skip to main content
10.1145/3508352.3549398acmconferencesArticle/Chapter ViewAbstractPublication PagesiccadConference Proceedingsconference-collections
research-article

DeePEB: A Neural Partial Differential Equation Solver for Post Exposure Baking Simulation in Lithography

Published: 22 December 2022 Publication History

Abstract

Post Exposure Baking (PEB) has been widely utilized in advanced lithography. PEB simulation is critical in the lithography simulation flow, as it bridges the optical simulation result and the final developed profile in the photoresist. The process of PEB can be described by coupled partial differential equations (PDE) and corresponding boundary and initial conditions. Recent years have witnessed growing presence of machine learning algorithms in lithography simulation, while PEB simulation is often ignored or treated with compact models, considering the huge cost of solving PDEs exactly. In this work, based on the observation of the physical essence of PEB, we propose DeePEB: a neural PDE Solver for PEB simulation. This model is capable of predicting the PEB latent image with high accuracy and >100 × acceleration (compared to the commercial rigorous simulation tool), paving the way for efficient and accurate photoresist modeling in lithography simulation and layout optimization.

References

[1]
C. A. Mack, Fundamental Principles of Optical Lithography: The Science of Microfabrication, 2007.
[2]
Synopsys, "Sentaurus Lithography," https://www.synopsys.com/silicon/mask-synthesis/sentaurus-lithography.html, 2016.
[3]
W. Ye, M. B. Alawieh, Y. Lin, and D. Z. Pan, "Lithogan: End-to-end lithography modeling with generative adversarial networks," in 2019 56th ACM/IEEE Design Automation Conference (DAC). IEEE, 2019, pp. 1--6.
[4]
W. Ye, M. B. Alawieh, Y. Watanabe, S. Nojima, Y. Lin, and D. Z. Pan, "Tempo: Fast mask topography effect modeling with deep learning," in Proceedings of the 2020 International Symposium on Physical Design, 2020, pp. 127--134.
[5]
H. Yang, Z. Li, K. Sastry, S. Mukhopadhyay, M. Kilgard, A. Anandkumar, B. Khailany, V. Singh, and H. Ren, "Generic lithography modeling with dual-band optics-inspired neural networks," in 59th Annual Design Automation Conference (DAC) 2022, 2022.
[6]
X. Zhou, M. Bohn, and M. Braylovska, "Lithography simulation using machine learning," Apr. 21 2022, uS Patent App. 17/467,682.
[7]
H. Yang, S. Jing, Z. Yi, Y. Bei, and E. Young, "Layout hotspot detection with feature tensor generation and deep biased learning," in the 54th Annual Design Automation Conference 2017, 2017.
[8]
Ding, Duo, Torres, J., Andres, Pan, David, and Z., "High performance lithography hotspot detection with successively refined pattern identifications and machine learning." tcad, vol. 30, no. 11, pp. 1621--1634, 2011.
[9]
S. Shim, S. Choi, and Y. Shin, "Machine learning-based 3D resist model," in Optical Microlithography XXX, A. Erdmann and J. Kye, Eds., vol. 10147, International Society for Optics and Photonics. SPIE, 2017, pp. 408 -- 417. [Online].
[10]
Y. Watanabe, T. Kimura, T. Matsunawa, and S. Nojima, "Accurate lithography simulation model based on convolutional neural networks," in Optical Microlithography XXX, vol. 10147. International Society for Optics and Photonics, 2017, p. 101470K.
[11]
R. A. Ferguson, J. M. Hutchinson, C. A. Spence, and A. R. Neureuther, "Modeling and simulation of a deep-ultraviolet acid hardening resist," Journal of Vacuum Science & Technology B Microelectronics Processing & Phenomena, vol. 8, no. 6, pp. 1423--1427, 1990.
[12]
H. Fukuda and S. Okazaki, "Kinetic model and simulation for chemical amplification resists," Journal of the Electrochemical Society, vol. 137, no. 2, p. 675, 1990.
[13]
M. Weiß, H. Binder, and R. Schwalm, "Modeling and simulation of a chemically amplified duv resist using the effective acid concept," Microelectronic Engineering, vol. 27, no. 1, pp. 405--408, 1995.
[14]
D. Matiut, A. Erdmann, B. Tollkuehn, and A. Semmler, "New models for the simulation of post-exposure bake of chemically amplifed resists," Proceedings of Spie the International Society for Optical Engineering, vol. 5039, 2003.
[15]
E. H. Croffie, Y. Lei, M. Cheng, and A. R. Neureuther, "Survey of chemically amplified resist models and simulator algorithms," in International Symposium on Microlithography, 2001.
[16]
W. D. Hinsberg, F. A. Houle, M. I. Sanchez, and G. M. Wallraff, "Chemical and physical aspects of the post-exposure baking process used for positive-tone chemically amplified resists," IBM Journal of Research & Development, vol. 45, no. 5, pp. 667--682, 2001.
