Abstract

An optimization method for the sensitivity of diffraction efficiency measurements is presented. I define the sensitivity as the estimation precision of the grating parameters. The optimization method called sensitivity analysis for fitting scans all the possible measurement configurations and selects the configuration that yields the best sensitivity. The scan is made over the domain of the experimental parameters of the arrangement, such as the azimuth angle of the grating and the orientation angles of the analyzer and the polarizer. These parameters can be freely varied, and among the multitude of possible combinations there is one configuration that provides optimum sensitivity. Comparison with experimental results reveals a qualitative agreement between theory and practice.

© 2002 Optical Society of America

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References

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  1. L. E. Ocola, D. S. Fryer, G. Reynolds, A. Krasnoperova, F. Cerina, “Scanning force microscopy measurements of latent image topography in chemically amplified resists,” Appl. Phys. Lett. 68, 717–719 (1996).
    [CrossRef]
  2. M. Postek, D. Joy, “Submicrometer microelectronics dimensional metrology: scanning electron microscopy,” J. Res. Natl. Bur. Stand. 92, 205–228 (1987).
    [CrossRef]
  3. A. Sicignano, M. Vaez-Iravani, “Precision metrology of integrated circuit critical dimensions using in situ differential scanning electron microscopy,” Scanning 10, 201–206 (1988).
    [CrossRef]
  4. I. Kallioniemi, J. Saarinen, E. Oja, “Characterization of diffraction gratings in a rigorous domain with optical scatterometry: hierarchical neural-network model,” Appl. Opt. 38, 5920–5930 (1999).
    [CrossRef]
  5. S. Hava, M. Auslender, “Optical scatterometry evaluation of groove depth in lamellar silicon grating structures,” Opt. Eng. 40, 1244–1248 (2001).
    [CrossRef]
  6. J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, S. R. Wilson, “Optical scatterometry,” in Encyclopedia of Materials Characterization, C. A. Evans, C. R. Brundle, S. Wilson, eds. (Manning, Boston, 1992).
  7. C. J. Raymond, J. R. McNeil, S. S. H. Naqvi, “Scatterometry for CD measurements of etched structures,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 720–728 (1996).
  8. 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,” Microlithogr. World 1, 16–22 (1992).
  9. 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).
  10. 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]
  11. S. A. Coulombe, P. C. Logofatu, B. K. Minhas, S. S. H. Naqvi, J. R. McNeil, “Ellipsometric scatterometry for sub-0.1-mm CD measurements,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 282–293 (1998).
  12. P. C. Logofatu, J. R. McNeil, “Sensitivity analysis of fitting for scatterometry,” in Metrology, Inspection, and Process Control for Microlithography XIII, B. Singh, ed., Proc. SPIE3677, 177–183 (1999).
  13. E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, New York, 1993).
  14. R. M. A. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with applications to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
    [CrossRef]
  15. 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]
  16. R. M. A. Azzam, “Application of generalized ellipsometry to anisotropic crystals,” J. Opt. Soc. Am. 64, 128–133 (1974).
    [CrossRef]
  17. P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, Boston, 1992).
  18. G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists (Academic, San Diego, Calif., 2001).
  19. L. Li, “Symmetries of cross-polarization diffraction coefficients of gratings,” J. Opt. Soc. Am. A 17, 881–887 (2000).
    [CrossRef]
  20. P. C. Logofatu, “Sensitivity-optimized scatterometry,” Ph.D. dissertation (University of New Mexico, Albuquerque, N. Mex., 2000).
  21. P. C. Logofatu, J. R. McNeil, “Identity of the cross-reflection coefficients for symmetric surface-relief gratings,” J. Opt. Soc. Am. A 16, 1108–1114 (1999).
    [CrossRef]

2001 (1)

S. Hava, M. Auslender, “Optical scatterometry evaluation of groove depth in lamellar silicon grating structures,” Opt. Eng. 40, 1244–1248 (2001).
[CrossRef]

2000 (1)

1999 (2)

1998 (1)

1996 (1)

L. E. Ocola, D. S. Fryer, G. Reynolds, A. Krasnoperova, F. Cerina, “Scanning force microscopy measurements of latent image topography in chemically amplified resists,” Appl. Phys. Lett. 68, 717–719 (1996).
[CrossRef]

1992 (1)

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,” Microlithogr. World 1, 16–22 (1992).

1988 (1)

A. Sicignano, M. Vaez-Iravani, “Precision metrology of integrated circuit critical dimensions using in situ differential scanning electron microscopy,” Scanning 10, 201–206 (1988).
[CrossRef]

1987 (1)

M. Postek, D. Joy, “Submicrometer microelectronics dimensional metrology: scanning electron microscopy,” J. Res. Natl. Bur. Stand. 92, 205–228 (1987).
[CrossRef]

1974 (1)

1972 (2)

R. M. A. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with applications to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[CrossRef]

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]

Arfken, G. B.

G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists (Academic, San Diego, Calif., 2001).

Auslender, M.

S. Hava, M. Auslender, “Optical scatterometry evaluation of groove depth in lamellar silicon grating structures,” Opt. Eng. 40, 1244–1248 (2001).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, “Application of generalized ellipsometry to anisotropic crystals,” J. Opt. Soc. Am. 64, 128–133 (1974).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with applications to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[CrossRef]

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]

Bashara, N. M.

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]

R. M. A. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with applications to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[CrossRef]

Bevington, P. R.

P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, Boston, 1992).

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,” Microlithogr. World 1, 16–22 (1992).

Cerina, F.

