Abstract

The zeroth-order cross-reflection coefficients of a surface-relief grating are shown to be equal from experimental evidence and numerical evidence by use of rigorous coupled-wave analysis simulations. This result is valid for any range of grating parameters as well as for anisotropic media that have the optic axis in the surface plane. This result is corroborated by effective-medium theory, which models the gratings as thin layers of uniaxial anisotropic media that have the optic axis in the surface plane. For asymmetric grating profiles the zeroth-order reflection coefficients are no longer identical. This property has potential for scatterometry applications.

© 1999 Optical Society of America

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  1. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 10, 1383–1392 (1982).
  2. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of grating diffraction—E-mode polarization and losses,” J. Opt. Soc. Am. 73, 451–455 (1983).
    [CrossRef]
  3. M. G. Moharam, E. B. Grann, D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [CrossRef]
  4. M. G. Moharam, D. A. Pommet, E. B. Grann, “Stable implementation of the rigorous coupled-wave theory for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
    [CrossRef]
  5. S. Peng, G. M. Morris, “Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings,” J. Opt. Soc. Am. A 12, 1087–1096 (1995).
    [CrossRef]
  6. C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, J. R. McNeil, “Metrology of subwavelength photoresist gratings using optical scatterometry,” J. Vac. Sci. Technol. B 13, 1484–1495 (1995).
    [CrossRef]
  7. 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 microelectronic processing,” Microlithography World 1, 16–22 (1992).
  8. J. Bischoff, L. Hutschenreuther, H. Truckenbrodt, “New aspects of optical scatterometry applied to microtechnology,” in In-Line Characterization Techniques for Performance and Yield Enhancement in Microelectronic Manufacturing, D. K. DeBusk, ed., Proc. SPIE3215, 144–155 (1997).
    [CrossRef]
  9. K. P. Bishop, S. M. Gaspar, L. M. Milner, S. S. H. Naqvi, J. R. McNeil, “Grating line shape characterization using scatterometry,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 64–73 (1991).
    [CrossRef]
  10. S. A. Coulombe, P. C. Logofatu, B. K. Minhas, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric scatterometry for sub-0.1-µm CD measurements,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 282–293 (1998).
    [CrossRef]
  11. S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, J. R. McNeil, “Scatterometry measurement of sub-0.1-µm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
    [CrossRef]
  12. B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Toward 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]
  13. B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric scatterometry for the metrology of sub-0.1-µm-linewidth structures,” Appl. Opt. 37, 5112–5115 (1998).
    [CrossRef]
  14. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [CrossRef]
  15. M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
    [CrossRef]
  16. M. G. Moharam, T. K. Gaylord, G. T. Sincerbox, H. Werlich, B. Yung, “Diffraction characteristics of photoresist surface-relief gratings,” Appl. Opt. 23, 3214–3220 (1984).
    [CrossRef] [PubMed]
  17. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. 3, 1780–1787 (1986).
    [CrossRef]
  18. R. M. A. Azzam, “Application of generalized ellipsometry to anisotropic crystals,” J. Opt. Soc. Am. 64, 128–133 (1974).
    [CrossRef]
  19. R. M. A. Azzam, N. M. Bashara, “Generalized ellipsometry for surfaces with directional preference: application to diffraction gratings,” J. Opt. Soc. Am. 62, 1521–1523 (1972).
    [CrossRef]
  20. G. Campbell, “Effective-medium theory of sinusoidally modulated volume holograms,” J. Opt. Soc. Am. A 12, 1113–1117 (1995).
    [CrossRef]
  21. D. H. Raguin, G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993).
    [CrossRef] [PubMed]
  22. T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
    [CrossRef] [PubMed]
  23. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1985), Chap. 14.
  24. T. P. Sosnowski, “Polarization mode filters for integrated optics,” Opt. Commun. 4, 408–412 (1972).
    [CrossRef]
  25. P. Yeh, “Optics of anisotropic layered media: a new 4 4 matrix algebra,” Surf. Sci. 96, 41–53 (1980).
    [CrossRef]

1998

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, J. R. McNeil, “Scatterometry measurement of sub-0.1-µm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
[CrossRef]

B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric scatterometry for the metrology of sub-0.1-µm-linewidth structures,” Appl. Opt. 37, 5112–5115 (1998).
[CrossRef]

1995

1993

1992

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 microelectronic processing,” Microlithography World 1, 16–22 (1992).

