Abstract

Characterization of microstructures with features from submicrometers to hundreds of micrometers requires versatile methods. Profilometry and optical microscopy cannot cope with submicrometer features, and atomic-force microscopy, scanning-electron microscopy, and near-field microscopy are inherently slow, off-line methods. In optical scatterometry, the laser light scattered from a sample is measured and the sample profile is subsequently characterized. We propose the use of a two-stage model based on neural networks: rough categorization followed by refinement, thus reducing the need for prior information on the sample. We simulate the method for a submicrometer diffraction grating characterized by five parameters. It is shown that intensity measurements of few diffraction orders by use only of one wavelength are enough to yield rms errors of less than 2 nm for the parameters (approximately 2–3% of the optimal values of the parameters).

© 1999 Optical Society of America

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  4. Z. R. Hatab, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “16 MB DRAM trench depth characterization using dome scatterometry,” Appl. Surf. Sci. 86, 597–599 (1995).
    [CrossRef]
  5. S. Zaidi, S. L. Prins, J. R. McNeil, S. S. H. Naqvi, “Metrology sensors for advanced resists,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. H. Bennett, ed., Proc. SPIE2196, 341–351 (1994).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  18. C. M. Bishop, Neural Networks for Pattern Recognition (Oxford U. Press, New York, 1995).
  19. J. Saarinen, E. Noponen, J. Turunen, T. Suhara, H. Nishihara, “Asymmetric beam deflection by doubly grooved binary gratings,” Appl. Opt. 33, 2401–2405 (1995).
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1998 (1)

1997 (1)

B. W. Smith, “Strategies toward sub-0.25 µm lithography,” Opt. Photon. News 83(3), 23–27 (1997).
[CrossRef]

1995 (2)

Z. R. Hatab, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “16 MB DRAM trench depth characterization using dome scatterometry,” Appl. Surf. Sci. 86, 597–599 (1995).
[CrossRef]

J. Saarinen, E. Noponen, J. Turunen, T. Suhara, H. Nishihara, “Asymmetric beam deflection by doubly grooved binary gratings,” Appl. Opt. 33, 2401–2405 (1995).
[CrossRef]

1994 (2)

1993 (3)

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 2,” Solid State Technol. 36, 53–56 (1993).

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

1992 (1)

1991 (1)

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

1981 (1)

1977 (1)

Atkinson, J. T.

D. J. Search, C. A. Hobson, J. T. Atkinson, J. D. Pearson, “Diffraction pattern analysis for automatic defect classification in manufactured electronic assemblies,” in Machine Vision Applications in Industrial Inspection II, B. M. Dawson, S. S. Wilson, F. Y. Wu, eds., Proc. SPIE2183, 170–179 (1994).
[CrossRef]

Bauer, J. J.

J. Bischoff, J. W. Baumgart, H. Truckenbrodt, J. J. Bauer, “Photoresist metrology based on light scattering,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 678–689 (1996).
[CrossRef]

Baumgart, J. W.

J. Bischoff, J. W. Baumgart, H. Truckenbrodt, J. J. Bauer, “Photoresist metrology based on light scattering,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 678–689 (1996).
[CrossRef]

Bischoff, J.

J. Bischoff, J. W. Baumgart, H. Truckenbrodt, J. J. Bauer, “Photoresist metrology based on light scattering,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 678–689 (1996).
[CrossRef]

Bishop, C. M.

C. M. Bishop, Neural Networks for Pattern Recognition (Oxford U. Press, New York, 1995).

Bishop, K.

Bishop, K. P.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 2,” Solid State Technol. 36, 53–56 (1993).

Botten, L. C.

Clark, L. A.

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

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

Franke, J. E.

Gaspar, S. M.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 2,” Solid State Technol. 36, 53–56 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 1,” Solid State Technol. 36, 29–32 (1993).

Gaylord, T. K.

George, N.

Giapis, K. P.

