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IJAT Vol.19 No.5 pp. 879-889
doi: 10.20965/ijat.2025.p0879
(2025)

Research Paper:

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Real-Time Interfacial Pressure Prediction in CMP Using Machine Learning Surrogates of Finite Element Simulations

Tom Rothe*,***,†, Andre Lauff**, Alexey Shaporin*,*** ORCID Icon, Peter Thieme**, Mudassir Ali Sayyed*,*** ORCID Icon, Knut Gottfried***, Jörg Schuster*,*** ORCID Icon, Jan Langer*** ORCID Icon, Linda Jäckel*,*** ORCID Icon, Martin Stoll* ORCID Icon, and Harald Kuhn*,*** ORCID Icon

*Chemnitz University of Technology
Straße der Nationen 62, Chemnitz 09111, Germany

**Infineon Technologies Dresden GmbH & Co. KG
Dresden, Germany

***Fraunhofer Institute for Electronic Nano Systems ENAS
Chemnitz, Germany

†Corresponding author

Received:
February 5, 2025
Accepted:
June 28, 2025
Published:
September 5, 2025
Creative Commons License
Keywords:
chemical-mechanical polishing, machine learning, semiconductor process modelling, surrogate modelling, finite-element simulation
Abstract

Achieving uniform material removal in chemical-mechanical polishing requires precise tuning of interfacial pressure. High-fidelity finite-element simulations can accurately model pressure profiles essential for this tuning process. However, these simulations are too computationally intensive for extensive parameter studies. This work introduces a surrogate modelling approach for two-dimensional radial pressure profiles in five-zone polishing heads. Functional principal component analysis identifies a compact, data-driven basis from a dataset of finite-element-generated pressure profiles. Kernel ridge regression then maps applied zone loadings to the extracted coefficients. Validation across diverse loading scenarios shows that the proposed surrogate matches the accuracy of detailed finite-element simulations while delivering millisecond-level predictions and clear interpretability which inputs drive specific pressure‐profile changes. Researchers with existing high-fidelity models can adopt this framework to develop fast, interpretable surrogates for real-time process optimization.

