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Physics-Informed Neural Systems for the Simulation of EUV Electromagnetic Wave Diffraction from a Lithography Mask

Vasiliy A. Es'kin, Egor V. Ivanov

Abstract

Physics-informed neural networks (PINNs) and neural operators (NOs) for solving the problem of diffraction of Extreme Ultraviolet (EUV) electromagnetic waves from contemporary lithography masks are presented. A novel hybrid Waveguide Neural Operator (WGNO) is introduced, based on a waveguide method with its most computationally expensive components replaced by a neural network. To evaluate performance, the accuracy and inference time of PINNs and NOs are compared against modern numerical solvers for a series of problems with known exact solutions. The emphasis is placed on investigation of solution accuracy by considered artificial neural systems for 13.5 nm and 11.2 nm wavelengths. Numerical experiments on realistic 2D and 3D masks demonstrate that PINNs and neural operators achieve competitive accuracy and significantly reduced prediction times, with the proposed WGNO architecture reaching state-of-the-art performance. The presented neural operator has pronounced generalizing properties, meaning that for unseen problem parameters it delivers a solution accuracy close to that for parameters seen in the training dataset. These results provide a highly efficient solution for accelerating the design and optimization workflows of next-generation lithography masks.

Physics-Informed Neural Systems for the Simulation of EUV Electromagnetic Wave Diffraction from a Lithography Mask

Abstract

Physics-informed neural networks (PINNs) and neural operators (NOs) for solving the problem of diffraction of Extreme Ultraviolet (EUV) electromagnetic waves from contemporary lithography masks are presented. A novel hybrid Waveguide Neural Operator (WGNO) is introduced, based on a waveguide method with its most computationally expensive components replaced by a neural network. To evaluate performance, the accuracy and inference time of PINNs and NOs are compared against modern numerical solvers for a series of problems with known exact solutions. The emphasis is placed on investigation of solution accuracy by considered artificial neural systems for 13.5 nm and 11.2 nm wavelengths. Numerical experiments on realistic 2D and 3D masks demonstrate that PINNs and neural operators achieve competitive accuracy and significantly reduced prediction times, with the proposed WGNO architecture reaching state-of-the-art performance. The presented neural operator has pronounced generalizing properties, meaning that for unseen problem parameters it delivers a solution accuracy close to that for parameters seen in the training dataset. These results provide a highly efficient solution for accelerating the design and optimization workflows of next-generation lithography masks.
Paper Structure (18 sections, 32 equations, 18 figures, 6 tables)

This paper contains 18 sections, 32 equations, 18 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Formulation of the problem and basic equations
  3. Solution Methods
  4. Finite Element Method (FEM)
  5. Waveguide Method
  6. Physics-Informed Neural Networks
  7. Waveguide Neural Operator
  8. Numerical Experiments
  9. Validation on Test Problems
  10. 2D Lithography Mask Simulation
  11. Wavelength 13.5 nm
  12. Wavelength 11.2 nm
  13. 3D Lithography Mask Simulation
  14. Generalization
  15. Conclusion
  16. ...and 3 more sections

Figures (18)

  • Figure 1: EUV lithography with (a) and without (b) optical proximity correction of mask.
  • Figure 2: Geometry of the problem
  • Figure 3: Schematic diagram of the waveguide method. Here "F" is forward Fourier transform, "Eigen" is calculating eigenvalues and eigenvectors of system (\ref{['eq13']}) for every layer, "Field calculation" is calculating field with Equations (\ref{['eq14']}) -- (\ref{['eq16']}).
  • Figure 4: Schematic diagram of the general PINN method.
  • Figure 5: Schematic diagram of the waveguide neural operator. Here "F" is forward Fourier transform, "Eigen" is calculating eigenvalues and eigenvectors of system (\ref{['eq13']}) for every layer, "Field calculation" is calculating field with Equations (\ref{['eq14']}) -- (\ref{['eq16']}).
  • ...and 13 more figures