Abstract
We propose an all-reflective two-mirror projection system for extreme ultraviolet (EUV) lithography operating at exposure wavelengths of 13.5~nm (Mo/Si) and 11.2~nm (Ru/Be), delivering a fourfold (4×) demagnification of the periodic mask pattern at a numerical aperture approaching unity (NAmax≈0.993). In contrast to conventional EUV projection objectives that incorporate 6--10 aspheric mirrors with an overall optical throughput of less than 15%, the proposed design redirects each accepted discrete spatial diffraction order scattered by the mask onto the wafer via a dedicated pair of planar mirror facets. The number of reflections is strictly fixed at two for all accepted orders, retaining 50--60% of the power leaving the mask in each accepted order. We derive a spatial geometry providing rigorous optical path length equalization across all diffraction orders, thereby removing order-dependent propagation phase shifts. Individually optimized 30-bilayer Bragg multilayer coatings are designed for each facet using the transfer matrix method combined with global evolutionary optimization algorithms. The architecture is generalized to a three-dimensional vector formulation with a two-dimensionally periodic mask. Utilizing inverse lithography technology, Fourier parameterization, and a differentiable electromagnetic modal waveguide solver, we solve the synthesis problem for binary absorber masks (La absorber on a Ru/Be/Sr multilayer mirror). We demonstrate simulated aerial images of sub-10-nm features on the wafer (isolated peaks with a full width at half maximum (FWHM) of approximately 5.4~nm and line pairs with a critical dimension of 6~nm) and find that the two peaks remain resolved for the tested wafer defocus values from 0 to 5~nm along the z-axis.
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Jun 24, 2026cs.LG
Gradient-based inverse lithography technology~(ILT) for extreme ultraviolet~(EUV) masks is presented. A novel framework treats the differentiable waveguide method and the recently proposed waveguide neural operator~(WGNO) as end-to-end physics engines, recovering the permittivity of the absorber of the mask through automatic differentiation of the full forward diffraction model. Numerical experiments on realistic 2D and 3D absorbers of the mask (TaBN, La, U) at
λ=11.2~nm show that the considered ILT methods make it possible to obtain a mask structure that achieves the desired field on the wafer.
Vasiliy A. Es'kin, Egor V. Ivanov
Jul 28, 2026physics.optics
We present a physics-informed neural operator (PINO) trained with pseudo-spectral frequency-domain (PSFD) equations for electromagnetic (EM) scattering problems in EUV lithography. The Fourier neural operator is factorized into a two-dimensional lateral (
xy) branch and a one-dimensional axial (
z) branch and is trained self-consistently with background decomposition.Thus, the full-vector coupling between the mask and the multilayer response is retained without invoking a finite-order Born approximation. In this way, the computational domain size is significantly reduced, thereby lowering the computational cost. The PINO is trained on approximately 16,000 mask designs from the LithoBench library sampled randomly at each training iteration without using precomputed EM field solutions. The PINO surrogate model yields predictions with a mean absolute error of about
7×10−3 for the scattered intensity of held-out mask patterns relative to the reference PSFD solution. Combined with spectral damping, the PINO warm-start initialization accelerates the background-decomposed PSFD solver on finer discretizations.
Doyun Kim, Werner Gillijns
May 29, 2026cs.LG
In semiconductor manufacturing, lithography projects circuit layouts onto silicon wafers through an optical mask. As circuit features shrink below the wavelength of light, optical diffraction causes the printed patterns to deviate from their intended layouts. Inverse Lithography Technology (ILT) addresses this challenge by generating optimized masks that enhance the fidelity of pattern transfer onto wafers. While ILT resembles an image synthesis task, its reliance on explicit physical metrics for mask evaluation limits the applicability of existing generative models. We introduce LithoGRPO, an ILT framework that integrates the flow-matching paradigm with GRPO-based reinforcement learning (RL) fine-tuning, enabling efficient exploration of diverse masks for a given target layout. Unlike purely generative or optimization-based approaches, RL in LithoGRPO exploits the explicitly defined, physics-based reward function of ILT, enabling optimization under complex, process-aware constraints. To the best of our knowledge, this is the first framework that unifies flow matching and RL for mask optimization. To improve RL sampling efficiency, we propose a fast shot-counting algorithm for manufacturability evaluation, achieving over 130x speedup while preserving the mask ranking of the traditional shot-count metric. Extensive experiments demonstrate that LithoGRPO achieves state-of-the-art performance over both optimization-based and learning-based methods, while maintaining efficient mask generation.
Yao Lai, Xuyuan Xiong, Zeyue Xue +7