[17]
F. H. Dill, W. P. Hornberger, P. S. Hauge, and J. M. Shaw, "Characterization of positive photoresist," Electron Devices IEEE Transactions on, vol. 22, no. 7, pp. 445--452, 1975.
[18]
C. Mack, M. J. Maslow, A. Sekiguchi, and R. A. Carpio, "New model for the effect of developer temperature on photoresist dissolution," International Society for Optics and Photonics, vol. 3333, p. 1218, 1998.
[19]
J. A. Sethian, "Fast-marching level-set methods for three-dimensional photolithography development," Proc Spie, vol. 2726, pp. 262--272, 1996.
[20]
W.-K. Jeong and R. T. Whitaker, "A fast iterative method for eikonal equations," SIAM Journal on Scientific Computing, vol. 30, no. 5, pp. 2512--2534, 2008. [Online]. Available: https://github.com/SCIInstitute/StructuredEikonal
[21]
M. Raissi, P. Perdikaris, and G. Karniadakis, "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations," Journal of Computational Physics, vol. 378, pp. 686--707, 2019. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0021999118307125
[22]
. Weinan, E. and B. Yu, "The deep ritz method: A deep learning-based numerical algorithm for solving variational problems," Communications in Mathematics & Statistics, vol. 6, no. 1, pp. 1--12, 2018.
[23]
X. Guo, W. Li, and F. Iorio, "Convolutional neural networks for steady flow approximation," in Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, 2016, pp. 481--490.
[24]
A. Li, R. Chen, A. B. Farimani, and Y. J. Zhang, "Reaction diffusion system prediction based on convolutional neural network," Scientific Reports, vol. 10, no. 1, p. 3894, 2020.
[25]
T. Chen and H. Chen, "Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems," IEEE Trans Neural Netw, vol. 6, no. 4, pp. 911--917, 1995.
[26]
L. Lu, P. Jin, and G. E. Karniadakis, "Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators," 2019.
[27]
N. Kovachki, Z. Li, B. Liu, K. Azizzadenesheli, and A. Anandkumar, "Neural operator: Learning maps between function spaces," 2021.
[28]
Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar, "Fourier neural operator for parametric partial differential equations," arXiv preprint arXiv:2010.08895, 2020.
[29]
N. Kovachki, S. Lanthaler, and S. Mishra, "On universal approximation and error bounds for fourier neural operators," 2021.
[30]
Y. Lin, M. Li, Y. Watanabe, T. Kimura, T. Matsunawa, S. Nojima, and D. Z. Pan, "Data efficient lithography modeling with transfer learning and active data selection," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 38, no. 10, pp. 1900--1913, 2019.
[31]
D. P. Kingma and J. Ba, "Adam: A method for stochastic optimization," 2017.
[32]
A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Kopf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala, "Pytorch: An imperative style, high-performance deep learning library," in Advances in Neural Information Processing Systems 32. Curran Associates, Inc., 2019, pp. 8024--8035. [Online]. Available: http://papers.neurips.cc/paper/9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf
[33]
Y. Watanabe, T. Kimura, T. Matsunawa, and S. Nojima, "Accurate lithography simulation model based on convolutional neural networks," in Spie Advanced Lithography, 2017.
[34]
K. He, X. Zhang, S. Ren, and J. Sun, "Deep residual learning for image recognition," 2015.
[35]
M. Mirza and S. Osindero, "Conditional generative adversarial nets," Computer Science, pp. 2672--2680, 2014.

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences
ICCAD '22: Proceedings of the 41st IEEE/ACM International Conference on Computer-Aided Design
October 2022
1467 pages
ISBN:9781450392174
DOI:10.1145/3508352
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

In-Cooperation

  • IEEE-EDS: Electronic Devices Society
  • IEEE CAS
  • IEEE CEDA

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 22 December 2022

Permissions

Request permissions for this article.

Check for updates

Qualifiers

  • Research-article

Conference

ICCAD '22
Sponsor:
ICCAD '22: IEEE/ACM International Conference on Computer-Aided Design
October 30 - November 3, 2022
California, San Diego

Acceptance Rates

Overall Acceptance Rate 457 of 1,762 submissions, 26%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • 0
    Total Citations
  • 212
    Total Downloads
  • Downloads (Last 12 months)63
  • Downloads (Last 6 weeks)3
Reflects downloads up to 28 Feb 2025

Other Metrics

Citations

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media