Gaussian Process Regression for Virtual Metrology of Microchip Quality and the Resulting Selective Sampling Scheme

  • Tyler Darwin
  • Roman Garnett
  • Dragan Djurdjanovic
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


Manufacturing of integrated circuits involves many sequential processes executed to nanoscale tolerances, and the yield depends on the often-unmeasured quality of intermediate steps. Taking physical quality measurements in this high-throughput industry can be expensive and time-consuming. Instead, we seek to predict product quality characteristics using readily available sensor readings of the tool environment during processing of each wafer and employ Gaussian Process Regression (GPR) paradigm to realize this Virtual Metrology (VM) concept. Convergence of the GPR based VM estimation of product quality is hastened through an active sampling scheme, whereby the predictive uncertainty of the GPR model informs which wafer’s quality to measure next in order to obtain maximal additional information for the VM model. We evaluate these methods using a large dataset collected from a plasma-enhanced chemical vapor deposition (PECVD) process, with relevant tool sensor readings and the corresponding physical measurements of mean film thicknesses for 32,000 wafers. By selecting which wafers to physically measure for VM model updates, the GPR based VM method achieves ~10% greater accuracy on average than the partial least squares based method.


Virtual metrology Gaussian process regression Plasma-enhanced chemical vapor deposition Semiconductor manufacturing Virtual metrology Process drift 


  1. 1.
    Ringwood, J.V., Lynn, S., Bacelli, G., Ma, B., Ragnioli, E., McLoon, S.: Estimation and control in semiconductor etch: practice and possibilities. IEEE Trans. Semicond. Manuf. 23(1), 87–98 (2010)CrossRefGoogle Scholar
  2. 2.
    An-Jhih, S., Jeng, J.-C., Huang, H.-P., Cheng-Ching, Yu., Hung, S.-Y., Chao, C.-K.: Control relevant issues in semiconductor manufacturing: overview with some new results. Control Eng. Pract. 15(10), 1268–1279 (2007)CrossRefGoogle Scholar
  3. 3.
    Yang, Y., Wang, M., Kushner, M.J.: Progress, opportunities and challenges in modeling of plasma etching. In: Proceedings of the 2008 IEEE International Interconnect Technology Conference (IITC), Burlingame, CA, USA, 1–4 June 2008 (2008).
  4. 4.
    Hirai, T., Kano, M.: Adaptive virtual metrology design for semiconductor dry etching process through locally weighted partial least squares. IEEE Trans. Semicond. Manuf. 28(2), 137–144 (2015)CrossRefGoogle Scholar
  5. 5.
    Bleakie, A., Djurdjanovic, D.: Growing structure multiple model system for quality estimation in manufacturing processes. IEEE Trans. Semicond. Manuf. 29(2), 79–97 (2016)CrossRefGoogle Scholar
  6. 6.
    Lynn, S.A., Ringwood, J., MacGearailt, N.: Global and local virtual metrology models for a plasma etch process. IEEE Trans. Semicond. Manuf. 25(1), 94–103 (2012)CrossRefGoogle Scholar
  7. 7.
    Lee, S., Kang, P., Cho, S.: Probabilistic local reconstruction for k-NN regression and its application to virtual metrology in semiconductor manufacturing. Neurocomputing 131(5), 427–439 (2014)CrossRefGoogle Scholar
  8. 8.
    Rasmussen, C.E.: Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006). ISBN 026218253XGoogle Scholar
  9. 9.
    Garnett, R., Osborne, M.A., Hennig, P.: Active learning of linear embeddings for gaussian processes. In: Proceedings of the 13th Conference on Uncertainty in Artificial Intelligence, Quebec City, Quebec, Canada, 23–27 July 2014, pp. 230–239 (2014)Google Scholar
  10. 10.
    Osborne, M.A., Garnett, R., Roberts, S.J.: Gaussian processes for global optimization. In: Proceedings of the 3rd International Conference on Learning and Intelligent Optimization, 14–18 January 2009, Trento, Italy (2009)Google Scholar
  11. 11.
    Neal, R.M.: Bayesian Learning for Neural Networks. Springer Science and Business Media, New York (1996)CrossRefGoogle Scholar
  12. 12.
    Wold, S., Sjöström, M., Eriksson, L.: PLS-regression: a basic tool of chemometrics. Chemometr. Intell. Lab. Syst. 58(2), 109–130 (2001)CrossRefGoogle Scholar
  13. 13.
    Kullback, S., Leibler, R.A.: On information and sufficiency. Ann. Math. Stat. 22(1), 79–86 (1951)MathSciNetCrossRefGoogle Scholar
  14. 14.
    McInerney, E.J.: Chemical vapor deposition. In: Geng, H. (ed.) Semiconductor Manufacturing Handbook. McGraw-Hill Inc., New York (2005). Chapter 14Google Scholar
  15. 15.
    Bleakie, A., Djurdjanovic, D.: Feature extraction, condition monitoring and fault modeling in semiconductor manufacturing systems. Comput. Ind. 64(3), 203–213 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Tyler Darwin
    • 1
  • Roman Garnett
    • 2
  • Dragan Djurdjanovic
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of Texas at AustinAustinUSA
  2. 2.Department of Computer Science and EngineeringWashington University in St. LouisSt. LouisUSA

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