IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i20p3179-d1496479.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/20/3179/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/20/3179/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    2. Carstensen, Kai & Heinrich, Markus & Reif, Magnus & Wolters, Maik H., 2020. "Predicting ordinary and severe recessions with a three-state Markov-switching dynamic factor model," International Journal of Forecasting, Elsevier, vol. 36(3), pages 829-850.
    3. Hou-Tai Chang & Ping-Huai Wang & Wei-Fang Chen & Chen-Ju Lin, 2022. "Risk Assessment of Early Lung Cancer with LDCT and Health Examinations," IJERPH, MDPI, vol. 19(8), pages 1-12, April.
    4. Wang, Qiao & Zhou, Wei & Cheng, Yonggang & Ma, Gang & Chang, Xiaolin & Miao, Yu & Chen, E, 2018. "Regularized moving least-square method and regularized improved interpolating moving least-square method with nonsingular moment matrices," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 120-145.
    5. Mkhadri, Abdallah & Ouhourane, Mohamed, 2013. "An extended variable inclusion and shrinkage algorithm for correlated variables," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 631-644.
    6. Lucian Belascu & Alexandra Horobet & Georgiana Vrinceanu & Consuela Popescu, 2021. "Performance Dissimilarities in European Union Manufacturing: The Effect of Ownership and Technological Intensity," Sustainability, MDPI, vol. 13(18), pages 1-19, September.
    7. Candelon, B. & Hurlin, C. & Tokpavi, S., 2012. "Sampling error and double shrinkage estimation of minimum variance portfolios," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 511-527.
    8. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2025. "Specification Choices in Quantile Regression for Empirical Macroeconomics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 40(1), pages 57-73, January.
    9. Kim, Hyun Hak & Swanson, Norman R., 2018. "Mining big data using parsimonious factor, machine learning, variable selection and shrinkage methods," International Journal of Forecasting, Elsevier, vol. 34(2), pages 339-354.
    10. Shuichi Kawano, 2014. "Selection of tuning parameters in bridge regression models via Bayesian information criterion," Statistical Papers, Springer, vol. 55(4), pages 1207-1223, November.
    11. Chuliá, Helena & Garrón, Ignacio & Uribe, Jorge M., 2024. "Daily growth at risk: Financial or real drivers? The answer is not always the same," International Journal of Forecasting, Elsevier, vol. 40(2), pages 762-776.
    12. Enrico Bergamini & Georg Zachmann, 2020. "Exploring EU’s Regional Potential in Low-Carbon Technologies," Sustainability, MDPI, vol. 13(1), pages 1-28, December.
    13. Qianyun Li & Runmin Shi & Faming Liang, 2019. "Drug sensitivity prediction with high-dimensional mixture regression," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-18, February.
    14. Jung, Yoon Mo & Whang, Joyce Jiyoung & Yun, Sangwoon, 2020. "Sparse probabilistic K-means," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    15. Christopher J Greenwood & George J Youssef & Primrose Letcher & Jacqui A Macdonald & Lauryn J Hagg & Ann Sanson & Jenn Mcintosh & Delyse M Hutchinson & John W Toumbourou & Matthew Fuller-Tyszkiewicz &, 2020. "A comparison of penalised regression methods for informing the selection of predictive markers," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-14, November.
    16. Norman R. Swanson & Weiqi Xiong, 2018. "Big data analytics in economics: What have we learned so far, and where should we go from here?," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 51(3), pages 695-746, August.
    17. Joseph, Andreas & Potjagailo, Galina & Chakraborty, Chiranjit & Kapetanios, George, 2024. "Forecasting UK inflation bottom up," International Journal of Forecasting, Elsevier, vol. 40(4), pages 1521-1538.
    18. Soave, David & Lawless, Jerald F., 2023. "Regularized regression for two phase failure time studies," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    19. Moharil Janhavi & May Paul & Gaile Daniel P. & Blair Rachael Hageman, 2016. "Belief propagation in genotype-phenotype networks," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 15(1), pages 39-53, March.
    20. Won Hee Lee, 2023. "The Choice of Machine Learning Algorithms Impacts the Association between Brain-Predicted Age Difference and Cognitive Function," Mathematics, MDPI, vol. 11(5), pages 1-15, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3179-:d:1496479. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.