/A$, the assumed heat-flow mechanism is wrong and the collector-mirror recommendation would rest on correlation rather than cause.
The tin-pest cleaning step could be combined with hydrogen-radical etching, with pest handling thick splats and radicals handling thin films, potentially covering the full size range of tin contamination in one in-situ procedure.
Because the paper notes coated samples violate the homogeneous semi-infinite assumption, deriving a corrected contact temperature for the full layer stack rather than using substrate bulk values would let the model make quantitative predictions worth testing.

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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

Worth knowing: this is a solid, well-scoped experimental paper. The central observation—tin splats stick strongly on these substrates near 90 °C and generally do not stick at -50 °C—is directly supported by a consistent matrix of samples, photographs, and profilometry. The most useful new results are the vacuum dripping data at substrate temperatures below room temperature, the observation of self-contraction rather than only self-peeling, and the demonstration that tin-pest transformation can detach tin splats from ZrN- and ZrO2-capped Mo/Si multilayer coatings without visible coating damage. There are no fitted parameters and no circular steps; the tin-pest cleaning demonstration stands on its own.

The paper also builds fairly on prior work. It extends de Ruiter et al.'s room-temperature self-peeling results into vacuum and onto EUV-relevant cap layers, and it is honest about the limits of the contact-temperature model. The authors state that Eq. (1) is not valid for coated samples, then use the coating thermal-resistance ranking of Table 2 to interpret sticking trends. That is a real soft spot: Table 2 gives nearly identical thermal resistance for uncapped and capped ML coatings, yet their sticking behavior at 23 °C differs, so surface chemistry is doing work the model does not capture. The qualitative ~1 N push classification is another limit; adhesion is not measured quantitatively. These issues do not overturn the main temperature trend, but they weaken the mechanism story.

The biggest gap is the operating recommendation. Section 4 proposes collector super-cooling with inlet temperatures below -20 °C or -30 °C. The experiments only test roughly 90 °C, 23 °C, -50 °C, and one glass case at -100 °C. There is no data between 23 °C and -50 °C, so the threshold below which self-peeling reliably dominates is unknown. The model cannot fill that gap for coated samples, and the extrapolation from millimeter-size drops to EUV microdroplets is explicitly hedged—appropriately so.

Overall, this is an honest, useful paper for the EUV collector community and for people studying droplet impact and solidification. It deserves a serious referee. Before the cooling recommendation is treated as established, it needs quantitative adhesion measurements, more substrate temperatures between -50 °C and room temperature, and a clearer statement of how far the contact-temperature model can be pushed for coated samples. With those changes, I would be comfortable seeing it published.

Referee Report

4 major / 4 minor

Summary. The paper reports an experimental study in which molten tin droplets (3.0–3.6 mm diameter, ~250 °C) are dripped under vacuum onto silicon wafers and Mo/Si multilayer-coated mirror samples with various cap layers. The authors characterize whether the solidified splats stick, self-peel, or self-contract as a function of substrate temperature (-100 °C to ~95 °C) and coating type, and they demonstrate an in-situ cleaning method based on infection with gray tin powder to induce the β-Sn to α-Sn (tin pest) transformation. The central claims are that droplet adhesion is strong at ~90 °C, largely non-sticking at -50 °C (except on glass), and that transformation to gray tin always leads to embrittlement and detachment, enabling contamination removal without coating damage. The paper further proposes that super-cooling EUV collector mirrors below -20 °C or -30 °C would reduce tin sticking during source operation.

Significance. If the reported temperature-dependent sticking behavior holds, the study has practical value for EUV lithography source development, where tin debris contamination of collector mirrors is a known lifetime issue. The paper contributes a useful observational matrix of sticking and detachment behavior across relevant collector-mirror coatings (ZrN- and ZrO2-capped Mo/Si multilayers), and demonstrates that tin-pest transformation is a reproducible cleaning route for strongly adhering deposits, with photographic time series and profilometry supporting the morphological claims. The work is largely free of fitted parameters: the sticking matrix is observational and the contact-temperature values are computed from literature material properties, which is a strength. The main limitations are the qualitative adhesion classification (a manual ~1 N push) and the extrapolation of a simplified heat-transfer model to coated samples for which the model is acknowledged to be invalid; these limit the strength of the causal explanation and the proposed operating recommendation.

major comments (4)

