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Enhancing Parameters Tuning of Overlay Models with Ridge Regression: Addressing Multicollinearity in High-Dimensional Data

Author

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  • Aris Magklaras

    (Department of Electrical and Computer Engineering, University of Patras, 26504 Patras, Greece)

  • Christos Gogos

    (Department of Informatics and Telecommunications, University of Ioannina, 47100 Arta, Greece)

  • Panayiotis Alefragis

    (Department of Electrical and Computer Engineering, University of Peloponnese, 26334 Patras, Greece)

  • Alexios Birbas

    (Department of Electrical and Computer Engineering, University of Patras, 26504 Patras, Greece)

Abstract

The extreme ultraviolet (EUV) photolithography process is a cornerstone of semiconductor manufacturing and operates under demanding precision standards realized via nanometer-level overlay (OVL) error modeling. This procedure allows the machine to anticipate and correct OVL errors before impacting the wafer, thereby facilitating near-optimal image exposure while simultaneously minimizing the overall OVL error. Such models are usually high dimensional and exhibit rigorous statistical phenomena such as collinearities that play a crucial role in the process of tuning their parameters. Ordinary least squares (OLS) is the most widely used method for parameters tuning of overlay models, but in most cases it fails to compensate for such phenomena. In this paper, we propose the usage of ridge regression, a widely known machine learning (ML) algorithm especially suitable for datasets that exhibit high multicollinearity. The proposed method was applied in perturbed data from a 300 mm wafer fab, and the results show reduced residuals when ridge regression is applied instead of OLS.

Suggested Citation

  • Aris Magklaras & Christos Gogos & Panayiotis Alefragis & Alexios Birbas, 2024. "Enhancing Parameters Tuning of Overlay Models with Ridge Regression: Addressing Multicollinearity in High-Dimensional Data," Mathematics, MDPI, vol. 12(20), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3179-:d:1496479
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    References listed on IDEAS

    as
    1. Jie Yu & S. Qin, 2009. "Variance component analysis based fault diagnosis of multi-layer overlay lithography processes," IISE Transactions, Taylor & Francis Journals, vol. 41(9), pages 764-775.
    2. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    3. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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