Abstract

In this paper, we present a novel interpretable machine learning technique that uses unique physical insights about noisy optical images and a few training samples to classify nanoscale defects in noisy optical images of a semiconductor wafer. Using this technique, we not only detected both parallel bridge defects and previously undetectable perpendicular bridge defects in a 9-nm node wafer using visible light microscopy [Proc. SPIE 9424, 942416 (2015)], but we also accurately classified their shapes and estimated their sizes. Detection and classification of nanoscale defects in optical images is a challenging task. The quality of images is affected by diffraction and noise. Machine learning techniques can reduce noise and recognize patterns using a large training set. However, for detecting a rare “killer” defect, acquisition of a sufficient training set of high quality experimental images can be prohibitively expensive. In addition, there are technical challenges involved in using electromagnetic simulations and optimization of the machine learning algorithm. This paper proposes solutions to address each of the aforementioned challenges.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Regularized pseudo-phase imaging for inspecting and sensing nanoscale features

Jinlong Zhu, Renjie Zhou, Lenan Zhang, Baoliang Ge, Chongxin Luo, and Lynford L. Goddard
Opt. Express 27(5) 6719-6733 (2019)

Automated tree detection from 3D lidar images using image processing and machine learning

Kenta Itakura and Fumiki Hosoi
Appl. Opt. 58(14) 3807-3811 (2019)

Open-source, machine and deep learning-based automated algorithm for gestational age estimation through smartphone lens imaging

Arjun D. Desai, Chunlei Peng, Leyuan Fang, Dibyendu Mukherjee, Andrew Yeung, Stephanie J. Jaffe, Jennifer B. Griffin, and Sina Farsiu
Biomed. Opt. Express 9(12) 6038-6052 (2018)

References

  • View by:
  • |
  • |
  • |

  1. R. Zhou, C. Edwards, C. A. Bryniarski, G. Popescu, and L. L. Goddard, “9nm node wafer defect inspection using three-dimensional scanning, a 405nm diode laser, and a broadband source,” Proc. SPIE 9424, 942416 (2015).
    [Crossref]
  2. B. Johnson, S. T. Wang, S. F. Jacobson, and J. Walker, “Learning from IoT/OT implementation in semiconductor manufacturing,” https://www.gartner.com/doc/3442917/learning-iotot-implementation-semiconductor-manufacturing (2016).
  3. N. G. Shankar and Z. W. Zhong, “Defect detection on semiconductor wafer surfaces,” Microelectron. Eng 77, 337–346 (2005).
    [Crossref]
  4. D. Carrera, F. Manganini, G. Boracchi, and E. Lanzarone, “Defect detection in SEM Images of nanofibrous materials,” IEEE Trans. Ind. Inform 13, 551–561 (2017).
    [Crossref]
  5. P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
    [Crossref]
  6. B. M. Barnes, M. Y. Sohn, F. Goasmat, H. Zhou, A. E. Vladár, R. M. Silver, and A. Arceo, “Three-dimensional deep sub-wavelength defect detection using λ = 193 nm optical microscopy,” Opt. Express 21, 26219–26226 (2013).
    [Crossref] [PubMed]
  7. R. Zhou, C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Detecting 20 nm defects in large area nanopatterns using optical interferometric microscopy,” Nano Lett. 13, 3716–3721 (2013).
    [Crossref] [PubMed]
  8. R. Zhou, C. Edwards, G. Popescu, and L. L. Goddard, “9 nm node wafer inspection using visible light,” Proc. SPIE 9050, 905017 (2014).
    [Crossref]
  9. P. Thony, D. Herisson, D. Henry, E. Severgnini, and M. Vasconi, “Review of CD measurement and scatterometry,” in AIP Conf. Proc, vol. 683 (2003), pp. 381–388.
  10. A. J. Boef, “Optical wafer metrology sensors for process-robust CD and overlay control in semiconductor device manufacturing,” Surf. Topogr. Metrol. Prop. 4, 023001 (2016).
    [Crossref]
  11. H. Ng, “Automatic thresholding for defect detection,” Pattern Recogn. Lett 27, 1644–1649 (2006).
    [Crossref]
  12. A. Kumar, “Computer-vision-based fabric defect detection: a survey,” IEEE Trans. Ind. Electron 55, 348–363 (2008).
    [Crossref]
  13. L. Xie, R. Huang, and Z. Cao, “Detection and classification of defect patterns in optical inspection using support vector machines,” in Intelligent Computing Theories. ICIC 2013. Lecture Notes in Computer Science, vol. 7995D. S. Huang, V. Bevilacqua, J. C. Figueroa, and P. Premaratne, eds. (Springer, Berlin, Heidelberg, 2013), pp. 376–384.
  14. L. Waller and L. Tian, “Computational imaging: machine learning for 3D microscopy,” Nature 523, 416–417 (2015).
    [Crossref] [PubMed]
  15. D. Weimer, B. Scholz-Reiter, and M. Shpitalni, “Design of deep convolutional neural network architectures for automated feature extraction in industrial inspection,” CIRP Ann. Manuf. Techn 65, 417–420 (2016).
    [Crossref]
  16. C. L. Chen, A. Mahjoubfar, L. Tai, I. K. Blaby, A. Huang, K. R. Niazi, and B. Jalali, “Deep learning in label-free cell classification,” Sci. Reports 6, 21471 (2016).
    [Crossref]
  17. N. H. Saad, A. E. Ahmad, and H. M. S. A. Hasan, “Automatic semiconductor wafer image segmentation for defect detection using multilevel thresholding,” in MATEC Web Conf, vol. 78 (2016), p. 01103.
    [Crossref]
  18. J. K. Park, B. K. Kwon, and J. H. Park, “Machine learning-based imaging system for surface defect inspection,” Int. J. of Precis. Eng. and Manuf.-Green Tech 3, 303–310 (2016).
    [Crossref]
  19. A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4, 1117–1125 (2017).
    [Crossref]
  20. L. Xing, Y. Rivenson, N. T. Yardimci, M. Veli, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” CoRR 361, 1004–1008 (2018).
  21. N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. E. Vladar, “Metrology for the next generation of semiconductor devices,” Nat. Electron. 1, 532–547 (2018).
    [Crossref]
  22. L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recogn 43, 1531–1549 (2010).
    [Crossref]
  23. C. Edwards, R. Zhou, S. W. Hwang, S. J. McKeown, K. Wang, B. Bhaduri, R. Ganti, P. J. Yunker, A. G. Yodh, J. A. Rogers, L. L. Goddard, and G. Popescu, “Diffraction phase microscopy: monitoring nanoscale dynamics in materials science,” Appl. Opt. 53, G33–G43 (2014).
    [Crossref] [PubMed]
  24. J. Zhu, Y. Shi, L. L. Goddard, and S. Liu, “Application of measurement configuration optimization for accurate metrology of sub-wavelength dimensions in multilayer gratings using optical scatterometry,” Appl. Opt. 55, 6844–6849 (2016).
    [Crossref] [PubMed]
  25. J. Zhu, K. Zhang, N. Davoudzadeh, and X. Wang, “Electromagnetic field modeling for defect detection in 7 nm node patterned wafers,” Proc. SPIE 9778, 97780 (2016).
    [Crossref]
  26. J. Zhu, Y. Shi, S. Liu, and L. L. Goddard, “Generalized measurement configuration optimization for accurate reconstruction of periodic nanostructures using optical scatterometry,” Proc. SPIE 9778, 977823 (2016).
    [Crossref]
  27. S. Weisenburger and V. Sandoghdar, “Light microscopy: an ongoing contemporary revolution,” Contemp. Phys. 52, 123–143 (2015).
    [Crossref]
  28. R. Szeliski, Computer vision: algorithms and applications(Springer Science & Business Media , 2010).
  29. R. Gonzalez and R. E. Woods, Digital image processing, vol. 2 (Prentice-Hall, Inc., 2006). Chapter 2 and Chapter 4.
  30. A. K. Jain, Fundamentals of digital image processing(Prentice-Hall, Inc., 1989). Chapter 4.
  31. R. Pascanu, T. Mikolov, and Y. Bengio, “Understanding the exploding gradient problem,” Comput. Res. Repos. (CoRR)abs/1211.5063 (2012).
  32. D. P. Kingma and J. Ba, “Adam: a method for stochastic optimization,” Comput. Res. Repos. (CoRR)abs/1412.6980 (2015).
  33. S. J. Reddi, S. Kale, and S. Kumar, “On the convergence of Adam and beyond,” Comput. Res. Repos. (CoRR)abs/1904.09237 (2019).
  34. A. Y. Kruger, “On Fréchet subdifferentials,” Journal of Mathematical Sciences 116, 3325–3358 (2003).
    [Crossref]

