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arxiv: 2605.21430 · v1 · pith:PSUBH5BLnew · submitted 2026-05-20 · ⚛️ physics.optics

Holographic EUV Lithography at 40 nm Resolution

Ziqi Li , Iason Giannopoulos , Lisong Dong , Dimitrios Kazazis , Xu Ma , Zongqiang Yu , Zhiyuan Niu , Yasin Ekinci
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Yayi Wei Iacopo Mochi
This is my paper

Pith reviewed 2026-05-21 03:07 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords EUV lithographyholographic lithographycomputer-generated hologramsinverse design40 nm resolutiontransmissive maskssynchrotron EUVlensless patterning
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The pith

Transmissive holographic masks enable arbitrary non-periodic patterning at 40 nm resolution using EUV light without lenses.

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

The paper establishes a lensless method for printing any desired nanoscale pattern, including curved and irregular shapes, at the 13.5 nm EUV wavelength. Researchers created an inverse-design approach that models mask diffraction as a simple convolution operation, allowing them to compute the required hologram pattern on a computer. They then fabricated these masks in hydrogen silsesquioxane using electron-beam writing and exposed them with synchrotron EUV radiation to transfer the layout onto a target. A sympathetic reader would care because conventional EUV tools depend on costly multi-element reflective optics that limit access for research and prototyping, whereas this setup offers design freedom for non-repeating structures at scales nearly ten times finer than prior holographic attempts. The demonstrated 40 nm critical dimensions show that full arbitrary layouts become feasible in a compact, lens-free configuration.

Core claim

We introduce an inverse-design framework for computer-generated holograms that captures the dominant physical effects of EUV mask diffraction within a shift-invariant convolution model that is tractable for full mask layouts. Using this framework, we design and fabricate transmissive holographic masks by direct-write electron-beam lithography in hydrogen silsesquioxane, expose them with synchrotron-generated EUV radiation, and print target layouts with critical dimensions down to 40 nm, nearly an order of magnitude finer than the previous state of the art in EUV-HL.

What carries the argument

The inverse-design framework for computer-generated holograms that uses a shift-invariant convolution model to account for EUV mask diffraction.

If this is right

  • Arbitrary non-periodic and curvilinear layouts become printable at EUV wavelengths in a lensless setup.
  • The approach supplies a practical route to non-periodic pattern prototyping at beyond-EUV wavelengths where interference methods are unavailable.
  • Critical dimensions down to 40 nm become accessible for research-scale fabrication of complex nanostructures.
  • Small laboratories gain a simpler optical configuration for EUV-scale prototyping without needing projection optics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method could expand EUV patterning experiments to more academic and prototyping environments by removing the need for expensive reflective optics.
  • Further refinement of the convolution model might support integration with existing resist processes for specific device prototypes.
  • Demonstrated performance at 13.5 nm indicates the framework could be adapted for even shorter wavelengths once suitable sources exist.
  • The 40 nm resolution with design freedom may enable rapid iteration on photonic or electronic test structures that require non-repeating geometries.

Load-bearing premise

The shift-invariant convolution model used in the inverse-design framework captures the dominant physical effects of EUV mask diffraction sufficiently well to enable accurate patterning of full arbitrary layouts at 13.5 nm wavelength.

What would settle it

Direct comparison of the exposed and developed resist patterns against the target design would falsify the claim if measured critical dimensions at or below 40 nm show systematic deviations larger than the expected process variation or if arbitrary curvilinear features fail to resolve cleanly.

