Abstract

Scatterometry has been widely applied in microelectronic manufacturing process monitoring. As a key part in scatterometry, inverse problem uses scatter signature to determine the shape of profile structure. The most common solutions for the inverse problem are model-based methods, such as library search, Levenberg-Marquardt algorithm and artificial neural network (ANN). However, they all require a pre-defined geometric model to extract 3D profile of the structure. When facing the complex structure in manufacturing process monitoring, the model-based methods will cost a long time and may fail to build a valid geometric model. Without the assumption of the geometric model, model-free methods are developed to find a mapping between profile parameter named label Y and corresponding spectral signature X. These methods need lots of labeled data obtained from transmission electron microscopy (TEM) or cross-sectional scanning electron microscopy (XSEM) with time-consuming and highly cost, leading to the increase of production costs. To address these issues, this paper develops a novel model-free method, called maximum contributed component regression (MCCR). It utilizes canonical correlation analysis (CCA) to estimate the maximum contributed components from pairwise relationship of economic unlabeled data with few expensive labeled data. In MCCR, the maximum contributed components are used to guide the solution of the inverse problem based on the conventional regression methods. Experimental results on both synthetic and real-world semiconductor datasets demonstrate the effectiveness of the proposed method given small amount of labeled data.

© 2017 Optical Society of America

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References

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2015 (1)

2014 (2)

2013 (2)

X. Chen, S. Liu, C. Zhang, and H. Jiang, “Improved measurement accuracy in optical scatterometry using correction-based library search,” Appl. Opt. 52, 6726–6734 (2013).
[Crossref] [PubMed]

J. Zhu, S. Liu, C. Zhang, X. Chen, and Z. Dong, “Identification and reconstruction of diffraction structures in optical scatterometry using support vector machine method,” J. Micro/Nanolithography, MEMS, and MOEMS 12, 013004 (2013).
[Crossref]

2012 (2)

2009 (1)

2008 (2)

I. Gereige, S. Robert, S. Thiria, F. Badran, G. Granet, and J. J. Rousseau, “Recognition of diffraction-grating profile using a neural network classifier in optical scatterometry,” JOSA A 25, 1661–1667 (2008).
[Crossref] [PubMed]

A. Kato, Y. Ikeda, Y. Kasahara, J. Shimanuki, T. Suda, T. Hasegawa, H. Sawabe, and S. Kohjiya, “Optical transparency and silica network structure in cross-linked natural rubber as revealed by spectroscopic and three-dimensional transmission electron microscopy techniques,” JOSA B 25, 1602–1615 (2008).
[Crossref]

2006 (1)

2005 (1)

C. Raymond, “Overview of scatterometry applications in high volume silicon manufacturing,” Characterization and Metrology for ULSI Technology 2005 788, 394–402 (2005).
[Crossref]

2004 (1)

H.-T. Huang and F. L. Terry, “Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455, 828–836 (2004).
[Crossref]

2002 (1)

S. Robert, A. Mure-Ravaud, and D. Lacour, “Characterization of optical diffraction gratings by use of a neural method,” JOSA A 19, 24–32 (2002).
[Crossref] [PubMed]

2001 (1)

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14, 97–111 (2001).
[Crossref]

1998 (1)

1997 (2)

M. Hanke, “A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems,” Inv. Prob. 13, 79 (1997).
[Crossref]

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. A 15, 361–368 (1997).
[Crossref]

1994 (1)

S. Naqvi, J. Franke, D. Haaland, R. Gottscho, A. Kornblit, T. Niemczyk, R. Krukar, and J. McNeil, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” JOSA A 11, 2485–2493 (1994).
[Crossref]

1993 (1)

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, and R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

1986 (2)

G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56, 930 (1986).
[Crossref] [PubMed]

P. Geladi and B. R. Kowalski, “Partial least-squares regression: a tutorial,” Anal. Chim. Acta 185, 1–17 (1986).
[Crossref]

1985 (1)

Y. Lepetre, J.-J. Metois, G. Rasigni, R. Rivoira, and R. Philip, “Characterization of layered synthetic microstructures using transmission electron microscopy,” JOSA A 2, 1356–1362 (1985).
[Crossref]

1933 (1)

H. Hotelling, “Analysis of a complex of statistical variables into principal components,” J. Edu. Psychol. 24, 417–441 (1933).
[Crossref]

Arai, A. Y.

Badran, F.

