NONPARAMETRIC VIRTUAL SENSORS FOR SEMICONDUCTOR MANUFACTURING - Using Information Theoretic Learning and Kernel Machines

Andrea Schirru, Simone Pampuri, Cristina De Luca, Giuseppe De Nicolao

2011

Abstract

In this paper, a novel learning methodology is presented and discussed with reference to the application of virtual sensors in the semiconductor manufacturing environment. Density estimation techniques are used jointly with Renyi’s entropy to define a loss function for the learning problem (relying on Information Theoretic Learning concepts). Furthermore, Reproducing Kernel Hilbert Spaces (RKHS) theory is employed to handle nonlinearities and include regularization capabilities in the model. The proposed algorithm allows to estimate the structure of the predictive model, as well as the associated probabilistic uncertainty, in a nonparametric fashion. The methodology is then validated using simulation studies and process data from the semiconductor manufacturing industry. The proposed approach proves to be especially effective in strongly nongaussian environments and presents notable outlier filtering capabilities.

References

  1. Ackerman, F., Stanton, E., and Bueno, R. (2010). Fat tails, exponents, extreme uncertainty: Simulating catastrophe in DICE. Ecological Economics, 69(8):1657- 1665.
  2. Ackerman, F., Stanton, E., and Bueno, R. (2010). Fat tails, exponents, extreme uncertainty: Simulating catastrophe in DICE. Ecological Economics, 69(8):1657- 1665.
  3. Hastie, T., Tibshirani, R., Friedman, J., and Franklin, J. (2005). The elements of statistical learning: data mining, inference and prediction. The Mathematical Intelligencer, 27(2):83-85.
  4. Hastie, T., Tibshirani, R., Friedman, J., and Franklin, J. (2005). The elements of statistical learning: data mining, inference and prediction. The Mathematical Intelligencer, 27(2):83-85.
  5. Miller, K. (1964). Multidimensional gaussian distributions. Wiley New York.
  6. Miller, K. (1964). Multidimensional gaussian distributions. Wiley New York.
  7. Parzen, E. (1962). On estimation of a probability density function and mode. The annals of mathematical statistics, 33(3):1065-1076.
  8. Parzen, E. (1962). On estimation of a probability density function and mode. The annals of mathematical statistics, 33(3):1065-1076.
  9. Popovic, D., Milosavljevic, V., Zekic, A., Macgearailt, N., and Daniels, S. (2009). Impact of low pressure plasma discharge on etch rate of SiO2 wafer. In APS Meeting Abstracts, volume 1, page 8037P.
  10. Popovic, D., Milosavljevic, V., Zekic, A., Macgearailt, N., and Daniels, S. (2009). Impact of low pressure plasma discharge on etch rate of SiO2 wafer. In APS Meeting Abstracts, volume 1, page 8037P.
  11. Principe, J. (2010). Information Theoretic Learning: Renyi's Entropy and Kernel Perspectives. Springer Verlag.
  12. Principe, J. (2010). Information Theoretic Learning: Renyi's Entropy and Kernel Perspectives. Springer Verlag.
  13. Principe, J., Xu, D., Zhao, Q., and Fisher, J. (2000). Learning from examples with information theoretic criteria. The Journal of VLSI Signal Processing, 26(1):61-77.
  14. Principe, J., Xu, D., Zhao, Q., and Fisher, J. (2000). Learning from examples with information theoretic criteria. The Journal of VLSI Signal Processing, 26(1):61-77.
  15. Rallo, R., Ferre-Giné, J., Arenas, A., and Giralt, F. (2002). Neural virtual sensor for the inferential prediction of product quality from process variables. Computers & Chemical Engineering, 26(12):1735-1754.
  16. Rallo, R., Ferre-Giné, J., Arenas, A., and Giralt, F. (2002). Neural virtual sensor for the inferential prediction of product quality from process variables. Computers & Chemical Engineering, 26(12):1735-1754.
  17. Scholkopf, B. and Smola, A. (2002). Learning with kernels, volume 64. Citeseer.
  18. Scholkopf, B. and Smola, A. (2002). Learning with kernels, volume 64. Citeseer.
  19. Silverman, B. (1986). Density Estimation for Statistics and Data Analysis. Number 26 in Monographs on statistics and applied probability.
  20. Silverman, B. (1986). Density Estimation for Statistics and Data Analysis. Number 26 in Monographs on statistics and applied probability.
  21. Wang, P. and Vachtsevanos, G. (2001). Fault prognostics using dynamic wavelet neural networks. AI EDAM, 15(04):349-365.
  22. Wang, P. and Vachtsevanos, G. (2001). Fault prognostics using dynamic wavelet neural networks. AI EDAM, 15(04):349-365.
  23. Weber, A. (2007). Virtual metrology and your technology watch list: ten things you should know about this emerging technology. Future Fab International, 22:52-54.
  24. Weber, A. (2007). Virtual metrology and your technology watch list: ten things you should know about this emerging technology. Future Fab International, 22:52-54.
Download


Paper Citation


in Harvard Style

Schirru A., Pampuri S., De Luca C. and De Nicolao G. (2011). NONPARAMETRIC VIRTUAL SENSORS FOR SEMICONDUCTOR MANUFACTURING - Using Information Theoretic Learning and Kernel Machines . In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO, ISBN 978-989-8425-75-1, pages 349-358. DOI: 10.5220/0003520403490358


in Harvard Style

Schirru A., Pampuri S., De Luca C. and De Nicolao G. (2011). NONPARAMETRIC VIRTUAL SENSORS FOR SEMICONDUCTOR MANUFACTURING - Using Information Theoretic Learning and Kernel Machines . In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO, ISBN 978-989-8425-75-1, pages 349-358. DOI: 10.5220/0003520403490358


in Bibtex Style

@conference{icinco11,
author={Andrea Schirru and Simone Pampuri and Cristina De Luca and Giuseppe De Nicolao},
title={NONPARAMETRIC VIRTUAL SENSORS FOR SEMICONDUCTOR MANUFACTURING - Using Information Theoretic Learning and Kernel Machines},
booktitle={Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},
year={2011},
pages={349-358},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003520403490358},
isbn={978-989-8425-75-1},
}


in Bibtex Style

@conference{icinco11,
author={Andrea Schirru and Simone Pampuri and Cristina De Luca and Giuseppe De Nicolao},
title={NONPARAMETRIC VIRTUAL SENSORS FOR SEMICONDUCTOR MANUFACTURING - Using Information Theoretic Learning and Kernel Machines},
booktitle={Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},
year={2011},
pages={349-358},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003520403490358},
isbn={978-989-8425-75-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,
TI - NONPARAMETRIC VIRTUAL SENSORS FOR SEMICONDUCTOR MANUFACTURING - Using Information Theoretic Learning and Kernel Machines
SN - 978-989-8425-75-1
AU - Schirru A.
AU - Pampuri S.
AU - De Luca C.
AU - De Nicolao G.
PY - 2011
SP - 349
EP - 358
DO - 10.5220/0003520403490358


in EndNote Style

TY - CONF
JO - Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,
TI - NONPARAMETRIC VIRTUAL SENSORS FOR SEMICONDUCTOR MANUFACTURING - Using Information Theoretic Learning and Kernel Machines
SN - 978-989-8425-75-1
AU - Schirru A.
AU - Pampuri S.
AU - De Luca C.
AU - De Nicolao G.
PY - 2011
SP - 349
EP - 358
DO - 10.5220/0003520403490358