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

Gottscho, R. A.

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

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

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

Haaland, D. M.

Hatab, Z. R.

Z. R. Hatab, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “16 MB DRAM trench depth characterization using dome scatterometry,” Appl. Surf. Sci. 86, 597–599 (1995).
[CrossRef]

Haykin, S.

S. Haykin, Neural Networks—A Comprehensive Foundation, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1999).

Hickman, K.

Hickman, K. C.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 2,” Solid State Technol. 36, 53–56 (1993).

Hobson, C. A.

D. J. Search, C. A. Hobson, J. T. Atkinson, J. D. Pearson, “Diffraction pattern analysis for automatic defect classification in manufactured electronic assemblies,” in Machine Vision Applications in Industrial Inspection II, B. M. Dawson, S. S. Wilson, F. Y. Wu, eds., Proc. SPIE2183, 170–179 (1994).
[CrossRef]

Kallioniemi, I.

Kaspar, S.

Kornblit, A.

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

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

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

Krukar, R.

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

Krukar, R. H.

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

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 2,” Solid State Technol. 36, 53–56 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 1,” Solid State Technol. 36, 29–32 (1993).

Kruskal, J.

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

Kruskal, J. B.

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

Lambert, D.

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

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

McNeil, J. R.

Z. R. Hatab, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “16 MB DRAM trench depth characterization using dome scatterometry,” Appl. Surf. Sci. 86, 597–599 (1995).
[CrossRef]

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

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 2,” Solid State Technol. 36, 53–56 (1993).

S. S. H. Naqvi, S. Kaspar, K. Hickman, K. Bishop, J. R. McNeil, “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt. 31, 1377–1384 (1992).
[CrossRef] [PubMed]

S. Zaidi, S. L. Prins, J. R. McNeil, S. S. H. Naqvi, “Metrology sensors for advanced resists,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. H. Bennett, ed., Proc. SPIE2196, 341–351 (1994).

C. J. Raymond, M. R. Murmane, S. S. H. Naqvi, J. R. McNeil, “A scatterometric sensor for lithography,” in Manufacturing Process Control for Microelectronic Devices and Circuits, A. G. Sabnis, ed., Proc. SPIE2336, 37–49 (1994).
[CrossRef]

B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Towards sub-0.1 µm CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 729–739 (1996).
[CrossRef]

Milner, L. M.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 2,” Solid State Technol. 36, 53–56 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 1,” Solid State Technol. 36, 29–32 (1993).

Minhas, B. K.

B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Towards sub-0.1 µm CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 729–739 (1996).
[CrossRef]

Moharam, M. G.

Murmane, M. R.

C. J. Raymond, M. R. Murmane, S. S. H. Naqvi, J. R. McNeil, “A scatterometric sensor for lithography,” in Manufacturing Process Control for Microelectronic Devices and Circuits, A. G. Sabnis, ed., Proc. SPIE2336, 37–49 (1994).
[CrossRef]

Naqvi, S. S. H.

Z. R. Hatab, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “16 MB DRAM trench depth characterization using dome scatterometry,” Appl. Surf. Sci. 86, 597–599 (1995).
[CrossRef]

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

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 2,” Solid State Technol. 36, 53–56 (1993).

S. S. H. Naqvi, S. Kaspar, K. Hickman, K. Bishop, J. R. McNeil, “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt. 31, 1377–1384 (1992).
[CrossRef] [PubMed]

S. Zaidi, S. L. Prins, J. R. McNeil, S. S. H. Naqvi, “Metrology sensors for advanced resists,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. H. Bennett, ed., Proc. SPIE2196, 341–351 (1994).

C. J. Raymond, M. R. Murmane, S. S. H. Naqvi, J. R. McNeil, “A scatterometric sensor for lithography,” in Manufacturing Process Control for Microelectronic Devices and Circuits, A. G. Sabnis, ed., Proc. SPIE2336, 37–49 (1994).
[CrossRef]

B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Towards sub-0.1 µm CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 729–739 (1996).
[CrossRef]

Nguyen, D.