I. Gereige, S. Robert, S. Thiria, F. Badran, G. Granet, and J. J. Rousseau, “Recognition of diffraction-grating profile using a neural network classifier in optical scatterometry,” JOSA A 25, 1661–1667 (2008).
[Crossref] [PubMed]

Balduzzi, D.

B. McWilliams, D. Balduzzi, and J. M. Buhmann, “Correlated random features for fast semi-supervised learning,” in Proc. Adv. Neural Inf. Process. Syst. (2013), pp. 440–448.

Bao, J.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14, 97–111 (2001).
[Crossref]

Barnes, B. M.

Binnig, G.

G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56, 930 (1986).
[Crossref] [PubMed]

Bovatsek, J.

Bricchi, E.

Buhmann, J. M.

B. McWilliams, D. Balduzzi, and J. M. Buhmann, “Correlated random features for fast semi-supervised learning,” in Proc. Adv. Neural Inf. Process. Syst. (2013), pp. 440–448.

Chaudhuri, K.

K. Chaudhuri, S. M. Kakade, K. Livescu, and K. Sridharan, “Multi-view clustering via canonical correlation analysis,” in Proc. Int. Conf. Mach. Learn. (ACM, 2009), pp. 129–136.

Chen, X.

Clark, L. A.

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, and R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

Coene, W. M.

Dong, Z.

J. Zhu, S. Liu, C. Zhang, X. Chen, and Z. Dong, “Identification and reconstruction of diffraction structures in optical scatterometry using support vector machine method,” J. Micro/Nanolithography, MEMS, and MOEMS 12, 013004 (2013).
[Crossref]

Du, W.

El Gawhary, O.

Foster, D. P.

S. M. Kakade and D. P. Foster, “Multi-view regression via canonical correlation analysis,” in Learning theory (Springer, 2007), pp. 82–96.
[Crossref]

Franke, J.

S. Naqvi, J. Franke, D. Haaland, R. Gottscho, A. Kornblit, T. Niemczyk, R. Krukar, and J. McNeil, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” JOSA A 11, 2485–2493 (1994).
[Crossref]

Fujiwara, H.

H. Fujiwara, Spectroscopic ellipsometry: principles and applications (John Wiley & Sons, 2007).
[Crossref]

Geladi, P.

P. Geladi and B. R. Kowalski, “Partial least-squares regression: a tutorial,” Anal. Chim. Acta 185, 1–17 (1986).
[Crossref]

Gerber, C.

G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56, 930 (1986).
[Crossref] [PubMed]

Gereige, I.

I. Gereige, S. Robert, S. Thiria, F. Badran, G. Granet, and J. J. Rousseau, “Recognition of diffraction-grating profile using a neural network classifier in optical scatterometry,” JOSA A 25, 1661–1667 (2008).
[Crossref] [PubMed]

Gottscho, R.

S. Naqvi, J. Franke, D. Haaland, R. Gottscho, A. Kornblit, T. Niemczyk, R. Krukar, and J. McNeil, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” JOSA A 11, 2485–2493 (1994).
[Crossref]

Gottscho, R. A.

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, and R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

Granet, G.

I. Gereige, S. Robert, S. Thiria, F. Badran, G. Granet, and J. J. Rousseau, “Recognition of diffraction-grating profile using a neural network classifier in optical scatterometry,” JOSA A 25, 1661–1667 (2008).
[Crossref] [PubMed]

Haaland, D.

S. Naqvi, J. Franke, D. Haaland, R. Gottscho, A. Kornblit, T. Niemczyk, R. Krukar, and J. McNeil, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” JOSA A 11, 2485–2493 (1994).
[Crossref]

Hanke, M.

M. Hanke, “A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems,” Inv. Prob. 13, 79 (1997).
[Crossref]

Hao, Y.

Hasegawa, T.

A. Kato, Y. Ikeda, Y. Kasahara, J. Shimanuki, T. Suda, T. Hasegawa, H. Sawabe, and S. Kohjiya, “Optical transparency and silica network structure in cross-linked natural rubber as revealed by spectroscopic and three-dimensional transmission electron microscopy techniques,” JOSA B 25, 1602–1615 (2008).
[Crossref]

Hosch, J. W.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. A 15, 361–368 (1997).
[Crossref]

Hotelling, H.

H. Hotelling, “Analysis of a complex of statistical variables into principal components,” J. Edu. Psychol. 24, 417–441 (1933).
[Crossref]

Hu, J.