1986

M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. 3, 1780–1787 (1986).
[CrossRef]

T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
[CrossRef] [PubMed]

1984

1983

1982

M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 10, 1383–1392 (1982).

1981

1980

P. Yeh, “Optics of anisotropic layered media: a new 4 4 matrix algebra,” Surf. Sci. 96, 41–53 (1980).
[CrossRef]

1974

1972

Azzam, R. M. A.

Baird, W. E.

Bashara, N. M.

Bischoff, J.

J. Bischoff, L. Hutschenreuther, H. Truckenbrodt, “New aspects of optical scatterometry applied to microtechnology,” in In-Line Characterization Techniques for Performance and Yield Enhancement in Microelectronic Manufacturing, D. K. DeBusk, ed., Proc. SPIE3215, 144–155 (1997).
[CrossRef]

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 microelectronic processing,” Microlithography World 1, 16–22 (1992).

K. P. Bishop, S. M. Gaspar, L. M. Milner, S. S. H. Naqvi, J. R. McNeil, “Grating line shape characterization using scatterometry,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 64–73 (1991).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1985), Chap. 14.

Campbell, G.

Coulombe, S. A.

B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric scatterometry for the metrology of sub-0.1-µm-linewidth structures,” Appl. Opt. 37, 5112–5115 (1998).
[CrossRef]

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, J. R. McNeil, “Scatterometry measurement of sub-0.1-µm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
[CrossRef]

S. A. Coulombe, P. C. Logofatu, B. K. Minhas, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric scatterometry for sub-0.1-µm CD measurements,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 282–293 (1998).
[CrossRef]

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 microelectronic processing,” Microlithography World 1, 16–22 (1992).

K. P. Bishop, S. M. Gaspar, L. M. Milner, S. S. H. Naqvi, J. R. McNeil, “Grating line shape characterization using scatterometry,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 64–73 (1991).
[CrossRef]

Gaylord, T. K.

Grann, E. B.

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 microelectronic processing,” Microlithography World 1, 16–22 (1992).

Hutschenreuther, L.

J. Bischoff, L. Hutschenreuther, H. Truckenbrodt, “New aspects of optical scatterometry applied to microtechnology,” in In-Line Characterization Techniques for Performance and Yield Enhancement in Microelectronic Manufacturing, D. K. DeBusk, ed., Proc. SPIE3215, 144–155 (1997).
[CrossRef]

Krukar, R. H.

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 microelectronic processing,” Microlithography World 1, 16–22 (1992).

Logofatu, P. C.

S. A. Coulombe, P. C. Logofatu, B. K. Minhas, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric scatterometry for sub-0.1-µm CD measurements,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 282–293 (1998).
[CrossRef]

McNeil, J. R.

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, J. R. McNeil, “Scatterometry measurement of sub-0.1-µm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
[CrossRef]

B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric scatterometry for the metrology of sub-0.1-µm-linewidth structures,” Appl. Opt. 37, 5112–5115 (1998).
[CrossRef]

C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, J. R. McNeil, “Metrology of subwavelength photoresist gratings using optical scatterometry,” J. Vac. Sci. Technol. B 13, 1484–1495 (1995).
[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 microelectronic processing,” Microlithography World 1, 16–22 (1992).

K. P. Bishop, S. M. Gaspar, L. M. Milner, S. S. H. Naqvi, J. R. McNeil, “Grating line shape characterization using scatterometry,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 64–73 (1991).
[CrossRef]

S. A. Coulombe, P. C. Logofatu, B. K. Minhas, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric scatterometry for sub-0.1-µm CD measurements,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 282–293 (1998).
[CrossRef]

B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Toward 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 microelectronic processing,” Microlithography World 1, 16–22 (1992).

