Global-in-time Spectral Duhamel-Picard Method for Post-Exposure Bake Simulation and Physics-Informed Neural Operators for EUV Lithography
Abstract
We present a global-in-time spectral Duhamel-Picard method with polynomial expansions for post-exposure bake (PEB) simulation. The coupled acid-quencher reaction-diffusion equations are reformulated as nonlinear Volterra integral equations using the Duhamel principle. Full trajectories are represented by finite polynomial expansions, with temporal coefficient fields determined over the bake interval by Anderson-accelerated Picard iteration, thereby avoiding sequential time marching. In 3-D PEB simulations, we employ Chebyshev and Legendre temporal bases while evaluating the Duhamel integrals using the corresponding Gaussian quadrature rules. We demonstrate that the proposed method simulates a large domain of 1200×1200×100 voxels on the order of one minute. The representation is further incorporated into a physics-informed neural operator (PINO) with a mixed-transform variant of a factorized Fourier neural operator, which is trained without precomputed solution trajectories. Together, the integral formulation and its PINO extension enable accelerated, time-marching-free prediction of concentration fields at arbitrary times within the bake interval.
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BibTeX
@misc{kim2026globalintime,
title = {{Global-in-time Spectral Duhamel-Picard Method for Post-Exposure Bake Simulation and Physics-Informed Neural Operators for EUV Lithography}},
author = {Doyun Kim and Mircea Dusa and Werner Gilijns and Philippe Leray},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20655},
eprint = {2610.20655},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20655},
}
RIS
TY - UNPB
TI - Global-in-time Spectral Duhamel-Picard Method for Post-Exposure Bake Simulation and Physics-Informed Neural Operators for EUV Lithography
AU - Doyun Kim
AU - Mircea Dusa
AU - Werner Gilijns
AU - Philippe Leray
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.20655
UR - https://arxiv.org/abs/2610.20655
AB - We present a global-in-time spectral Duhamel-Picard method with polynomial expansions for post-exposure bake (PEB) simulation. The coupled acid-quencher reaction-diffusion equations are reformulated as nonlinear Volterra integral equations using the Duhamel principle. Full trajectories are represented by finite polynomial expansions, with temporal coefficient fields determined over the bake interval by Anderson-accelerated Picard iteration, thereby avoiding sequential time marching. In 3-D PEB simulations, we employ Chebyshev and Legendre temporal bases while evaluating the Duhamel integrals using the corresponding Gaussian quadrature rules. We demonstrate that the proposed method simulates a large domain of 1200×1200×100 voxels on the order of one minute. The representation is further incorporated into a physics-informed neural operator (PINO) with a mixed-transform variant of a factorized Fourier neural operator, which is trained without precomputed solution trajectories. Together, the integral formulation and its PINO extension enable accelerated, time-marching-free prediction of concentration fields at arbitrary times within the bake interval.
ER -