Huang, H.-T.

H.-T. Huang and F. L. Terry, “Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455, 828–836 (2004).
[Crossref]

Ikeda, Y.

A. Kato, Y. Ikeda, Y. Kasahara, J. Shimanuki, T. Suda, T. Hasegawa, H. Sawabe, and S. Kohjiya, “Optical transparency and silica network structure in cross-linked natural rubber as revealed by spectroscopic and three-dimensional transmission electron microscopy techniques,” JOSA B 25, 1602–1615 (2008).
[Crossref]

Jakatdar, N.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14, 97–111 (2001).
[Crossref]

Jiang, H.

Kakade, S. M.

K. Chaudhuri, S. M. Kakade, K. Livescu, and K. Sridharan, “Multi-view clustering via canonical correlation analysis,” in Proc. Int. Conf. Mach. Learn. (ACM, 2009), pp. 129–136.

S. M. Kakade and D. P. Foster, “Multi-view regression via canonical correlation analysis,” in Learning theory (Springer, 2007), pp. 82–96.
[Crossref]

Kallioniemi, I.

Kasahara, Y.

A. Kato, Y. Ikeda, Y. Kasahara, J. Shimanuki, T. Suda, T. Hasegawa, H. Sawabe, and S. Kohjiya, “Optical transparency and silica network structure in cross-linked natural rubber as revealed by spectroscopic and three-dimensional transmission electron microscopy techniques,” JOSA B 25, 1602–1615 (2008).
[Crossref]

Kato, A.

A. Kato, Y. Ikeda, Y. Kasahara, J. Shimanuki, T. Suda, T. Hasegawa, H. Sawabe, and S. Kohjiya, “Optical transparency and silica network structure in cross-linked natural rubber as revealed by spectroscopic and three-dimensional transmission electron microscopy techniques,” JOSA B 25, 1602–1615 (2008).
[Crossref]

Kazansky, P. G.

Kim, Y.-N.

Kohjiya, S.

A. Kato, Y. Ikeda, Y. Kasahara, J. Shimanuki, T. Suda, T. Hasegawa, H. Sawabe, and S. Kohjiya, “Optical transparency and silica network structure in cross-linked natural rubber as revealed by spectroscopic and three-dimensional transmission electron microscopy techniques,” JOSA B 25, 1602–1615 (2008).
[Crossref]

Kornblit, A.

S. Naqvi, J. Franke, D. Haaland, R. Gottscho, A. Kornblit, T. Niemczyk, R. Krukar, and J. McNeil, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” JOSA A 11, 2485–2493 (1994).
[Crossref]

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, and R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

Kowalski, B. R.

P. Geladi and B. R. Kowalski, “Partial least-squares regression: a tutorial,” Anal. Chim. Acta 185, 1–17 (1986).
[Crossref]

Krukar, R.

S. Naqvi, J. Franke, D. Haaland, R. Gottscho, A. Kornblit, T. Niemczyk, R. Krukar, and J. McNeil, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” JOSA A 11, 2485–2493 (1994).
[Crossref]

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, and R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

Kruskal, J.

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, and R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

Kumar, N.

Lacour, D.

S. Robert, A. Mure-Ravaud, and D. Lacour, “Characterization of optical diffraction gratings by use of a neural method,” JOSA A 19, 24–32 (2002).
[Crossref] [PubMed]

Lambert, D.

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, and R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

Lee, S.

Lepetre, Y.

Y. Lepetre, J.-J. Metois, G. Rasigni, R. Rivoira, and R. Philip, “Characterization of layered synthetic microstructures using transmission electron microscopy,” JOSA A 2, 1356–1362 (1985).
[Crossref]

Li, Z.-Y.

Liu, S.

Liu, Y.

Liu, Z.

Livescu, K.

K. Chaudhuri, S. M. Kakade, K. Livescu, and K. Sridharan, “Multi-view clustering via canonical correlation analysis,” in Proc. Int. Conf. Mach. Learn. (ACM, 2009), pp. 129–136.

McGahan, W.

McNeil, J.

S. Naqvi, J. Franke, D. Haaland, R. Gottscho, A. Kornblit, T. Niemczyk, R. Krukar, and J. McNeil, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” JOSA A 11, 2485–2493 (1994).
[Crossref]

McNeil, J. R.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. A 15, 361–368 (1997).
[Crossref]

McWilliams, B.