K. P. Bishop, S. M. Gaspar, L. M. Milner, S. S. H. Naqvi, J. R. McNeil, “Grating line shape characterization using scatterometry,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 64–73 (1991).
[CrossRef]

Minhas, B. K.

B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric scatterometry for the metrology of sub-0.1-µm-linewidth structures,” Appl. Opt. 37, 5112–5115 (1998).
[CrossRef]

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, J. R. McNeil, “Scatterometry measurement of sub-0.1-µm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
[CrossRef]

B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Toward 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]

S. A. Coulombe, P. C. Logofatu, B. K. Minhas, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric scatterometry for sub-0.1-µm CD measurements,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 282–293 (1998).
[CrossRef]

Moharam, M. G.

M. G. Moharam, D. A. Pommet, E. B. Grann, “Stable implementation of the rigorous coupled-wave theory for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
[CrossRef]

M. G. Moharam, E. B. Grann, D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
[CrossRef]

M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. 3, 1780–1787 (1986).
[CrossRef]

T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
[CrossRef] [PubMed]

M. G. Moharam, T. K. Gaylord, G. T. Sincerbox, H. Werlich, B. Yung, “Diffraction characteristics of photoresist surface-relief gratings,” Appl. Opt. 23, 3214–3220 (1984).
[CrossRef] [PubMed]

M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of grating diffraction—E-mode polarization and losses,” J. Opt. Soc. Am. 73, 451–455 (1983).
[CrossRef]

M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
[CrossRef]

M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 10, 1383–1392 (1982).

M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
[CrossRef]

Morris, G. M.

Murnane, M. R.

C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, J. R. McNeil, “Metrology of subwavelength photoresist gratings using optical scatterometry,” J. Vac. Sci. Technol. B 13, 1484–1495 (1995).
[CrossRef]

Naqvi, S. S. H.

B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric scatterometry for the metrology of sub-0.1-µm-linewidth structures,” Appl. Opt. 37, 5112–5115 (1998).
[CrossRef]

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, J. R. McNeil, “Scatterometry measurement of sub-0.1-µm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
[CrossRef]

C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, J. R. McNeil, “Metrology of subwavelength photoresist gratings using optical scatterometry,” J. Vac. Sci. Technol. B 13, 1484–1495 (1995).
[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 microelectronic processing,” Microlithography World 1, 16–22 (1992).

K. P. Bishop, S. M. Gaspar, L. M. Milner, S. S. H. Naqvi, J. R. McNeil, “Grating line shape characterization using scatterometry,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 64–73 (1991).
[CrossRef]

B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Toward 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]

S. A. Coulombe, P. C. Logofatu, B. K. Minhas, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric scatterometry for sub-0.1-µm CD measurements,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 282–293 (1998).
[CrossRef]

Peng, S.

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 microelectronic processing,” Microlithography World 1, 16–22 (1992).

Pommet, D. A.

Prins, S. L.

B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Toward 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]

Raguin, D. H.

Raymond, C. J.

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, J. R. McNeil, “Scatterometry measurement of sub-0.1-µm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
[CrossRef]

C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, J. R. McNeil, “Metrology of subwavelength photoresist gratings using optical scatterometry,” J. Vac. Sci. Technol. B 13, 1484–1495 (1995).
[CrossRef]

Sincerbox, G. T.

Sosnowski, T. P.

T. P. Sosnowski, “Polarization mode filters for integrated optics,” Opt. Commun. 4, 408–412 (1972).
[CrossRef]

Truckenbrodt, H.

J. Bischoff, L. Hutschenreuther, H. Truckenbrodt, “New aspects of optical scatterometry applied to microtechnology,” in In-Line Characterization Techniques for Performance and Yield Enhancement in Microelectronic Manufacturing, D. K. DeBusk, ed., Proc. SPIE3215, 144–155 (1997).
[CrossRef]

Werlich, H.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1985), Chap. 14.

Yeh, P.

P. Yeh, “Optics of anisotropic layered media: a new 4 4 matrix algebra,” Surf. Sci. 96, 41–53 (1980).
[CrossRef]

Yung, B.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, J. R. McNeil, “Scatterometry measurement of sub-0.1-µm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
[CrossRef]

C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, J. R. McNeil, “Metrology of subwavelength photoresist gratings using optical scatterometry,” J. Vac. Sci. Technol. B 13, 1484–1495 (1995).
[CrossRef]

Microlithography World

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 microelectronic processing,” Microlithography World 1, 16–22 (1992).