2018 (2)

L. Xing, Y. Rivenson, N. T. Yardimci, M. Veli, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” CoRR 361, 1004–1008 (2018).

N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. E. Vladar, “Metrology for the next generation of semiconductor devices,” Nat. Electron. 1, 532–547 (2018).
[Crossref]

2017 (3)

A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4, 1117–1125 (2017).
[Crossref]

D. Carrera, F. Manganini, G. Boracchi, and E. Lanzarone, “Defect detection in SEM Images of nanofibrous materials,” IEEE Trans. Ind. Inform 13, 551–561 (2017).
[Crossref]

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

2016 (7)

J. Zhu, K. Zhang, N. Davoudzadeh, and X. Wang, “Electromagnetic field modeling for defect detection in 7 nm node patterned wafers,” Proc. SPIE 9778, 97780 (2016).
[Crossref]

J. Zhu, Y. Shi, S. Liu, and L. L. Goddard, “Generalized measurement configuration optimization for accurate reconstruction of periodic nanostructures using optical scatterometry,” Proc. SPIE 9778, 977823 (2016).
[Crossref]

A. J. Boef, “Optical wafer metrology sensors for process-robust CD and overlay control in semiconductor device manufacturing,” Surf. Topogr. Metrol. Prop. 4, 023001 (2016).
[Crossref]

D. Weimer, B. Scholz-Reiter, and M. Shpitalni, “Design of deep convolutional neural network architectures for automated feature extraction in industrial inspection,” CIRP Ann. Manuf. Techn 65, 417–420 (2016).
[Crossref]

C. L. Chen, A. Mahjoubfar, L. Tai, I. K. Blaby, A. Huang, K. R. Niazi, and B. Jalali, “Deep learning in label-free cell classification,” Sci. Reports 6, 21471 (2016).
[Crossref]

J. K. Park, B. K. Kwon, and J. H. Park, “Machine learning-based imaging system for surface defect inspection,” Int. J. of Precis. Eng. and Manuf.-Green Tech 3, 303–310 (2016).
[Crossref]

J. Zhu, Y. Shi, L. L. Goddard, and S. Liu, “Application of measurement configuration optimization for accurate metrology of sub-wavelength dimensions in multilayer gratings using optical scatterometry,” Appl. Opt. 55, 6844–6849 (2016).
[Crossref] [PubMed]

2015 (3)

R. Zhou, C. Edwards, C. A. Bryniarski, G. Popescu, and L. L. Goddard, “9nm node wafer defect inspection using three-dimensional scanning, a 405nm diode laser, and a broadband source,” Proc. SPIE 9424, 942416 (2015).
[Crossref]

S. Weisenburger and V. Sandoghdar, “Light microscopy: an ongoing contemporary revolution,” Contemp. Phys. 52, 123–143 (2015).
[Crossref]

L. Waller and L. Tian, “Computational imaging: machine learning for 3D microscopy,” Nature 523, 416–417 (2015).
[Crossref] [PubMed]

2014 (2)

2013 (2)

B. M. Barnes, M. Y. Sohn, F. Goasmat, H. Zhou, A. E. Vladár, R. M. Silver, and A. Arceo, “Three-dimensional deep sub-wavelength defect detection using λ = 193 nm optical microscopy,” Opt. Express 21, 26219–26226 (2013).
[Crossref] [PubMed]

R. Zhou, C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Detecting 20 nm defects in large area nanopatterns using optical interferometric microscopy,” Nano Lett. 13, 3716–3721 (2013).
[Crossref] [PubMed]

2010 (1)

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recogn 43, 1531–1549 (2010).
[Crossref]

2008 (1)

A. Kumar, “Computer-vision-based fabric defect detection: a survey,” IEEE Trans. Ind. Electron 55, 348–363 (2008).
[Crossref]

2006 (1)

H. Ng, “Automatic thresholding for defect detection,” Pattern Recogn. Lett 27, 1644–1649 (2006).
[Crossref]

2005 (1)

N. G. Shankar and Z. W. Zhong, “Defect detection on semiconductor wafer surfaces,” Microelectron. Eng 77, 337–346 (2005).
[Crossref]

2003 (1)

A. Y. Kruger, “On Fréchet subdifferentials,” Journal of Mathematical Sciences 116, 3325–3358 (2003).
[Crossref]

Ahmad, A. E.

