Physically covariant, curvilinear thick-mask model for full-chip computational lithography

In advanced lithography processes, as the critical dimensions (CD) continue to shrink, the three-dimensional electromagnetic scattering effects of thick masks have become increasingly pronounced. Concurrently, driven by the maturation of inverse lithography technology (ILT) and multi-beam mask writing, curvilinear masks with larger process windows and improved CD uniformity are being increasingly adopted. However, the complex topology of curvilinear masks poses severe challenges to existing Manhattan architecture-based thick-mask models. When applied to curvilinear masks, these traditional models are constrained by their underlying frameworks and must approximate curves using orthogonal line segments. This approach introduces inherent geometric errors and severely compromises the physical covariance of the model. Therefore, how to rigorously preserve the physical covariance of curvilinear mask models while maintaining full-chip computational efficiency has become a core challenge urgently requiring resolution in the field of computational lithography.

 

In a new paper published in Light: Advanced Manufacturing, a team of scientists led by Shiyuan Liu and Hao Jiang at Huazhong University of Science and Technology, and David H. Wei at Yuwei Optica Co., Ltd., has developed a physically covariant curvilinear thick-mask model based on edge diffraction correction for rapid full-chip layout simulation. This framework eliminates computational errors inherent in traditional Manhattan architecture-based thick-mask models. Compared to Finite-Difference Time-Domain benchmarks, the proposed model achieves curvilinear mask near-field RMS error below 0.03 while delivering over a 2600-fold speedup. Relative to conventional thick-mask models, the proposed model reduces prediction error by approximately 2 times and enhances rotational invariance by nearly 10 times. This work offers a robust basis for efficient and accurate forward modeling in computational lithography.

 

The research team derives universal kernels through rigorous simulation and mathematical analysis. The kernels are aligned in real time with full-chip curvilinear edges via multi-channel convolution, ensuring computational efficiency and strict physical covariance. These scientists summarize the contributions of their work:

 

“(1) Derivation of Differential Edge Diffraction Kernels (DEDKs). Based on the projection-slice theorem and Huygens’ principle, we mathematically derive a diffraction kernel produced by an infinitesimal edge segment that is decoupled from specific mask geometries. These DEDKs are directly applicable to arbitrary curvilinear layouts.

 

(2) Construction of a physically covariant mapping between DEDKs and curvilinear edges. By leveraging the physically covariant nature of electromagnetic effects, a mapping relation is constructed between DEDKs and curvilinear edge segments at arbitrary angles, ensuring model consistency and numerical accuracy.

 

(3) Efficient synthesis of mask diffraction effects for full-chip layouts. We introduce a nine-channel tensor convolution framework to perform efficient path integration of DEDKs along mask edges. This approach enables rapid reconstruction of the full-chip diffraction effects and meets the computational efficiency requirements of practical forward modeling for computational lithography.”

 

“This work lays a theoretical foundation for rapid and accurate mask near-field computation in forward computational lithography workflows, and it also offers support for fast optical simulation of metasurfaces and metamaterials,” the scientists added.

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