B. McWilliams, D. Balduzzi, and J. M. Buhmann, “Correlated random features for fast semi-supervised learning,” in Proc. Adv. Neural Inf. Process. Syst. (2013), pp. 440–448.

Meng, Z.-M.

Metois, J.-J.

Y. Lepetre, J.-J. Metois, G. Rasigni, R. Rivoira, and R. Philip, “Characterization of layered synthetic microstructures using transmission electron microscopy,” JOSA A 2, 1356–1362 (1985).
[Crossref]

Moré, J. J.

J. J. Moré, “The Levenberg-Marquardt algorithm: implementation and theory,” in Numer. Anal. (Springer, 1978), pp. 105–116.

Mure-Ravaud, A.

S. Robert, A. Mure-Ravaud, and D. Lacour, “Characterization of optical diffraction gratings by use of a neural method,” JOSA A 19, 24–32 (2002).
[Crossref] [PubMed]

Murnane, M. R.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. A 15, 361–368 (1997).
[Crossref]

Naqvi, H.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. A 15, 361–368 (1997).
[Crossref]

Naqvi, S.

S. Naqvi, J. Franke, D. Haaland, R. Gottscho, A. Kornblit, T. Niemczyk, R. Krukar, and J. McNeil, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” JOSA A 11, 2485–2493 (1994).
[Crossref]

Niemczyk, T.

S. Naqvi, J. Franke, D. Haaland, R. Gottscho, A. Kornblit, T. Niemczyk, R. Krukar, and J. McNeil, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” JOSA A 11, 2485–2493 (1994).
[Crossref]

Niu, X.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14, 97–111 (2001).
[Crossref]

Oja, E.

Paek, J.-S.

Pereira, S. F.

Petrik, P.

Philip, R.

Y. Lepetre, J.-J. Metois, G. Rasigni, R. Rivoira, and R. Philip, “Characterization of layered synthetic microstructures using transmission electron microscopy,” JOSA A 2, 1356–1362 (1985).
[Crossref]

Prins, S. L.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. A 15, 361–368 (1997).
[Crossref]

Qin, F.

Quate, C. F.

G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56, 930 (1986).
[Crossref] [PubMed]

Rabello, S.

Ramanandan, G. K.

Rasigni, G.

Y. Lepetre, J.-J. Metois, G. Rasigni, R. Rivoira, and R. Philip, “Characterization of layered synthetic microstructures using transmission electron microscopy,” JOSA A 2, 1356–1362 (1985).
[Crossref]

Raymond, C.

C. Raymond, “Overview of scatterometry applications in high volume silicon manufacturing,” Characterization and Metrology for ULSI Technology 2005 788, 394–402 (2005).
[Crossref]

Raymond, C. J.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. A 15, 361–368 (1997).
[Crossref]

Reitman, E. A.

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, and R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

Rivoira, R.

Y. Lepetre, J.-J. Metois, G. Rasigni, R. Rivoira, and R. Philip, “Characterization of layered synthetic microstructures using transmission electron microscopy,” JOSA A 2, 1356–1362 (1985).
[Crossref]

Robert, S.

I. Gereige, S. Robert, S. Thiria, F. Badran, G. Granet, and J. J. Rousseau, “Recognition of diffraction-grating profile using a neural network classifier in optical scatterometry,” JOSA A 25, 1661–1667 (2008).
[Crossref] [PubMed]

S. Robert, A. Mure-Ravaud, and D. Lacour, “Characterization of optical diffraction gratings by use of a neural method,” JOSA A 19, 24–32 (2002).
[Crossref] [PubMed]

Rousseau, J. J.

I. Gereige, S. Robert, S. Thiria, F. Badran, G. Granet, and J. J. Rousseau, “Recognition of diffraction-grating profile using a neural network classifier in optical scatterometry,” JOSA A 25, 1661–1667 (2008).
[Crossref] [PubMed]

Roy, S.

Saarinen, J.

Sawabe, H.

A. Kato, Y. Ikeda, Y. Kasahara, J. Shimanuki, T. Suda, T. Hasegawa, H. Sawabe, and S. Kohjiya, “Optical transparency and silica network structure in cross-linked natural rubber as revealed by spectroscopic and three-dimensional transmission electron microscopy techniques,” JOSA B 25, 1602–1615 (2008).
[Crossref]

Shimanuki, J.