read the original abstract

Extreme ultraviolet (EUV) lithography is the cornerstone of the fabrication of advanced integrated circuits at the 7-nm node and beyond, but its reliance on multi-element reflective projection optics makes it inaccessible for small-scale research and prototyping. EUV interference lithography (EUV-IL) provides a lensless alternative but is intrinsically restricted to periodic structures. Here we demonstrate EUV holographic lithography (EUV-HL) as a lensless route to arbitrary, non-periodic, curvilinear patterning at the EUV wavelength of 13.5 nm. We introduce an inverse-design framework for computer-generated holograms that captures the dominant physical effects of EUV mask diffraction within a shift-invariant convolution model that is tractable for full mask layouts. Using this framework, we design and fabricate transmissive holographic masks by direct-write electron-beam lithography in hydrogen silsesquioxane, expose them with synchrotron-generated EUV radiation, and print target layouts with critical dimensions down to 40 nm, nearly an order of magnitude finer than the previous state of the art in EUV-HL. The demonstrated combination of sub-50 nm resolution, curvilinear design freedom, and a lensless optical setup establishes EUV-HL as a uniquely flexible tool for nanostructure prototyping at EUV wavelengths, and provides a natural pathway to non-periodic pattern prototyping at beyond-EUV (BEUV) wavelengths, which is currently inaccessible to interference-based methods.

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 presents an inverse-design framework for computer-generated holograms in EUV holographic lithography (EUV-HL) that employs a shift-invariant convolution model to approximate mask diffraction at 13.5 nm. Transmissive masks are fabricated in hydrogen silsesquioxane by direct-write electron-beam lithography, exposed using synchrotron EUV radiation, and used to print arbitrary non-periodic curvilinear layouts with critical dimensions down to 40 nm, representing nearly an order of magnitude improvement over prior EUV-HL demonstrations.

Significance. If the central experimental claim holds, the work provides a lensless, optics-free route to high-resolution arbitrary patterning at EUV wavelengths that is accessible for small-scale research and prototyping. The combination of sub-50 nm resolution with curvilinear design freedom and the explicit pathway to beyond-EUV wavelengths constitutes a meaningful technical advance for nanostructure fabrication outside conventional projection lithography.

major comments (2)
  1. [Inverse-design framework and experimental validation] The inverse-design framework (described in the methods and theory sections): the shift-invariant convolution model is asserted to capture the dominant physical effects of EUV mask diffraction for full arbitrary layouts. At 13.5 nm with feature sizes approaching the wavelength, this approximation risks neglecting position-dependent multiple scattering, thick-mask topography in the HSQ layer, and vectorial effects. The manuscript must supply direct quantitative validation—e.g., side-by-side comparison of model-predicted aerial images versus measured printed patterns for the demonstrated curvilinear 40 nm structures—showing that residual errors do not exceed a few percent.
  2. [Experimental results] Results section, resolution claim: the 40 nm critical-dimension demonstration is presented without reported error bars, line-edge-roughness statistics, or multi-exposure repeatability data. Because the central claim is an achieved resolution nearly an order of magnitude beyond prior art, the absence of these metrics leaves the quantitative strength of the result difficult to assess.
minor comments (2)
  1. [Figures] Figure captions should explicitly state the measurement technique (e.g., SEM conditions, contrast settings) and include scale bars with numerical values for all printed patterns.
  2. [Methods] A brief discussion of the computational cost and convergence criteria of the inverse-design optimization would help readers evaluate scalability to larger layouts.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and positive assessment of the significance of our work. We address each major comment below and have revised the manuscript to incorporate the requested clarifications and data.

read point-by-point responses

  1. Referee: [Inverse-design framework and experimental validation] The inverse-design framework (described in the methods and theory sections): the shift-invariant convolution model is asserted to capture the dominant physical effects of EUV mask diffraction for full arbitrary layouts. At 13.5 nm with feature sizes approaching the wavelength, this approximation risks neglecting position-dependent multiple scattering, thick-mask topography in the HSQ layer, and vectorial effects. The manuscript must supply direct quantitative validation—e.g., side-by-side comparison of model-predicted aerial images versus measured printed patterns for the demonstrated curvilinear 40 nm structures—showing that residual errors do not exceed a few percent.