N. H. Saad, A. E. Ahmad, and H. M. S. A. Hasan, “Automatic semiconductor wafer image segmentation for defect detection using multilevel thresholding,” in MATEC Web Conf, vol. 78 (2016), p. 01103.
[Crossref]

Alkemade, P. F. A.

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

Arango, F. A. B.

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

Arbabi, A.

R. Zhou, C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Detecting 20 nm defects in large area nanopatterns using optical interferometric microscopy,” Nano Lett. 13, 3716–3721 (2013).
[Crossref] [PubMed]

Arceo, A.

Ba, J.

D. P. Kingma and J. Ba, “Adam: a method for stochastic optimization,” Comput. Res. Repos. (CoRR)abs/1412.6980 (2015).

Badaroglu, M.

N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. E. Vladar, “Metrology for the next generation of semiconductor devices,” Nat. Electron. 1, 532–547 (2018).
[Crossref]

Barbastathis, G.

Barnes, B. M.

N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. E. Vladar, “Metrology for the next generation of semiconductor devices,” Nat. Electron. 1, 532–547 (2018).
[Crossref]

B. M. Barnes, M. Y. Sohn, F. Goasmat, H. Zhou, A. E. Vladár, R. M. Silver, and A. Arceo, “Three-dimensional deep sub-wavelength defect detection using λ = 193 nm optical microscopy,” Opt. Express 21, 26219–26226 (2013).
[Crossref] [PubMed]

Beitia, C.

N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. E. Vladar, “Metrology for the next generation of semiconductor devices,” Nat. Electron. 1, 532–547 (2018).
[Crossref]

Bengio, Y.

R. Pascanu, T. Mikolov, and Y. Bengio, “Understanding the exploding gradient problem,” Comput. Res. Repos. (CoRR)abs/1211.5063 (2012).

Bhaduri, B.

Blaby, I. K.

C. L. Chen, A. Mahjoubfar, L. Tai, I. K. Blaby, A. Huang, K. R. Niazi, and B. Jalali, “Deep learning in label-free cell classification,” Sci. Reports 6, 21471 (2016).
[Crossref]

Boef, A. J.

A. J. Boef, “Optical wafer metrology sensors for process-robust CD and overlay control in semiconductor device manufacturing,” Surf. Topogr. Metrol. Prop. 4, 023001 (2016).
[Crossref]

Boracchi, G.

D. Carrera, F. Manganini, G. Boracchi, and E. Lanzarone, “Defect detection in SEM Images of nanofibrous materials,” IEEE Trans. Ind. Inform 13, 551–561 (2017).
[Crossref]

Bryniarski, C. A.

R. Zhou, C. Edwards, C. A. Bryniarski, G. Popescu, and L. L. Goddard, “9nm node wafer defect inspection using three-dimensional scanning, a 405nm diode laser, and a broadband source,” Proc. SPIE 9424, 942416 (2015).
[Crossref]

Bunday, B. D.

N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. E. Vladar, “Metrology for the next generation of semiconductor devices,” Nat. Electron. 1, 532–547 (2018).
[Crossref]

Cao, Z.

L. Xie, R. Huang, and Z. Cao, “Detection and classification of defect patterns in optical inspection using support vector machines,” in Intelligent Computing Theories. ICIC 2013. Lecture Notes in Computer Science, vol. 7995D. S. Huang, V. Bevilacqua, J. C. Figueroa, and P. Premaratne, eds. (Springer, Berlin, Heidelberg, 2013), pp. 376–384.

Carrera, D.

D. Carrera, F. Manganini, G. Boracchi, and E. Lanzarone, “Defect detection in SEM Images of nanofibrous materials,” IEEE Trans. Ind. Inform 13, 551–561 (2017).
[Crossref]

Celano, U.

N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. E. Vladar, “Metrology for the next generation of semiconductor devices,” Nat. Electron. 1, 532–547 (2018).
[Crossref]

Chen, C. L.

C. L. Chen, A. Mahjoubfar, L. Tai, I. K. Blaby, A. Huang, K. R. Niazi, and B. Jalali, “Deep learning in label-free cell classification,” Sci. Reports 6, 21471 (2016).
[Crossref]

Davoudzadeh, N.

J. Zhu, K. Zhang, N. Davoudzadeh, and X. Wang, “Electromagnetic field modeling for defect detection in 7 nm node patterned wafers,” Proc. SPIE 9778, 97780 (2016).
[Crossref]

de Jong, A.

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

Dong, W.

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recogn 43, 1531–1549 (2010).
[Crossref]

Edwards, C.

R. Zhou, C. Edwards, C. A. Bryniarski, G. Popescu, and L. L. Goddard, “9nm node wafer defect inspection using three-dimensional scanning, a 405nm diode laser, and a broadband source,” Proc. SPIE 9424, 942416 (2015).
[Crossref]

R. Zhou, C. Edwards, G. Popescu, and L. L. Goddard, “9 nm node wafer inspection using visible light,” Proc. SPIE 9050, 905017 (2014).
[Crossref]

C. Edwards, R. Zhou, S. W. Hwang, S. J. McKeown, K. Wang, B. Bhaduri, R. Ganti, P. J. Yunker, A. G. Yodh, J. A. Rogers, L. L. Goddard, and G. Popescu, “Diffraction phase microscopy: monitoring nanoscale dynamics in materials science,” Appl. Opt. 53, G33–G43 (2014).
[Crossref] [PubMed]

R. Zhou, C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Detecting 20 nm defects in large area nanopatterns using optical interferometric microscopy,” Nano Lett. 13, 3716–3721 (2013).
[Crossref] [PubMed]

Ganti, R.

Goasmat, F.

Goddard, L. L.

