Accelerating extreme ultraviolet lithography simulation with weakly guiding approximation and source position dependent transmission cross coefficient formula

Hiroyoshi Tanabe; Akira Jinguji; Atsushi Takahashi

doi:10.1117/1.JMM.23.1.014201

2 January 2024 Accelerating extreme ultraviolet lithography simulation with weakly guiding approximation and source position dependent transmission cross coefficient formula

Hiroyoshi Tanabe, Akira Jinguji, Atsushi Takahashi

Author Affiliations +

Journal of Micro/Nanopatterning, Materials, and Metrology, Vol. 23, Issue 1, 014201 (January 2024). https://doi.org/10.1117/1.JMM.23.1.014201

Abstract

Background

Mask three-dimensional (3D) effects distort diffraction amplitudes from extreme ultraviolet masks. In a previous work, we developed a convolutional neural network (CNN) that predicted distorted diffraction amplitudes very fast from input mask patterns.

Aim

In this work, we reduce both the time for preparing the training data and the time for image intensity integration.

Approach

We reduce the time for preparing the training data by applying weakly guiding approximation to 3D waveguide model. The model solves Helmholtz type coupled vector wave equations of two polarizations. The approximation decomposes the coupled vector wave equations into two scalar wave equations, reducing the computation time to solve the equations. Regarding the image intensity integration, Abbe’s theory has been used in electromagnetic (EM) simulations. The transmission cross coefficient (TCC) formula is known to be faster than Abbe’s theory, but the TCC formula cannot be applied to source position dependent diffraction amplitudes in EM simulations. We derive source position dependent TCC (STCC) formula starting from Abbe’s theory to reduce the image intensity integration time.

Results

Weakly guiding approximation reduces the time of EM simulation by a factor of 5, from 50 to 10 min. STCC formula reduces the time of the image intensity integration by a factor of 140, from 10 to 0.07 s.

Conclusions

The total time of the image intensity prediction for 512 nm×512 nm area on a wafer is ∼0.1 s. A remaining issue is the accuracy of the CNN.

CC BY: © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 International License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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Hiroyoshi Tanabe, Akira Jinguji, and Atsushi Takahashi "Accelerating extreme ultraviolet lithography simulation with weakly guiding approximation and source position dependent transmission cross coefficient formula," Journal of Micro/Nanopatterning, Materials, and Metrology 23(1), 014201 (2 January 2024). https://doi.org/10.1117/1.JMM.23.1.014201

Received: 28 September 2023; Accepted: 14 December 2023; Published: 2 January 2024

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KEYWORDS

3D modeling

3D mask effects

Diffraction

Extreme ultraviolet lithography

Light sources and illumination

Waveguide modes

Waveguides

Background

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Approach

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