[Section 4 and Table 3] The recommendation to operate EUV collectors at inlet temperatures below -20 °C or -30 °C is an extrapolation beyond the presented data. The sticking matrix (Table 3) contains only substrate temperatures near -50 °C, 23 °C, and ~90 °C (plus one glass point at -100 °C); no measurement exists in the interval between -50 °C and 23 °C. Since the proposed operating window lies in this unmeasured interval, the statement that surface temperatures 'sufficiently low for the dominance of splat self-peeling' would be reached is not directly supported. Please either add dripping experiments at intermediate substrate temperatures (e.g., -20 °C and -30 °C) on at least the ML-coated samples, or explicitly restrict the conclusion to temperatures at or below -50 °C.
[Section 3.1, Eq. (1) and Table 2] The contact-temperature model is acknowledged to be invalid for coated samples ('the assumption of a homogeneous semi-infinite body below the tin splat is no longer valid'), yet the paper uses Eq. (1) together with the one-dimensional coating thermal resistance ranking to interpret the sticking trends. This is internally problematic: Table 2 gives nearly equal thermal resistance per area for uncapped Mo/Si (319), ZrN-capped (318), and ZrO2-capped (323) coatings, but Table 3 shows qualitatively different behavior at 23 °C (peels vs. sticks or peels). The thermal-resistance ranking alone therefore cannot explain the differences among the capped and uncapped ML samples, indicating that surface chemistry (wetting and adhesion) contributes as well. The paper should either develop a layered heat-transfer model that accounts for finite coating thickness and contact resistance, or explicitly present the thermal-resistance ranking as a qualitative tendency rather than as the explanatory mechanism.
[Section 3.2, last paragraph] The claim that the observed sticking and detachment trend is 'generally consistent with the sample ranking based on thermal resistance per unit area' is weakened by the Si-ZrO2 case. This sample has R_t/A of only 5.3 m²K GW⁻¹ (Table 2) and yet shows self-contraction at -50 °C and sometimes even at 23 °C (Table 3), whereas the uncapped Mo/Si sample (R_t/A = 319) only peels or contracts. The very thin ZrO2 layer has negligible thermal resistance, so the observed self-contraction on Si-ZrO2 cannot be explained by heat conduction alone. Please address this counterexample explicitly or adjust the proposed ranking.
[Section 2.2 and Abstract] Adhesion is classified by a manual push force of up to about 1 N, yielding only a binary 'strong' versus 'weak/zero' distinction. The Abstract's statement that 'the adhesion strength of solidified tin splats decreased strongly with decreasing substrate temperature' is therefore stronger than the measurement supports. I recommend rewording to 'sticking tendency' or 'sticking probability', or adding a quantitative pull-off measurement to substantiate the strength claim.

minor comments (4)

[Section 3.2] Two subsections are numbered 3.2 ('Tin splat morphology' and 'Delamination behavior of non-sticking tin droplets'); the second should be renumbered as 3.3 and the subsequent 'Transformation behavior' as 3.4.
[Fig. 5 caption and text] The caption of Fig. 5 states that the tin drop was dripped at Ts = 90 °C, while the text in Section 3.3 says 'dripped (at Ts = 82 °C)'. Please make the values consistent.
[Fig. 6 caption] The caption gives 'mass: 0.154 mg', which is likely a typo for 0.154 g (the text elsewhere reports drop masses of ~100–170 mg). Please correct the unit.
[Table 3 and Section 3.2] The reported substrate temperatures are rounded ('~90 °C', '-50 °C'), but no uncertainty or measured range is provided. Adding the spread or uncertainty of the thermocouple readings would make the comparison among samples more quantitative.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the sticking matrix is observational, the heat-transfer numbers are independent calculations, and tin-pest cleaning is demonstrated directly in this paper.

full rationale

I walked the claimed derivation chain and found no step where a predicted quantity reduces by construction to an input. The central sticking matrix (Table 3) is observational: drips were made at set substrate temperatures and adhesion was classified by a manual push test. The contact-temperature values from Eq. (1) are computed from literature thermal properties of tin, silicon, glass, and multilayer coatings, not fitted to the observed sticking data. The coating thermal-resistance ranking in Table 2 is likewise an independent calculation from layer thicknesses and published conductivities; the authors then compare this ranking with observed behavior as a consistency check, not as an input. The authors' own caveat that Eq. (1) is not strictly valid for coated samples is a limitation of the explanatory model, not a circularity. The tin-pest cleaning procedure is supported by prior same-author references [19, 20], but this paper independently demonstrates the phase transformation in-situ with time-lapse imaging, conversion-fraction data, and successful detachment on multiple coated samples, so the self-citations are not load-bearing. The recommendation to super-cool EUV collectors below -20 to -30 °C is an extrapolation beyond the tested temperatures (-50 °C and 23 °C), but that is an empirical validation gap, not a circular derivation. No fitted parameter is renamed as a prediction, and no uniqueness claim is imported from the authors' own work. Accordingly, the circularity score is 0.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new entities and fits no parameters. It relies on literature material properties and on the operational assumptions listed above.