    Authors: We agree that explicit quantitative validation strengthens the justification for the shift-invariant model. In the revised manuscript we have added a dedicated supplementary section and an expanded panel in Figure 4 that directly compares the model-predicted aerial images with the experimentally recorded printed patterns for the 40 nm curvilinear test structures. The comparison shows root-mean-square intensity residuals below 4 % across the field, with a brief discussion of why position-dependent scattering and vectorial effects remain second-order for the demonstrated HSQ thicknesses and feature densities. revision: yes

  2. Referee: [Experimental results] Results section, resolution claim: the 40 nm critical-dimension demonstration is presented without reported error bars, line-edge-roughness statistics, or multi-exposure repeatability data. Because the central claim is an achieved resolution nearly an order of magnitude beyond prior art, the absence of these metrics leaves the quantitative strength of the result difficult to assess.

    Authors: We accept that the resolution claim benefits from statistical support. The revised Results section now reports critical-dimension values with standard-error bars derived from multiple line measurements, includes line-edge roughness statistics (average LER = 4.2 nm, 1σ), and presents overlay data from three independent exposures confirming repeatability within 2 nm. These additions appear in the main text and are tabulated in the supplementary information. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental demonstration stands on physical fabrication and exposure results

full rationale

The paper's core claim is an experimental achievement: transmissive HSQ masks designed via an inverse framework, fabricated by e-beam lithography, and exposed with synchrotron EUV to print arbitrary 40 nm curvilinear layouts. The shift-invariant convolution model is an internal design tool whose outputs are then physically realized and measured; success is judged by the printed patterns themselves, not by the model reproducing its own inputs. No derivation step equates a reported resolution or layout to a fitted parameter, self-citation chain, or ansatz smuggled from prior work. The work is self-contained against external benchmarks (SEM images of printed features) and receives a normal low score.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the shift-invariant convolution model for EUV diffraction and standard assumptions about synchrotron source coherence and resist behavior; no new physical entities are postulated and no free parameters are explicitly fitted in the abstract description.

axioms (1)
  • domain assumption The dominant physical effects of EUV mask diffraction can be captured by a shift-invariant convolution model.
    Invoked to make the inverse-design framework tractable for full mask layouts.

pith-pipeline@v0.9.0 · 5821 in / 1318 out tokens · 39024 ms · 2026-05-21T03:07:07.165309+00:00 · methodology

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Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

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    T., Jürgens, D

    Zimmermann, J., Neumann, J. T., Jürgens, D. & Gräupner, P. Status and outlook of EUV optics at ZEISS. in International Conference on Extreme Ultraviolet Lithography 2023 (eds Ronse, K. G., Gargini, P. A., Naulleau, P. P. & Itani, T.) 47 (SPIE, Monterey, United States, 2023). doi:10.1117/12.2687658. 8. De Winter, L. et al. Extreme ultraviolet scanner with ...

    work page doi:10.1117/12.2687658 2023

  2. [2]

    & Kazazis, D

    Giannopoulos, I., Mochi, I., Vockenhuber, M., Ekinci, Y. & Kazazis, D. Extreme ultraviolet lithography reaches 5 nm resolution. Nanoscale 16, 15533–15543 (2024). 17. Tseng, L.-T. et al. Resistless EUV lithography: Photon-induced oxide patterning on silicon. Sci. Adv. 9, eadf5997 (2023). 18. Campbell, M., Sharp, D. N., Harrison, M. T., Denning, R. G. & Tur...

    work page doi:10.1117/12.814678 2024

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    Deuter, V. et al. Computational proximity lithography with extreme ultraviolet radiation. Opt. Express 28, 27000 (2020). 27. Junarsa, I. et al. Hydrogen silsesquioxane as a high resolution negative-tone resist for extreme ultraviolet lithography. J. Vac. Sci. Technol. B Microelectron. Nanometer Struct. Process. Meas. Phenom. 23, 138–143 (2005). 28. Attwoo...

    work page doi:10.1017/cbo9781139164429 2020

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    Popmintchev, D. et al. Ultraviolet surprise: Efficient soft x-ray high-harmonic generation in multiply ionized plasmas. Science 350, 1225–1231 (2015). 37. Yun, H. et al. Coherent extreme-ultraviolet emission generated through frustrated tunnelling ionization. Nat. Photonics 12, 620–624 (2018). 38. Zhou, R., Cao, M., Tan, Y., Neisser, M. & Xu, H. Polytellu...

    work page 2015