J. Zhu, Y. Shi, L. L. Goddard, and S. Liu, “Application of measurement configuration optimization for accurate metrology of sub-wavelength dimensions in multilayer gratings using optical scatterometry,” Appl. Opt. 55, 6844–6849 (2016).
[Crossref] [PubMed]

J. Zhu, Y. Shi, S. Liu, and L. L. Goddard, “Generalized measurement configuration optimization for accurate reconstruction of periodic nanostructures using optical scatterometry,” Proc. SPIE 9778, 977823 (2016).
[Crossref]

R. Zhou, C. Edwards, C. A. Bryniarski, G. Popescu, and L. L. Goddard, “9nm node wafer defect inspection using three-dimensional scanning, a 405nm diode laser, and a broadband source,” Proc. SPIE 9424, 942416 (2015).
[Crossref]

R. Zhou, C. Edwards, G. Popescu, and L. L. Goddard, “9 nm node wafer inspection using visible light,” Proc. SPIE 9050, 905017 (2014).
[Crossref]

C. Edwards, R. Zhou, S. W. Hwang, S. J. McKeown, K. Wang, B. Bhaduri, R. Ganti, P. J. Yunker, A. G. Yodh, J. A. Rogers, L. L. Goddard, and G. Popescu, “Diffraction phase microscopy: monitoring nanoscale dynamics in materials science,” Appl. Opt. 53, G33–G43 (2014).
[Crossref] [PubMed]

R. Zhou, C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Detecting 20 nm defects in large area nanopatterns using optical interferometric microscopy,” Nano Lett. 13, 3716–3721 (2013).
[Crossref] [PubMed]

Gonzalez, R.

R. Gonzalez and R. E. Woods, Digital image processing, vol. 2 (Prentice-Hall, Inc., 2006). Chapter 2 and Chapter 4.

Hasan, H. M. S. A.

N. H. Saad, A. E. Ahmad, and H. M. S. A. Hasan, “Automatic semiconductor wafer image segmentation for defect detection using multilevel thresholding,” in MATEC Web Conf, vol. 78 (2016), p. 01103.
[Crossref]

Henry, D.

P. Thony, D. Herisson, D. Henry, E. Severgnini, and M. Vasconi, “Review of CD measurement and scatterometry,” in AIP Conf. Proc, vol. 683 (2003), pp. 381–388.

Herisson, D.

P. Thony, D. Herisson, D. Henry, E. Severgnini, and M. Vasconi, “Review of CD measurement and scatterometry,” in AIP Conf. Proc, vol. 683 (2003), pp. 381–388.

Huang, A.

C. L. Chen, A. Mahjoubfar, L. Tai, I. K. Blaby, A. Huang, K. R. Niazi, and B. Jalali, “Deep learning in label-free cell classification,” Sci. Reports 6, 21471 (2016).
[Crossref]

Huang, R.

L. Xie, R. Huang, and Z. Cao, “Detection and classification of defect patterns in optical inspection using support vector machines,” in Intelligent Computing Theories. ICIC 2013. Lecture Notes in Computer Science, vol. 7995D. S. Huang, V. Bevilacqua, J. C. Figueroa, and P. Premaratne, eds. (Springer, Berlin, Heidelberg, 2013), pp. 376–384.

Hwang, S. W.

Jain, A. K.

A. K. Jain, Fundamentals of digital image processing(Prentice-Hall, Inc., 1989). Chapter 4.

Jalali, B.

C. L. Chen, A. Mahjoubfar, L. Tai, I. K. Blaby, A. Huang, K. R. Niazi, and B. Jalali, “Deep learning in label-free cell classification,” Sci. Reports 6, 21471 (2016).
[Crossref]

Jarrahi, M.

L. Xing, Y. Rivenson, N. T. Yardimci, M. Veli, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” CoRR 361, 1004–1008 (2018).

Kale, S.

S. J. Reddi, S. Kale, and S. Kumar, “On the convergence of Adam and beyond,” Comput. Res. Repos. (CoRR)abs/1904.09237 (2019).

Kingma, D. P.

D. P. Kingma and J. Ba, “Adam: a method for stochastic optimization,” Comput. Res. Repos. (CoRR)abs/1412.6980 (2015).

Kline, R. J.

N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. E. Vladar, “Metrology for the next generation of semiconductor devices,” Nat. Electron. 1, 532–547 (2018).
[Crossref]

Kramer, E.

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

Kruger, A. Y.

A. Y. Kruger, “On Fréchet subdifferentials,” Journal of Mathematical Sciences 116, 3325–3358 (2003).
[Crossref]

Kumar, A.

A. Kumar, “Computer-vision-based fabric defect detection: a survey,” IEEE Trans. Ind. Electron 55, 348–363 (2008).
[Crossref]

Kumar, S.

S. J. Reddi, S. Kale, and S. Kumar, “On the convergence of Adam and beyond,” Comput. Res. Repos. (CoRR)abs/1904.09237 (2019).

Kwon, B. K.

J. K. Park, B. K. Kwon, and J. H. Park, “Machine learning-based imaging system for surface defect inspection,” Int. J. of Precis. Eng. and Manuf.-Green Tech 3, 303–310 (2016).
[Crossref]

Lanzarone, E.

D. Carrera, F. Manganini, G. Boracchi, and E. Lanzarone, “Defect detection in SEM Images of nanofibrous materials,” IEEE Trans. Ind. Inform 13, 551–561 (2017).
[Crossref]

Lee, J.

Li, S.

Liu, S.

J. Zhu, Y. Shi, L. L. Goddard, and S. Liu, “Application of measurement configuration optimization for accurate metrology of sub-wavelength dimensions in multilayer gratings using optical scatterometry,” Appl. Opt. 55, 6844–6849 (2016).
[Crossref] [PubMed]

J. Zhu, Y. Shi, S. Liu, and L. L. Goddard, “Generalized measurement configuration optimization for accurate reconstruction of periodic nanostructures using optical scatterometry,” Proc. SPIE 9778, 977823 (2016).
[Crossref]

Maas, D.

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

Mahjoubfar, A.

C. L. Chen, A. Mahjoubfar, L. Tai, I. K. Blaby, A. Huang, K. R. Niazi, and B. Jalali, “Deep learning in label-free cell classification,” Sci. Reports 6, 21471 (2016).
[Crossref]

Manganini, F.