Opt. Commun.

T. P. Sosnowski, “Polarization mode filters for integrated optics,” Opt. Commun. 4, 408–412 (1972).
[CrossRef]

Surf. Sci.

P. Yeh, “Optics of anisotropic layered media: a new 4 4 matrix algebra,” Surf. Sci. 96, 41–53 (1980).
[CrossRef]

Other

J. Bischoff, L. Hutschenreuther, H. Truckenbrodt, “New aspects of optical scatterometry applied to microtechnology,” in In-Line Characterization Techniques for Performance and Yield Enhancement in Microelectronic Manufacturing, D. K. DeBusk, ed., Proc. SPIE3215, 144–155 (1997).
[CrossRef]

K. P. Bishop, S. M. Gaspar, L. M. Milner, S. S. H. Naqvi, J. R. McNeil, “Grating line shape characterization using scatterometry,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. SPIE1545, 64–73 (1991).
[CrossRef]

S. A. Coulombe, P. C. Logofatu, B. K. Minhas, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric scatterometry for sub-0.1-µm CD measurements,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 282–293 (1998).
[CrossRef]

B. K. Minhas, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “Toward 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]

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1985), Chap. 14.

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Figures (8)

Fig. 1
Fig. 1

Spatial parameters of the rectangular shape: the pitch or the period of the grating, Λ; the linewidth, lw; and the depth, thk. The grating vector K is in the direction of the periodic structure. Ne, the extraordinary refractive index, corresponds to the direction of the optic axis, while No, the ordinary refractive index, corresponds to the other two rectangular axes.

Fig. 2
Fig. 2

Cross-reflection coefficients for the P1000 sample (developed photoresist on silicon substrate). Experimental data versus RCWA simulations for (a) diffraction efficiency and (b) phase.

Fig. 3
Fig. 3

Same as Fig. 2 but for the P750 sample (developed photoresist over antireflection coating, polysilicon, and silicon oxide layers on silicon substrate).

Fig. 4
Fig. 4

Same as Fig. 2 but for the P360 sample (developed photoresist over antireflection-coating layer on silicon substrate).

Fig. 5
Fig. 5

(a)–(d) Various grating profiles and the corresponding grating vectors and symmetry axes (S.A.). K is always parallel to the surface. (a) and (b) are symmetric, while (c) and (d) are asymmetric about reflection on the xz plane.

Fig. 6
Fig. 6

RCWA simulations for the cross-reflection coefficients of a grating with symmetric trapezoidal shape for (a) diffraction efficiency and (b) phase.

Fig. 7
Fig. 7

EMT simulation for the P360 sample.

Fig. 8
Fig. 8

RCWA simulations of the cross-reflection coefficients for a modified model of the P360 sample with a grating profile with slanted parallel walls.

Tables (2)

Tables Icon

Table 1 Fitted Parameters of the Samples

Tables Icon

Table 2 Nominal (Predetermined) Parameters of the Samples

Equations (16)

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

rˆ=rpprsprpsrss,
rps=A1 A2(B2-B1)A1+A2,
rsp=B3-B4A1+A2,
A1=J tan φn sin2 θ+J cos θ,
A2=N0 tan φ(I+nN0 cos θ)IN0 cos θ+nJ2,
B1=n cos θ-Jn cos θ+J,
B2=nN0 cos θ-InN0 cos θ+I,
B3=N02 cos θ-nJN02 cos θ+nJ,
B4=IN0 cos θ-nJ2IN0 cos θ+nJ2,
I2=N02Ne2-n2 sin2 θ(N02 sin2 φ+Ne2 cos2 φ),
J2=N02-n2 sin2 θ,
rps=rsp.
A1 A2(B2-B1)=B3-B4,
(n cos θ+J)(n sin2 θ+J cos θ)=(N02 cos θ+nJ).
J2=N02-n2 sin2 θ,
rps=-rsp.

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