D. Nguyen, B. Widrow, “The truck back-upper: an example of self-learning in neural networks,” in Neural Networks for Robotics and Control, W. T. Miller, R. Sutton, P. Werbos, eds. (MIT Press, Cambridge, Mass., 1990).

Niemczyk, T. M.

Nishihara, H.

J. Saarinen, E. Noponen, J. Turunen, T. Suhara, H. Nishihara, “Asymmetric beam deflection by doubly grooved binary gratings,” Appl. Opt. 33, 2401–2405 (1995).
[CrossRef]

Noponen, E.

J. Saarinen, E. Noponen, J. Turunen, T. Suhara, H. Nishihara, “Asymmetric beam deflection by doubly grooved binary gratings,” Appl. Opt. 33, 2401–2405 (1995).
[CrossRef]

Oja, E.

Pearson, J. D.

D. J. Search, C. A. Hobson, J. T. Atkinson, J. D. Pearson, “Diffraction pattern analysis for automatic defect classification in manufactured electronic assemblies,” in Machine Vision Applications in Industrial Inspection II, B. M. Dawson, S. S. Wilson, F. Y. Wu, eds., Proc. SPIE2183, 170–179 (1994).
[CrossRef]

Petersen, G. A.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 2,” Solid State Technol. 36, 53–56 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 1,” Solid State Technol. 36, 29–32 (1993).

Prins, S. L.

Z. R. Hatab, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “16 MB DRAM trench depth characterization using dome scatterometry,” Appl. Surf. Sci. 86, 597–599 (1995).
[CrossRef]

S. Zaidi, S. L. Prins, J. R. McNeil, S. S. H. Naqvi, “Metrology sensors for advanced resists,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. H. Bennett, ed., Proc. SPIE2196, 341–351 (1994).

B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Towards sub-0.1 µm CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 729–739 (1996).
[CrossRef]

Raymond, C. J.

C. J. Raymond, M. R. Murmane, S. S. H. Naqvi, J. R. McNeil, “A scatterometric sensor for lithography,” in Manufacturing Process Control for Microelectronic Devices and Circuits, A. G. Sabnis, ed., Proc. SPIE2336, 37–49 (1994).
[CrossRef]

Reitman, E. A.

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

Saarinen, J.

I. Kallioniemi, J. Saarinen, E. Oja, “Optical scatterometry of subwavelength diffraction gratings: neural network approach,” Appl. Opt. 37, 5830–5835 (1998).
[CrossRef]

J. Saarinen, E. Noponen, J. Turunen, T. Suhara, H. Nishihara, “Asymmetric beam deflection by doubly grooved binary gratings,” Appl. Opt. 33, 2401–2405 (1995).
[CrossRef]

Search, D. J.

D. J. Search, C. A. Hobson, J. T. Atkinson, J. D. Pearson, “Diffraction pattern analysis for automatic defect classification in manufactured electronic assemblies,” in Machine Vision Applications in Industrial Inspection II, B. M. Dawson, S. S. Wilson, F. Y. Wu, eds., Proc. SPIE2183, 170–179 (1994).
[CrossRef]

Sinatore, D.

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

Smith, B. W.

B. W. Smith, “Strategies toward sub-0.25 µm lithography,” Opt. Photon. News 83(3), 23–27 (1997).
[CrossRef]

Stern, M. B.

M. B. Stern, “Binary optics fabrication,” in Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997).

Suhara, T.

J. Saarinen, E. Noponen, J. Turunen, T. Suhara, H. Nishihara, “Asymmetric beam deflection by doubly grooved binary gratings,” Appl. Opt. 33, 2401–2405 (1995).
[CrossRef]

Truckenbrodt, H.