D. Carrera, F. Manganini, G. Boracchi, and E. Lanzarone, “Defect detection in SEM Images of nanofibrous materials,” IEEE Trans. Ind. Inform 13, 551–561 (2017).
[Crossref]

McKeown, S. J.

Mikolov, T.

R. Pascanu, T. Mikolov, and Y. Bengio, “Understanding the exploding gradient problem,” Comput. Res. Repos. (CoRR)abs/1211.5063 (2012).

Mulckhuyse, W.

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

Nanda, G.

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

Neisser, M.

N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. E. Vladar, “Metrology for the next generation of semiconductor devices,” Nat. Electron. 1, 532–547 (2018).
[Crossref]

Ng, H.

H. Ng, “Automatic thresholding for defect detection,” Pattern Recogn. Lett 27, 1644–1649 (2006).
[Crossref]

Niazi, K. R.

C. L. Chen, A. Mahjoubfar, L. Tai, I. K. Blaby, A. Huang, K. R. Niazi, and B. Jalali, “Deep learning in label-free cell classification,” Sci. Reports 6, 21471 (2016).
[Crossref]

Nijsten, L.

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

Obeng, Y.

N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. E. Vladar, “Metrology for the next generation of semiconductor devices,” Nat. Electron. 1, 532–547 (2018).
[Crossref]

Orji, N. G.

N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. E. Vladar, “Metrology for the next generation of semiconductor devices,” Nat. Electron. 1, 532–547 (2018).
[Crossref]

Ozcan, A.

L. Xing, Y. Rivenson, N. T. Yardimci, M. Veli, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” CoRR 361, 1004–1008 (2018).

Park, J. H.

J. K. Park, B. K. Kwon, and J. H. Park, “Machine learning-based imaging system for surface defect inspection,” Int. J. of Precis. Eng. and Manuf.-Green Tech 3, 303–310 (2016).
[Crossref]

Park, J. K.

J. K. Park, B. K. Kwon, and J. H. Park, “Machine learning-based imaging system for surface defect inspection,” Int. J. of Precis. Eng. and Manuf.-Green Tech 3, 303–310 (2016).
[Crossref]

Pascanu, R.

R. Pascanu, T. Mikolov, and Y. Bengio, “Understanding the exploding gradient problem,” Comput. Res. Repos. (CoRR)abs/1211.5063 (2012).

Pereira, S.

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

Popescu, G.

R. Zhou, C. Edwards, C. A. Bryniarski, G. Popescu, and L. L. Goddard, “9nm node wafer defect inspection using three-dimensional scanning, a 405nm diode laser, and a broadband source,” Proc. SPIE 9424, 942416 (2015).
[Crossref]

R. Zhou, C. Edwards, G. Popescu, and L. L. Goddard, “9 nm node wafer inspection using visible light,” Proc. SPIE 9050, 905017 (2014).
[Crossref]

C. Edwards, R. Zhou, S. W. Hwang, S. J. McKeown, K. Wang, B. Bhaduri, R. Ganti, P. J. Yunker, A. G. Yodh, J. A. Rogers, L. L. Goddard, and G. Popescu, “Diffraction phase microscopy: monitoring nanoscale dynamics in materials science,” Appl. Opt. 53, G33–G43 (2014).
[Crossref] [PubMed]

R. Zhou, C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Detecting 20 nm defects in large area nanopatterns using optical interferometric microscopy,” Nano Lett. 13, 3716–3721 (2013).
[Crossref] [PubMed]

Reddi, S. J.

S. J. Reddi, S. Kale, and S. Kumar, “On the convergence of Adam and beyond,” Comput. Res. Repos. (CoRR)abs/1904.09237 (2019).

Rivenson, Y.

L. Xing, Y. Rivenson, N. T. Yardimci, M. Veli, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” CoRR 361, 1004–1008 (2018).

Rogers, J. A.

Saad, N. H.

N. H. Saad, A. E. Ahmad, and H. M. S. A. Hasan, “Automatic semiconductor wafer image segmentation for defect detection using multilevel thresholding,” in MATEC Web Conf, vol. 78 (2016), p. 01103.
[Crossref]

Sandoghdar, V.

S. Weisenburger and V. Sandoghdar, “Light microscopy: an ongoing contemporary revolution,” Contemp. Phys. 52, 123–143 (2015).
[Crossref]

Scholz-Reiter, B.

D. Weimer, B. Scholz-Reiter, and M. Shpitalni, “Design of deep convolutional neural network architectures for automated feature extraction in industrial inspection,” CIRP Ann. Manuf. Techn 65, 417–420 (2016).
[Crossref]

Severgnini, E.

P. Thony, D. Herisson, D. Henry, E. Severgnini, and M. Vasconi, “Review of CD measurement and scatterometry,” in AIP Conf. Proc, vol. 683 (2003), pp. 381–388.

Shankar, N. G.

N. G. Shankar and Z. W. Zhong, “Defect detection on semiconductor wafer surfaces,” Microelectron. Eng 77, 337–346 (2005).
[Crossref]

Shi, G.

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recogn 43, 1531–1549 (2010).
[Crossref]

Shi, Y.

J. Zhu, Y. Shi, S. Liu, and L. L. Goddard, “Generalized measurement configuration optimization for accurate reconstruction of periodic nanostructures using optical scatterometry,” Proc. SPIE 9778, 977823 (2016).
[Crossref]

J. Zhu, Y. Shi, L. L. Goddard, and S. Liu, “Application of measurement configuration optimization for accurate metrology of sub-wavelength dimensions in multilayer gratings using optical scatterometry,” Appl. Opt. 55, 6844–6849 (2016).
[Crossref] [PubMed]

Shpitalni, M.

D. Weimer, B. Scholz-Reiter, and M. Shpitalni, “Design of deep convolutional neural network architectures for automated feature extraction in industrial inspection,” CIRP Ann. Manuf. Techn 65, 417–420 (2016).
[Crossref]

Silver, R. M.

Sinha, A.

Sohn, M. Y.

Spruit, H.

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

Szeliski, R.

R. Szeliski, Computer vision: algorithms and applications(Springer Science & Business Media , 2010).

Tai, L.

C. L. Chen, A. Mahjoubfar, L. Tai, I. K. Blaby, A. Huang, K. R. Niazi, and B. Jalali, “Deep learning in label-free cell classification,” Sci. Reports 6, 21471 (2016).
[Crossref]

Thony, P.