A. Kato, Y. Ikeda, Y. Kasahara, J. Shimanuki, T. Suda, T. Hasegawa, H. Sawabe, and S. Kohjiya, “Optical transparency and silica network structure in cross-linked natural rubber as revealed by spectroscopic and three-dimensional transmission electron microscopy techniques,” JOSA B 25, 1602–1615 (2008).
[Crossref]

Silver, R. M.

Sohail, S.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. A 15, 361–368 (1997).
[Crossref]

Spanos, C. J.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14, 97–111 (2001).
[Crossref]

Sridharan, K.

K. Chaudhuri, S. M. Kakade, K. Livescu, and K. Sridharan, “Multi-view clustering via canonical correlation analysis,” in Proc. Int. Conf. Mach. Learn. (ACM, 2009), pp. 129–136.

Suda, T.

A. Kato, Y. Ikeda, Y. Kasahara, J. Shimanuki, T. Suda, T. Hasegawa, H. Sawabe, and S. Kohjiya, “Optical transparency and silica network structure in cross-linked natural rubber as revealed by spectroscopic and three-dimensional transmission electron microscopy techniques,” JOSA B 25, 1602–1615 (2008).
[Crossref]

Terry, F. L.

H.-T. Huang and F. L. Terry, “Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455, 828–836 (2004).
[Crossref]

Thiria, S.

I. Gereige, S. Robert, S. Thiria, F. Badran, G. Granet, and J. J. Rousseau, “Recognition of diffraction-grating profile using a neural network classifier in optical scatterometry,” JOSA A 25, 1661–1667 (2008).
[Crossref] [PubMed]

Thompson, B.

B. Thompson, “Canonical correlation analysis,” Encyclopedia of Statistics in Behavioral Science (2005).
[Crossref]

Urbach, H. P.

Yang, W.

Zhang, C.

Zhang, N. F.

Zhong, X.-L.

Zhou, H.

Zhu, J.

J. Zhu, S. Liu, X. Chen, C. Zhang, and H. Jiang, “Robust solution to the inverse problem in optical scatterometry,” Opt. Express 22, 22031–22042 (2014).
[Crossref] [PubMed]

J. Zhu, S. Liu, C. Zhang, X. Chen, and Z. Dong, “Identification and reconstruction of diffraction structures in optical scatterometry using support vector machine method,” J. Micro/Nanolithography, MEMS, and MOEMS 12, 013004 (2013).
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Anal. Chim. Acta (1)

P. Geladi and B. R. Kowalski, “Partial least-squares regression: a tutorial,” Anal. Chim. Acta 185, 1–17 (1986).
[Crossref]

Appl. Opt. (3)

Characterization and Metrology for ULSI Technology 2005 (1)

C. Raymond, “Overview of scatterometry applications in high volume silicon manufacturing,” Characterization and Metrology for ULSI Technology 2005 788, 394–402 (2005).
[Crossref]

IEEE Trans. Semicond. Manuf. (1)

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14, 97–111 (2001).
[Crossref]

Inv. Prob. (1)

M. Hanke, “A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems,” Inv. Prob. 13, 79 (1997).
[Crossref]

J. Appl. Phys. (1)

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, and R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

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H. Hotelling, “Analysis of a complex of statistical variables into principal components,” J. Edu. Psychol. 24, 417–441 (1933).
[Crossref]

J. Micro/Nanolithography, MEMS, and MOEMS (1)

J. Zhu, S. Liu, C. Zhang, X. Chen, and Z. Dong, “Identification and reconstruction of diffraction structures in optical scatterometry using support vector machine method,” J. Micro/Nanolithography, MEMS, and MOEMS 12, 013004 (2013).
[Crossref]

J. Vac. Sci. Technol. A (1)

C. J. Raymond, M. R. Murnane, S. L. Prins, S. Sohail, H. Naqvi, J. R. McNeil, and J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. A 15, 361–368 (1997).
[Crossref]

JOSA A (4)

S. Naqvi, J. Franke, D. Haaland, R. Gottscho, A. Kornblit, T. Niemczyk, R. Krukar, and J. McNeil, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” JOSA A 11, 2485–2493 (1994).
[Crossref]

I. Gereige, S. Robert, S. Thiria, F. Badran, G. Granet, and J. J. Rousseau, “Recognition of diffraction-grating profile using a neural network classifier in optical scatterometry,” JOSA A 25, 1661–1667 (2008).
[Crossref] [PubMed]

S. Robert, A. Mure-Ravaud, and D. Lacour, “Characterization of optical diffraction gratings by use of a neural method,” JOSA A 19, 24–32 (2002).
[Crossref] [PubMed]

