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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.09207 |
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| _version_ | 1866912671580815360 |
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| author | Tao, Ze Liu, Fujun Jin, Yuxi Xu, Ke Sun, Minghui Hu, Xiangsheng Cao, Qi Xu, Haoran Wang, Hanxuan |
| author_facet | Tao, Ze Liu, Fujun Jin, Yuxi Xu, Ke Sun, Minghui Hu, Xiangsheng Cao, Qi Xu, Haoran Wang, Hanxuan |
| contents | Thermal field reconstruction in post-exposure bake (PEB) is critical for advanced lithography, yet current physics-informed neural networks (PINNs) suffer from inconsistent accuracy due to a misalignment between geometric coordinates, physical fields, and differential operators. To resolve this, we introduce a novel architecture that unifies these elements on a single computation graph by integrating LSTM-gated mechanisms within a Liquid Neural Network (LNN) backbone. This specific combination of gated liquid layers is necessary to dynamically regulate the network's spectral behavior and enforce operator-level consistency, which ensures stable training and high-fidelity predictions. Applied to a 2D PEB scenario with internal heat generation and convective boundaries, our model formulates residuals via differential forms and a composite loss functional. The results demonstrate rapid convergence, uniformly low errors, strong agreement with FEM benchmarks, and stable training without late-stage oscillations, outperforming existing baselines in accuracy and robustness. Our framework thus establishes a reliable foundation for high-fidelity thermal modeling and offers a transferable strategy for operator-consistent neural surrogates in other physical domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09207 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Operator-Consistent Physics-Informed Learning for Wafer Thermal Reconstruction in Lithography Tao, Ze Liu, Fujun Jin, Yuxi Xu, Ke Sun, Minghui Hu, Xiangsheng Cao, Qi Xu, Haoran Wang, Hanxuan Mathematical Physics Thermal field reconstruction in post-exposure bake (PEB) is critical for advanced lithography, yet current physics-informed neural networks (PINNs) suffer from inconsistent accuracy due to a misalignment between geometric coordinates, physical fields, and differential operators. To resolve this, we introduce a novel architecture that unifies these elements on a single computation graph by integrating LSTM-gated mechanisms within a Liquid Neural Network (LNN) backbone. This specific combination of gated liquid layers is necessary to dynamically regulate the network's spectral behavior and enforce operator-level consistency, which ensures stable training and high-fidelity predictions. Applied to a 2D PEB scenario with internal heat generation and convective boundaries, our model formulates residuals via differential forms and a composite loss functional. The results demonstrate rapid convergence, uniformly low errors, strong agreement with FEM benchmarks, and stable training without late-stage oscillations, outperforming existing baselines in accuracy and robustness. Our framework thus establishes a reliable foundation for high-fidelity thermal modeling and offers a transferable strategy for operator-consistent neural surrogates in other physical domains. |
| title | Operator-Consistent Physics-Informed Learning for Wafer Thermal Reconstruction in Lithography |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2510.09207 |