Cite this article as:
T. Rothe, A. Lauff, A. Shaporin, P. Thieme, M. Sayyed, K. Gottfried, J. Schuster, J. Langer, L. Jäckel, M. Stoll, and H. Kuhn, “Real-Time Interfacial Pressure Prediction in CMP Using Machine Learning Surrogates of Finite Element Simulations,” Int. J. Automation Technol., Vol.19 No.5, pp. 879-889, 2025.
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References
  1. [1] S.-J. Shiul, C.-C. Yu, S.-H. Shen, and A.-J. Sul, “Multivariable control of multi-zone chemical mechanical polishing,” 2004 Semiconductor Manufacturing Technology Workshop Proc. (IEEE Cat. No.04EX846), pp. 107-110, 2004.
  2. [2] K.-S. Chen, H.-M. Yeh, J.-L. Yan, and Y.-T. Chen, “Finite-element analysis on wafer-level CMP contact stress: Reinvestigated issues and the effects of selected process parameters,” The Int. J. of Advanced Manufacturing Technology, Vol.42, pp. 1118-1130, 2009. https://doi.org/10.1007/s00170-008-1672-5
  3. [3] J. Yi, Y. Sheng, and C. S. Xu, “Neural network based uniformity profile control of linear chemical-mechanical planarization,” IEEE Trans. on Semiconductor Manufacturing, Vol.16, No.4, pp. 609-620, 2003.
  4. [4] T. Wang, X. Lu, D. Zhao, and Y. He, “Contact stress non-uniformity of wafer surface for multi-zone chemical mechanical polishing process,” Science China Technological Sciences, Vol.56, pp. 1974-1979, 2013. https://doi.org/10.1007/s11431-013-5245-y
  5. [5] T. Wang and X. Lu, “Numerical and experimental investigation on multi-zone chemical mechanical planarization,” Microelectronic Engineering, Vol.88, No.11, pp. 3327-3332, 2011. https://doi.org/10.1016/j.mee.2011.08.011
  6. [6] C. Ludwig and M. Kuna, “An analytical approach to determine the pressure distribution during chemical mechanical polishing,” J. of Electronic Materials, Vol.41, pp. 2606-2612, 2012. https://doi.org/10.1007/s11664-012-2151-1
  7. [7] G. Fu and A. Chandra, “An analytical dishing and step height reduction model for chemical mechanical planarization (CMP),” IEEE Trans. on Semiconductor Manufacturing, Vol.16, No.3, pp. 477-485, 2003. https://doi.org/10.1109/TSM.2003.815202
  8. [8] G. Fu and A. Chandra, “The relationship between wafer surface pressure and wafer backside loading in chemical mechanical polishing,” Thin Solid Films, Vol.474, Issues 1-2, pp. 217-221, 2005. https://doi.org/10.1016/j.tsf.2004.09.010
  9. [9] J. Kudela and R. Matousek, “Recent advances and applications of surrogate models for finite element method computations: A review,” Soft Computing, Vol.26, No.24, pp. 13709-13733, 2022. https://doi.org/10.1007/s00500-022-07362-8
  10. [10] R. Alizadeh, J. K. Allen, and F. Mistree, “Managing computational complexity using surrogate models: A critical review,” Research in Engineering Design, Vol.31, No.3, pp. 275-298, 2020. https://doi.org/10.1007/s00163-020-00336-7
  11. [11] Y. Cho, M. Kim, M. Hong, J. Han, H. J. Kim, H. Kim, and H. Lee, “Prediction of normalized material removal rate profile based on deep neural network in five-zone carrier head cmp system,” Int. J. of Precision Engineering and Manufacturing-Green Technology, Vol.12, pp. 869-883, 2025. https://doi.org/10.1007/s40684-025-00698-0
  12. [12] M. Iwayama, S. Wu, C. Liu, and R. Yoshida, “Functional output regression for machine learning in materials science,” J. of Chemical Information and Modeling, Vol.62, No.20, pp. 4837-4851, 2022. https://doi.org/10.1021/acs.jcim.2c00626
  13. [13] S. Vijayaraghavan, L. Wu, L. Noels, S. Bordas, S. Natarajan, and L. A. Beex, “A data-driven reduced-order surrogate model for entire elastoplastic simulations applied to representative volume elements,” Scientific Reports, Vol.13, No.1, Article No.12781, 2023. https://doi.org/10.1038/s41598-023-38104-x
  14. [14] ANSYS, Inc., “Ansys academic research mechanical.” https://www.ansys.com [Accessed August 20, 2025]
  15. [15] I. Goodfellow, Y. Bengio, and A. Courville, “Deep Learning,” MIT Press, 2016.
  16. [16] D. Gottlieb and C.-W. Shu, “On the gibbs phenomenon and its resolution,” SIAM Review, Vol.39, No.4, pp. 644-668, 1997. https://doi.org/10.1137/S0036144596301390
  17. [17] P. Kokoszka and M. Reimherr, “Introduction to Functional Data Analysis,” CRC Press, 2017. https://doi.org/10.1201/9781315117416
  18. [18] R. Ghanem and P. Spanos, “Stochastic Finite Elements: A Spectral Approach,” Dover Publications, 2003.
  19. [19] C. Ramos-Carreño, J. L. Torrecilla, M. Carbajo Berrocal, P. Marcos Manchón, and A. Suárez, “scikit-fda: A Python package for functional data analysis,” J. of Statistical Software, Vol.109, No.2, pp. 1-37, 2024. https://doi.org/10.18637/jss.v109.i02
  20. [20] T. scikit-fda developers, “scikit-fda: Functional data analysis in Python,” 2024. https://doi.org/10.5281/zenodo.3468127.
  21. [21] A. E. Hoerl and R. W. Kennard, “Ridge regression: Biased estimation for nonorthogonal problems,” Technometrics, Vol.12, No.1, pp. 55-67, 1970. https://doi.org/10.2307/1267351
  22. [22] R. Kohavi, “A study of cross-validation and bootstrap for accuracy estimation and model selection,” Proc. of the 14th Int. Joint Conf. on Artificial Intelligence, Vol.2, pp. 1137-1145, 1995.
  23. [23] A. J. Smola and B. Schölkopf, “On a kernel-based method for pattern recognition, regression, approximation, and operator inversion,” Algorithmica, Vol.22, pp. 211-231, 1998. https://doi.org/10.1007/PL00013831
  24. [24] F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, and D. Cournapean, “Scikit-learn: Machine learning in Python,” J. of Machine Learning Research, Vol.12, pp. 2825-2830, 2011.
  25. [25] Y. Hashimoto, T. Furumoto, T. Sato, N. Suzuki, H. Yasuda, S. Yamaki, and Y. Mochizuki, “Novel method to visualize preston’s coefficient distribution for chemical mechanical polishing process,” Japanese J. of Applied Physics, Vol.61, No.11, Article No.116502, 2022. https://doi.org/10.35848/1347-4065/ac916b
  26. [26] C. Zhao, J. Li, D. Yi, B. Li, and J. Cao, “Wafer flatness modeling in chemical mechanical polishing,” J. of Electronic Materials, Vol.49, pp. 353-363, 2020. https://doi.org/10.1007/s11664-019-07799-y
  27. [27] A. Fukuda, T. Fukuda, A. Fukunaga, and M. Tsujimura, “Influence of wafer edge geometry on removal rate profile in chemical mechanical polishing: Wafer edge roll-off and notch,” Japanese J. of Applied Physics, Vol.51, No.5S, Article No.05EF01, 2012. https://doi.org/10.1143/JJAP.51.05EF01
  28. [28] N. Suzuki, Y. Hashimoto, H. Yasuda, S. Yamaki, and Y. Mochizuki, “Prediction of polishing pressure distribution in cmp process with airbag type wafer carrier,” CIRP Annals, Vol.66, No.1, pp. 329-332, 2017. https://doi.org/10.1016/j.cirp.2017.04.088

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Last updated on Sep. 05, 2025