P. Thony, D. Herisson, D. Henry, E. Severgnini, and M. Vasconi, “Review of CD measurement and scatterometry,” in AIP Conf. Proc, vol. 683 (2003), pp. 381–388.

Tian, L.

L. Waller and L. Tian, “Computational imaging: machine learning for 3D microscopy,” Nature 523, 416–417 (2015).
[Crossref] [PubMed]

van den Berg, J. H.

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

van der donck, J.

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

van Langen-Suurling, A. K.

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

Vasconi, M.

P. Thony, D. Herisson, D. Henry, E. Severgnini, and M. Vasconi, “Review of CD measurement and scatterometry,” in AIP Conf. Proc, vol. 683 (2003), pp. 381–388.

Veli, M.

L. Xing, Y. Rivenson, N. T. Yardimci, M. Veli, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” CoRR 361, 1004–1008 (2018).

Vladar, A. E.

N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. E. Vladar, “Metrology for the next generation of semiconductor devices,” Nat. Electron. 1, 532–547 (2018).
[Crossref]

Vladár, A. E.

Walle, P.

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

Waller, L.

L. Waller and L. Tian, “Computational imaging: machine learning for 3D microscopy,” Nature 523, 416–417 (2015).
[Crossref] [PubMed]

Wang, K.

Wang, X.

J. Zhu, K. Zhang, N. Davoudzadeh, and X. Wang, “Electromagnetic field modeling for defect detection in 7 nm node patterned wafers,” Proc. SPIE 9778, 97780 (2016).
[Crossref]

Weimer, D.

D. Weimer, B. Scholz-Reiter, and M. Shpitalni, “Design of deep convolutional neural network architectures for automated feature extraction in industrial inspection,” CIRP Ann. Manuf. Techn 65, 417–420 (2016).
[Crossref]

Weisenburger, S.

S. Weisenburger and V. Sandoghdar, “Light microscopy: an ongoing contemporary revolution,” Contemp. Phys. 52, 123–143 (2015).
[Crossref]

Woods, R. E.

R. Gonzalez and R. E. Woods, Digital image processing, vol. 2 (Prentice-Hall, Inc., 2006). Chapter 2 and Chapter 4.

Xie, L.

L. Xie, R. Huang, and Z. Cao, “Detection and classification of defect patterns in optical inspection using support vector machines,” in Intelligent Computing Theories. ICIC 2013. Lecture Notes in Computer Science, vol. 7995D. S. Huang, V. Bevilacqua, J. C. Figueroa, and P. Premaratne, eds. (Springer, Berlin, Heidelberg, 2013), pp. 376–384.

Xing, L.

L. Xing, Y. Rivenson, N. T. Yardimci, M. Veli, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” CoRR 361, 1004–1008 (2018).

Yardimci, N. T.

L. Xing, Y. Rivenson, N. T. Yardimci, M. Veli, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” CoRR 361, 1004–1008 (2018).

Yodh, A. G.

Yunker, P. J.

Zeijl, E.

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

Zhang, D.

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recogn 43, 1531–1549 (2010).
[Crossref]

Zhang, K.

J. Zhu, K. Zhang, N. Davoudzadeh, and X. Wang, “Electromagnetic field modeling for defect detection in 7 nm node patterned wafers,” Proc. SPIE 9778, 97780 (2016).
[Crossref]

Zhang, L.

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recogn 43, 1531–1549 (2010).
[Crossref]

Zhong, Z. W.

N. G. Shankar and Z. W. Zhong, “Defect detection on semiconductor wafer surfaces,” Microelectron. Eng 77, 337–346 (2005).
[Crossref]

Zhou, H.

Zhou, R.

R. Zhou, C. Edwards, C. A. Bryniarski, G. Popescu, and L. L. Goddard, “9nm node wafer defect inspection using three-dimensional scanning, a 405nm diode laser, and a broadband source,” Proc. SPIE 9424, 942416 (2015).
[Crossref]

R. Zhou, C. Edwards, G. Popescu, and L. L. Goddard, “9 nm node wafer inspection using visible light,” Proc. SPIE 9050, 905017 (2014).
[Crossref]

C. Edwards, R. Zhou, S. W. Hwang, S. J. McKeown, K. Wang, B. Bhaduri, R. Ganti, P. J. Yunker, A. G. Yodh, J. A. Rogers, L. L. Goddard, and G. Popescu, “Diffraction phase microscopy: monitoring nanoscale dynamics in materials science,” Appl. Opt. 53, G33–G43 (2014).
[Crossref] [PubMed]

R. Zhou, C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Detecting 20 nm defects in large area nanopatterns using optical interferometric microscopy,” Nano Lett. 13, 3716–3721 (2013).
[Crossref] [PubMed]

Zhu, J.

J. Zhu, Y. Shi, L. L. Goddard, and S. Liu, “Application of measurement configuration optimization for accurate metrology of sub-wavelength dimensions in multilayer gratings using optical scatterometry,” Appl. Opt. 55, 6844–6849 (2016).
[Crossref] [PubMed]

J. Zhu, K. Zhang, N. Davoudzadeh, and X. Wang, “Electromagnetic field modeling for defect detection in 7 nm node patterned wafers,” Proc. SPIE 9778, 97780 (2016).
[Crossref]

J. Zhu, Y. Shi, S. Liu, and L. L. Goddard, “Generalized measurement configuration optimization for accurate reconstruction of periodic nanostructures using optical scatterometry,” Proc. SPIE 9778, 977823 (2016).
[Crossref]

Appl. Opt. (2)

CIRP Ann. Manuf. Techn (1)

D. Weimer, B. Scholz-Reiter, and M. Shpitalni, “Design of deep convolutional neural network architectures for automated feature extraction in industrial inspection,” CIRP Ann. Manuf. Techn 65, 417–420 (2016).
[Crossref]

Contemp. Phys. (1)

S. Weisenburger and V. Sandoghdar, “Light microscopy: an ongoing contemporary revolution,” Contemp. Phys. 52, 123–143 (2015).
[Crossref]

CoRR (1)

L. Xing, Y. Rivenson, N. T. Yardimci, M. Veli, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” CoRR 361, 1004–1008 (2018).