assumptions (5)

domain assumption Eq. (1): contact temperature for sudden contact of two semi-infinite homogeneous bodies with no contact resistance, using thermal effusivities from Table 1.
Used in §3.1 to calculate interfacial temperatures and explain sticking; authors note in the same section that it is not valid for coated samples because coatings are thin and heat conduction is anisotropic.
domain assumption One-dimensional thermal conduction through coating layers with neglected boundary contact resistances ranks samples by sticking tendency.
Table 2 lists effective thermal resistance Rt/A for each coating stack; this ranking is used to explain why coated samples stick more than bare Si. The authors state contact resistances are neglected.
ad hoc to paper Adhesion strength can be classified by a manual push force of up to about 1 N.
In §2.2, sticking is classified as weak or zero if deposits could be moved easily and strong if they could not be moved at all; this operational proxy underlies the claim that adhesion decreases strongly with temperature.
domain assumption Gray tin powder can reliably nucleate the beta-Sn to alpha-Sn transformation in high-purity tin under vacuum cooling.
The cleaning procedure in §3.3 assumes prior tin-pest results [19,20] and the observed infection procedure; the paper demonstrates it on multiple substrates.
domain assumption Millimeter-size free-fall drops at 2.84 m/s are representative of tin debris and droplet conditions in EUV sources.
The Conclusions extend the results to collector mirrors and tin microdroplets, although only drops of 3.0 to 3.6 mm diameter were tested; the paper hedges this with 'likely'.

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Cite this review

Pith. "Pith review of Sticking behavior and transformation of tin droplets on silicon wafers and multilayer-coated mirrors." pith.science (2026). https://pith.science/paper/MTGC2EOV

@misc{pith2026190803881,
  author       = {Pith},
  title        = {Pith review of: Sticking behavior and transformation of tin droplets on silicon wafers and multilayer-coated mirrors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MTGC2EOV}},
  note         = {Machine review of arXiv:1908.03881}
}

read the original abstract

Silicon wafer and multilayer-coated mirror samples were exposed to impact of drops of molten tin to examine the adhesion behavior and cleaning possibilities. The sticking of tin droplets to horizontal substrates was examined for different surface conditions in a high vacuum chamber. Silicon wafers without a coating, with thick oxide top layer, and also with differently capped Mo/Si multilayer coatings optimized for reflection at a wavelength of 13.5 nm were exposed to tin dripping. Dependent on substrate temperature and coating, adhesion as well as detachment with self-peeling and self-contraction of spreaded drops was observed. The adhesion strength of solidified tin splats decreased strongly with decreasing substrate temperature. Non-sticking surface conditions could be generated by substrate super-cooling. The morphology of non-sticking tin droplets was analyzed by profilometry. Adhering deposits were converted in-situ via induction of tin pest by infection with gray tin powder and cooling of the samples. The phase transition was recorded by photographic imaging. It caused material embrittlement and detachment after structural transformation within several hours and enabled facile removal of tin contamination without coating damage. The temperature-dependent contamination behavior of tin drops has implications for the preferred operating conditions of extreme ultraviolet light sources with collection optics exposed to tin debris.

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Josserand, S.T

C. Josserand, S.T. Thoroddsen, Annu. Rev. Fluid Mech. 48, 365 (2016)

work page 2016

[2] [2]

Maringer, Mater

R.E. Maringer, Mater. Sci. Eng. 98, 13 (1988)

work page 1988

[3] [3]

Chandra, P

S. Chandra, P. Fauchet, J. Therm. Spray Technol. 18, 148 (2009)

work page 2009

[4] [4]

Droplet sticking was found to be strong at surface temperatures of ~90 °C

Conclusions We have studied in detail the adhesion beh avior of molten tin droplets dripped under vacuum onto smooth samples with different coatings at substrate temperatures of -50 °C, 23 °C and ~90 °C. Droplet sticking was found to be strong at surface temperatures of ~90 °C. M ainly non-sticking behavior was observed at lower temperatures on silicon 32...

work page

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M. Pasandideh-Fard, R. Bhola, S. Chandra, J. Mostaghimi, Int. J. Heat Mass Tran. 41, 2929 (1998)

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