J. Bischoff, J. W. Baumgart, H. Truckenbrodt, J. J. Bauer, “Photoresist metrology based on light scattering,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 678–689 (1996).
[CrossRef]

Turunen, J.

J. Saarinen, E. Noponen, J. Turunen, T. Suhara, H. Nishihara, “Asymmetric beam deflection by doubly grooved binary gratings,” Appl. Opt. 33, 2401–2405 (1995).
[CrossRef]

Wang, S.-G.

Widrow, B.

D. Nguyen, B. Widrow, “The truck back-upper: an example of self-learning in neural networks,” in Neural Networks for Robotics and Control, W. T. Miller, R. Sutton, P. Werbos, eds. (MIT Press, Cambridge, Mass., 1990).

Wilson, I. J.

Zaidi, S.

S. Zaidi, S. L. Prins, J. R. McNeil, S. S. H. Naqvi, “Metrology sensors for advanced resists,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. H. Bennett, ed., Proc. SPIE2196, 341–351 (1994).

Appl. Opt. (5)

Appl. Surf. Sci. (1)

Z. R. Hatab, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “16 MB DRAM trench depth characterization using dome scatterometry,” Appl. Surf. Sci. 86, 597–599 (1995).
[CrossRef]

J. Appl. Phys. (1)

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

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

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

K. P. Giapis, R. A. Gottscho, L. A. Clark, J. B. Kruskal, D. Lambert, A. Kornblit, D. Sinatore, “Use of light scattering in characterizing reactively ion etched profiles,” J. Vac. Sci. Technol. A 9, 664–668 (1991).
[CrossRef]

Opt. Photon. News (1)

B. W. Smith, “Strategies toward sub-0.25 µm lithography,” Opt. Photon. News 83(3), 23–27 (1997).
[CrossRef]

Solid State Technol. (2)

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing. 2,” Solid State Technol. 36, 53–56 (1993).

Other (9)

S. Zaidi, S. L. Prins, J. R. McNeil, S. S. H. Naqvi, “Metrology sensors for advanced resists,” in Integrated Circuit Metrology, Inspection, and Process Control VII, M. H. Bennett, ed., Proc. SPIE2196, 341–351 (1994).

C. J. Raymond, M. R. Murmane, S. S. H. Naqvi, J. R. McNeil, “A scatterometric sensor for lithography,” in Manufacturing Process Control for Microelectronic Devices and Circuits, A. G. Sabnis, ed., Proc. SPIE2336, 37–49 (1994).
[CrossRef]

B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Towards sub-0.1 µm CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 729–739 (1996).
[CrossRef]

J. Bischoff, J. W. Baumgart, H. Truckenbrodt, J. J. Bauer, “Photoresist metrology based on light scattering,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 678–689 (1996).
[CrossRef]

D. J. Search, C. A. Hobson, J. T. Atkinson, J. D. Pearson, “Diffraction pattern analysis for automatic defect classification in manufactured electronic assemblies,” in Machine Vision Applications in Industrial Inspection II, B. M. Dawson, S. S. Wilson, F. Y. Wu, eds., Proc. SPIE2183, 170–179 (1994).
[CrossRef]

M. B. Stern, “Binary optics fabrication,” in Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997).

S. Haykin, Neural Networks—A Comprehensive Foundation, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1999).

C. M. Bishop, Neural Networks for Pattern Recognition (Oxford U. Press, New York, 1995).

D. Nguyen, B. Widrow, “The truck back-upper: an example of self-learning in neural networks,” in Neural Networks for Robotics and Control, W. T. Miller, R. Sutton, P. Werbos, eds. (MIT Press, Cambridge, Mass., 1990).