IEEE Trans. Ind. Electron (1)

A. Kumar, “Computer-vision-based fabric defect detection: a survey,” IEEE Trans. Ind. Electron 55, 348–363 (2008).
[Crossref]

IEEE Trans. Ind. Inform (1)

D. Carrera, F. Manganini, G. Boracchi, and E. Lanzarone, “Defect detection in SEM Images of nanofibrous materials,” IEEE Trans. Ind. Inform 13, 551–561 (2017).
[Crossref]

Int. J. of Precis. Eng. and Manuf.-Green Tech (1)

J. K. Park, B. K. Kwon, and J. H. Park, “Machine learning-based imaging system for surface defect inspection,” Int. J. of Precis. Eng. and Manuf.-Green Tech 3, 303–310 (2016).
[Crossref]

Journal of Mathematical Sciences (1)

A. Y. Kruger, “On Fréchet subdifferentials,” Journal of Mathematical Sciences 116, 3325–3358 (2003).
[Crossref]

Microelectron. Eng (1)

N. G. Shankar and Z. W. Zhong, “Defect detection on semiconductor wafer surfaces,” Microelectron. Eng 77, 337–346 (2005).
[Crossref]

Nano Lett. (1)

R. Zhou, C. Edwards, A. Arbabi, G. Popescu, and L. L. Goddard, “Detecting 20 nm defects in large area nanopatterns using optical interferometric microscopy,” Nano Lett. 13, 3716–3721 (2013).
[Crossref] [PubMed]

Nat. Electron. (1)

N. G. Orji, M. Badaroglu, B. M. Barnes, C. Beitia, B. D. Bunday, U. Celano, R. J. Kline, M. Neisser, Y. Obeng, and A. E. Vladar, “Metrology for the next generation of semiconductor devices,” Nat. Electron. 1, 532–547 (2018).
[Crossref]

Nature (1)

L. Waller and L. Tian, “Computational imaging: machine learning for 3D microscopy,” Nature 523, 416–417 (2015).
[Crossref] [PubMed]

Opt. Express (1)

Optica (1)

Pattern Recogn (1)

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recogn 43, 1531–1549 (2010).
[Crossref]

Pattern Recogn. Lett (1)

H. Ng, “Automatic thresholding for defect detection,” Pattern Recogn. Lett 27, 1644–1649 (2006).
[Crossref]

Proc. SPIE (5)

R. Zhou, C. Edwards, G. Popescu, and L. L. Goddard, “9 nm node wafer inspection using visible light,” Proc. SPIE 9050, 905017 (2014).
[Crossref]

P. Walle, E. Kramer, J. van der donck, W. Mulckhuyse, L. Nijsten, F. A. B. Arango, A. de Jong, E. Zeijl, H. Spruit, J. H. van den Berg, G. Nanda, A. K. van Langen-Suurling, P. F. A. Alkemade, S. Pereira, and D. Maas, “Deep sub-wavelength metrology for advanced defect classification,” Proc. SPIE 10329, 103294N (2017).
[Crossref]

R. Zhou, C. Edwards, C. A. Bryniarski, G. Popescu, and L. L. Goddard, “9nm node wafer defect inspection using three-dimensional scanning, a 405nm diode laser, and a broadband source,” Proc. SPIE 9424, 942416 (2015).
[Crossref]

J. Zhu, K. Zhang, N. Davoudzadeh, and X. Wang, “Electromagnetic field modeling for defect detection in 7 nm node patterned wafers,” Proc. SPIE 9778, 97780 (2016).
[Crossref]

J. Zhu, Y. Shi, S. Liu, and L. L. Goddard, “Generalized measurement configuration optimization for accurate reconstruction of periodic nanostructures using optical scatterometry,” Proc. SPIE 9778, 977823 (2016).
[Crossref]

Sci. Reports (1)

C. L. Chen, A. Mahjoubfar, L. Tai, I. K. Blaby, A. Huang, K. R. Niazi, and B. Jalali, “Deep learning in label-free cell classification,” Sci. Reports 6, 21471 (2016).
[Crossref]

Surf. Topogr. Metrol. Prop. (1)

A. J. Boef, “Optical wafer metrology sensors for process-robust CD and overlay control in semiconductor device manufacturing,” Surf. Topogr. Metrol. Prop. 4, 023001 (2016).
[Crossref]

Other (10)

L. Xie, R. Huang, and Z. Cao, “Detection and classification of defect patterns in optical inspection using support vector machines,” in Intelligent Computing Theories. ICIC 2013. Lecture Notes in Computer Science, vol. 7995D. S. Huang, V. Bevilacqua, J. C. Figueroa, and P. Premaratne, eds. (Springer, Berlin, Heidelberg, 2013), pp. 376–384.

N. H. Saad, A. E. Ahmad, and H. M. S. A. Hasan, “Automatic semiconductor wafer image segmentation for defect detection using multilevel thresholding,” in MATEC Web Conf, vol. 78 (2016), p. 01103.
[Crossref]

B. Johnson, S. T. Wang, S. F. Jacobson, and J. Walker, “Learning from IoT/OT implementation in semiconductor manufacturing,” https://www.gartner.com/doc/3442917/learning-iotot-implementation-semiconductor-manufacturing (2016).

P. Thony, D. Herisson, D. Henry, E. Severgnini, and M. Vasconi, “Review of CD measurement and scatterometry,” in AIP Conf. Proc, vol. 683 (2003), pp. 381–388.

R. Szeliski, Computer vision: algorithms and applications(Springer Science & Business Media , 2010).

R. Gonzalez and R. E. Woods, Digital image processing, vol. 2 (Prentice-Hall, Inc., 2006). Chapter 2 and Chapter 4.

A. K. Jain, Fundamentals of digital image processing(Prentice-Hall, Inc., 1989). Chapter 4.

R. Pascanu, T. Mikolov, and Y. Bengio, “Understanding the exploding gradient problem,” Comput. Res. Repos. (CoRR)abs/1211.5063 (2012).