Y. Lepetre, J.-J. Metois, G. Rasigni, R. Rivoira, and R. Philip, “Characterization of layered synthetic microstructures using transmission electron microscopy,” JOSA A 2, 1356–1362 (1985).
[Crossref]

JOSA B (1)

A. Kato, Y. Ikeda, Y. Kasahara, J. Shimanuki, T. Suda, T. Hasegawa, H. Sawabe, and S. Kohjiya, “Optical transparency and silica network structure in cross-linked natural rubber as revealed by spectroscopic and three-dimensional transmission electron microscopy techniques,” JOSA B 25, 1602–1615 (2008).
[Crossref]

Opt. Express (6)

Phys. Rev. Lett. (1)

G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 56, 930 (1986).
[Crossref] [PubMed]

Thin Solid Films (1)

H.-T. Huang and F. L. Terry, “Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455, 828–836 (2004).
[Crossref]

Other (6)

J. J. Moré, “The Levenberg-Marquardt algorithm: implementation and theory,” in Numer. Anal. (Springer, 1978), pp. 105–116.

B. Thompson, “Canonical correlation analysis,” Encyclopedia of Statistics in Behavioral Science (2005).
[Crossref]

B. McWilliams, D. Balduzzi, and J. M. Buhmann, “Correlated random features for fast semi-supervised learning,” in Proc. Adv. Neural Inf. Process. Syst. (2013), pp. 440–448.

S. M. Kakade and D. P. Foster, “Multi-view regression via canonical correlation analysis,” in Learning theory (Springer, 2007), pp. 82–96.
[Crossref]

K. Chaudhuri, S. M. Kakade, K. Livescu, and K. Sridharan, “Multi-view clustering via canonical correlation analysis,” in Proc. Int. Conf. Mach. Learn. (ACM, 2009), pp. 129–136.

H. Fujiwara, Spectroscopic ellipsometry: principles and applications (John Wiley & Sons, 2007).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Suppose there are only 10 samples, each of which has 132 dimensions. The components for data with deeper blue colors have higher contributions in regression. (a) shows the principal components from PCA; (b) shows the high contributed components in best situation.
Fig. 2
Fig. 2 Illustration of the proposed method MCCR.
Fig. 3
Fig. 3 (a) Measurement setup of the spectroscopic ellipsometry, and (b) the structure of the semiconductor.
Fig. 4
Fig. 4 Spatial structure of the six spectrum data projected to 3D space. Gradient color reflects the continous change of response variable in label values.
Fig. 5
Fig. 5 Comparison of our MCCR method to PCR and PLS with different number of labeled data, which is changed from 10 to 50 in (a) SiHT, (b) SiTCD, (c) SiBCD, (d) MaskHT, (e) SiO2HT, and (f) ROX.
Fig. 6
Fig. 6 Comparison of our MCCR method to PCR and PLS with different number of labeled data changing from 3 to 16 in a real dataset ROX.

Tables (4)

Tables Icon

Algorithm 1: Maximum contributed component regression (MCCR).

Tables Icon

Table 1 Statistical values for the six floating parameters.

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Table 2 The average improvement rates of MCCR to PCR and PLS for six parameters.

Tables Icon

Table 3 The time of training and testing time for the proposed MCCR, here N is the number of labeled data, s is the abbreviation of seconds.

Equations (7)

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y = β 0 + β 1 × z 1 + β 2 × z 2 + + β m × z m ,
β ^ = arg min β 1 n l i = 1 n l ( β T z i y i ) 2 .
ρ = w 1 T G 1 G 2 T w 2 ( w 1 T G 1 G 1 T w 1 ) ( w 2 T G 2 G 2 T w 2 ) .
max W 1 , W 2 Tr [ W 1 T G 1 G 2 T W 2 ] , s . t . W 1 T G 1 G 1 T W 1 = I , W 2 T G 2 G 2 T W 2 = I ,
{ G 1 G 2 T ( G 2 G 2 T ) 1 G 2 G 1 T w 1 = λ G 1 G 1 T w 1 , G 2 G 1 T ( G 1 G 1 T ) 1 G 1 G 1 T w 2 = λ G 2 G 2 T w 2 ,
W = [ W 1 , W 2 ] .
2 = [ 1 N 1 i = 1 N ( y i μ ) ( y ^ i μ ^ ) σ σ ^ ] 2 ,

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