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Figures (5)

Fig. 1
Fig. 1

Geometry of a doubly grooved binary diffraction grating used to deflect the laser beam into the +1st reflected diffraction order R 1 with an angle of reflection θ1. Monochromatic light of wavelength λ in vacuum is traveling in quartz (n 1 = 1.46) and impinges upon the grating at angle of incidence θ i . The grating is coated with gold (n 2 = 0.12 + i3.29), and the light is thus reflected. The grating is characterized by five independent parameters: the depth of the first groove h 1, the depth of the second groove h 2, and the three transition points t 1, t 2, and t 3. The groove walls are assumed to be vertical, i.e., α = 0°.

Fig. 2
Fig. 2

Diffraction efficiencies R for the +1st (solid curve), 0th (long-dashed curve), and -1st (short-dashed curve) reflected diffraction orders as a function of slope angle α of the grooves. Angle of incidence, θ i = 0°, incident light, TM polarized.

Fig. 3
Fig. 3

Top, neural networks are used in a hierarchical manner. First the level-A network is used to roughly classify samples according to groove depths h 1 and h 2. If the predicted depth values lie inside the range of interlaced networks B1, B2, and B3, the level-B networks are used to give a more accurate prediction of the grating geometry. Ranges of the networks are shown for the groove depths. Bottom, schematic distribution of groove depth values predicted by network A as the target values lie inside the range of network B1.

Fig. 4
Fig. 4

Diffraction efficiencies R of the reflected diffraction orders +1 (solid curves), 0 (dashed curves), and -1 (dotted curves) when the five-grating geometry parameters is varied over the range of the level-A network while the other parameters are kept fixed to the optimum values. The varied parameter is (a) the first transition point t 1, (b) the second transition point t 2, (c) the third transition point t 3, (d) the depth of the first groove h 1, and (e) the depth of the second groove h 2. Vertical lines, optimum cases for the parameters. Angle of incidence, θ i = 0°; incident light, TM polarized.

Fig. 5
Fig. 5

Diffraction efficiencies R for the +1st (solid curves), 0th (dashed curves), and -1st (dotted curves) reflected orders calculated for 20 nonoptimal grating geometries. The samples are obtained by adding or subtracting an amount Δ q from the optimal value of parameter q. The value of Δ q is chosen from the normal distribution N(rms q , 0.5 × rms q ) according to the corresponding rms errors for (a) σ = -∞ dB, (b) σ = -20 dB, (c) σ = -13 dB. Angle of incidence, θ i = 0°; incident light, TM polarized.

Tables (6)

Tables Icon

Table 1 Angles of Reflection θ-1 and θ1 for Diffraction Orders R-1 and R1 with Three Angles of Incidence θi = 10°; 15°, 30°a

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Table 2 Classification Performance of the Level-A Network for Test Sample Sets TB1 and TBc, Representing the Range of Network B1 and the Complement of the Range of Networks B1, B2, and B3, Respectivelya

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Table 3 Root-Mean-Square Errors of Prediction between Output yB1 from Network B1 and Target Parameters O, Averaged over 200 Test Samplesa

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Table 4 Same as Table 3 Except That Input Data Consist of Diffraction Intensities R0 and R-1 Calculated with Three Angles of Incidence, θi = 10°, 15°, 30°, and One State of Polarization, TE, i.e., Six Elements in Total

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Table 5 Target Values and Predictions Given by Networks B1, B2, and B3 for Four Sample Gratings Chosen from within the Combined Range of the Three-Level B networksa

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Table 6 Same as Table 5 Except That Here Gaussian Noise with Standard Deviation σ = -13 dB Relative to the Intensity Is Added To the Test Input Data

Equations (8)

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

p1V1, V2=number of samples from V2 classified into V1 by network Atotal number of samples from V2 classified by network A×100%,
VB1=Orange of B1.
TB1=OmVB1, m=1,, 1000
VB=Orange of B1, B2, or B3.
VBc=Ooutside the combined range of B1, B2, and B3
TBc=OmVBc, m=1,, 1000
qnopt=qopt±Δq,
Δq=Nrmsq, 0.5×rmsq.

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