D. P. Kingma and J. Ba, “Adam: a method for stochastic optimization,” Comput. Res. Repos. (CoRR)abs/1412.6980 (2015).

S. J. Reddi, S. Kale, and S. Kumar, “On the convergence of Adam and beyond,” Comput. Res. Repos. (CoRR)abs/1904.09237 (2019).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1 SEM images of a typical (a) parallel bridge defect, (b) perpendicular bridge defect, (c) e-beam stitching error, and (d) region with nanoscale dust. Microscope image after 2DIS post-processing of the (e) parallel and (f) perpendicular bridge defect dies.
Fig. 2
Fig. 2 Overview of the proposed approach. Given approximate simulated defect images, the set of random numbers, and a microscope image, we learn model parameters, w *, which can be used to generate an optimized synthetic defect library, L s y n, which can classify an experimental image as showing a defect or no defect. Section 3.6 provide image generation algorithm details.
Fig. 3
Fig. 3 (a) Zoomed in simulation geometry for a parallel bridge defect. The field of view is 900 nm ×   900 nm. (b) Raw simulation intensity image.
Fig. 4
Fig. 4 Images at various steps of synthetic library generation process. Processing of a simulated image showing the (step 1) (a) extracted defect and (b) processed defect, (step 2) (c) 2nd order difference, (step 3) (d) Gaussian blur and (e) Gaussian noise, and (step 4) (f) Cropped final synthetic defect image that has a tripole pattern. Post-processed experimental image blocks after cropping and normalization, showing (g) a parallel defect image. (h) A typical edge-based signal that needs to be rejected as a parallel defect.
Fig. 5
Fig. 5 Gaussian noise transformation.
Fig. 6
Fig. 6 Parallel defect image with 2nd order difference. (a) Before and (b) after PCA.
Fig. 7
Fig. 7 (a) Precision, and (b) Recall for the models from the three different categories for the parallel bridge defect for the entire die image.
Fig. 8
Fig. 8 Parallel defect image with 2DIS processing. (a) Before and (b) after applying PCA (c) SEM image of the region displaying stain.
Fig. 9
Fig. 9 Shape and size classification for 2DI non-interferometric image with parallel bridge defect for models (a) 1A, 1B (b) 2A, 2B (c) 3A, 3B. Classification for 2DIS interferometric image with parallel bridge defect for models (d) 1A, 1B (e) 2A, 2B (f) 3A, 3B. Classification for 2DIS interferometric noisy image with perpendicular bridge defect for models (g) 1A, 1B (h) 2A, 2B (i) 3A, 3B. All models successfully detect the perpendicular defect when using the 32-nm seed because their detection rate was above the 50% threshold that was set for deciding defect versus no-defect. (j) Eigen distance map identifies the parallel defect indicated with the light color box. It has the smallest Euclidean distance and thus is correctly identified. (k) Parallel defect identified. (l) Reconstructed defect. (m) Eigen distance map identifies the perpendicular defect indicated with the light color box. This region has the smallest Euclidean distance and thus is correctly identified. (n) Identified region for the perpendicular defect in the optical image is buried in the noisy background. (o) Reconstructed perpendicular defect image.
Fig. 10
Fig. 10 (a) Shape of rectangular-shaped simulated defect images. (b) Shape of defects for H shape image is formed by subtracting the background pattern of parallel bars from a pattern with defect.
Fig. 11
Fig. 11 Parallel defect non-interferometric image with 2nd order difference (2DI). (a) Before and (b) after applying PCA.
Fig. 12
Fig. 12 Perpendicular defect interferometric image with 2DIS. (a) Before and (b) after applying PCA. The defect signal is buried in background and noise.

Tables (8)

Tables Icon

Table 1 Loss functions

Tables Icon

Algorithm 1 Outline of sampling stage 1.

Tables Icon

Algorithm 2 Outline of sampling stage 2.

Tables Icon

Table 2 Models obtained during training stage. The experimental sample used for training consisted of N’ non-interferometric image blocks for the parallel defect die.

Tables Icon

Table 3 Defect detection with 32-nm seed.

Tables Icon

Table 4 Performance of the six models for different experimental and simulation inputs. All models successfully identify negative test cases and properly reject the incorrectly shaped simulation defects.

Tables Icon

Table 5 Peak intensity trends in the denoised simulated mutual interference images for various seeds.

Tables Icon

Table 6 Defect detection 32-nm.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

k * = arg  min  k { λ s   2 | | Γ P P   n ( v ) Γ s y n   k , t ( v , w * , M s i m , H k , t ) | | 2 } ,
E D n , t ( I P P n , v , w * ) = λ s   2 | | Γ P P   n ( v ) Γ s y n   k * , t ( v , w * , M s i m , H k * , t ) | | 2 .
z ^ n = φ [ φ ( E D n , t c × min  n { 1 , ...   , 10 6 } { E D n , t } ) t 1 2 ] .
f w ( G ) = φ [ E D n 0 , t ( I P P n 0 , v , w ) c × min   n { 1 , ...   , N   ' } { E D n , t ( I P P n   ' , v , w ) } ] t .
P w ( z n 0 = 1 | G ) = 1 ( 1 + exp  [ f w ( G ) ] ) .
L o s s 1 , w = log  [ P w ( z n 0 = 1 | G ) ] .
L o s s 2 , w = log  [ P w ( z n 0 = 1 | G ) ] log  [ 1 P w ( z n 0 = 1 | G ) ] .
I i m a g e ( x , y ) = I b ( x , y ) + 2 R e [ E b ( x , y ) E d ( x , y ) ] + I d ( x , y ) ,
I i m a g e ( x , y ) I b ( x , y ) + M b d ( x , y ) .
I P P ( x , y ) I i m a g e ( x + d x , y ) 2 I i m a g e ( x , y ) + I i m a g e ( x d x , y ) .
I P P ( x , y ) δ M b o ( x , y ) + M b d ( x + d x , y ) 2 M b d ( x , y ) + M b d ( x d x , y ) .
S = { w 1 max  ( M j ) } ; j { 1 , ...   , 5 } .
A j ( x , y ) = w 2 M s e e d ( x , y ) + ( δ M b o ) j ,
( δ M b o ) j = w 1 max ( M j ) w 2 max ( M s e e d ) .
A j A k = w 1 max  ( M j ) w 1 max  ( M k ) .
m 1 i = ( 1 β 1 ) ( ^ L w w ^ 1 ) ; m 2 i = ( 1 β 1 ) ( ^ L w w ^ 2 ) ,
u i = max  ( β 2 × u i 1 , | | ^ L w w ^ i | | ) ,
Δ w 1 i = α 1 β 1   2 ( m 1 i u i ) ; Δ w 2 i = α 1 β 1   2 ( m 2 i u i ) .

Metrics