L. E. Ocola, D. S. Fryer, G. Reynolds, A. Krasnoperova, F. Cerina, “Scanning force microscopy measurements of latent image topography in chemically amplified resists,” Appl. Phys. Lett. 68, 717–719 (1996).
[CrossRef]

Collett, E.

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, New York, 1993).

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

Fryer, D. S.

L. E. Ocola, D. S. Fryer, G. Reynolds, A. Krasnoperova, F. Cerina, “Scanning force microscopy measurements of latent image topography in chemically amplified resists,” Appl. Phys. Lett. 68, 717–719 (1996).
[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,” Microlithogr. World 1, 16–22 (1992).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, S. R. Wilson, “Optical scatterometry,” in Encyclopedia of Materials Characterization, C. A. Evans, C. R. Brundle, S. Wilson, eds. (Manning, Boston, 1992).

Hava, S.

S. Hava, M. Auslender, “Optical scatterometry evaluation of groove depth in lamellar silicon grating structures,” Opt. Eng. 40, 1244–1248 (2001).
[CrossRef]

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,” Microlithogr. World 1, 16–22 (1992).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, S. R. Wilson, “Optical scatterometry,” in Encyclopedia of Materials Characterization, C. A. Evans, C. R. Brundle, S. Wilson, eds. (Manning, Boston, 1992).

Joy, D.

M. Postek, D. Joy, “Submicrometer microelectronics dimensional metrology: scanning electron microscopy,” J. Res. Natl. Bur. Stand. 92, 205–228 (1987).
[CrossRef]

Kallioniemi, I.

Krasnoperova, A.

L. E. Ocola, D. S. Fryer, G. Reynolds, A. Krasnoperova, F. Cerina, “Scanning force microscopy measurements of latent image topography in chemically amplified resists,” Appl. Phys. Lett. 68, 717–719 (1996).
[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,” Microlithogr. World 1, 16–22 (1992).

Li, L.

Logofatu, P. C.

P. C. Logofatu, J. R. McNeil, “Identity of the cross-reflection coefficients for symmetric surface-relief gratings,” J. Opt. Soc. Am. A 16, 1108–1114 (1999).
[CrossRef]

P. C. Logofatu, “Sensitivity-optimized scatterometry,” Ph.D. dissertation (University of New Mexico, Albuquerque, N. Mex., 2000).

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

P. C. Logofatu, J. R. McNeil, “Sensitivity analysis of fitting for scatterometry,” in Metrology, Inspection, and Process Control for Microlithography XIII, B. Singh, ed., Proc. SPIE3677, 177–183 (1999).

McNeil, J. R.

P. C. Logofatu, J. R. McNeil, “Identity of the cross-reflection coefficients for symmetric surface-relief gratings,” J. Opt. Soc. Am. A 16, 1108–1114 (1999).
[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]

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,” Microlithogr. World 1, 16–22 (1992).

C. J. Raymond, J. R. McNeil, S. S. H. Naqvi, “Scatterometry for CD measurements of etched structures,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 720–728 (1996).

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

P. C. Logofatu, J. R. McNeil, “Sensitivity analysis of fitting for scatterometry,” in Metrology, Inspection, and Process Control for Microlithography XIII, B. Singh, ed., Proc. SPIE3677, 177–183 (1999).

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).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, S. R. Wilson, “Optical scatterometry,” in Encyclopedia of Materials Characterization, C. A. Evans, C. R. Brundle, S. Wilson, eds. (Manning, Boston, 1992).

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,” Microlithogr. World 1, 16–22 (1992).

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]

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).

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

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]

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,” Microlithogr. World 1, 16–22 (1992).

C. J. Raymond, J. R. McNeil, S. S. H. Naqvi, “Scatterometry for CD measurements of etched structures,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 720–728 (1996).

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

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).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, S. R. Wilson, “Optical scatterometry,” in Encyclopedia of Materials Characterization, C. A. Evans, C. R. Brundle, S. Wilson, eds. (Manning, Boston, 1992).

Ocola, L. E.

L. E. Ocola, D. S. Fryer, G. Reynolds, A. Krasnoperova, F. Cerina, “Scanning force microscopy measurements of latent image topography in chemically amplified resists,” Appl. Phys. Lett. 68, 717–719 (1996).
[CrossRef]

Oja, E.

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,” Microlithogr. World 1, 16–22 (1992).

Postek, M.

M. Postek, D. Joy, “Submicrometer microelectronics dimensional metrology: scanning electron microscopy,” J. Res. Natl. Bur. Stand. 92, 205–228 (1987).
[CrossRef]

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).

Raymond, C. J.

C. J. Raymond, J. R. McNeil, S. S. H. Naqvi, “Scatterometry for CD measurements of etched structures,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 720–728 (1996).

Reynolds, G.

L. E. Ocola, D. S. Fryer, G. Reynolds, A. Krasnoperova, F. Cerina, “Scanning force microscopy measurements of latent image topography in chemically amplified resists,” Appl. Phys. Lett. 68, 717–719 (1996).
[CrossRef]

Robinson, D. K.

P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, Boston, 1992).

Saarinen, J.

Sicignano, A.

A. Sicignano, M. Vaez-Iravani, “Precision metrology of integrated circuit critical dimensions using in situ differential scanning electron microscopy,” Scanning 10, 201–206 (1988).
[CrossRef]

Vaez-Iravani, M.

A. Sicignano, M. Vaez-Iravani, “Precision metrology of integrated circuit critical dimensions using in situ differential scanning electron microscopy,” Scanning 10, 201–206 (1988).
[CrossRef]

Weber, H. J.

G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists (Academic, San Diego, Calif., 2001).

Wilson, S. R.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, S. R. Wilson, “Optical scatterometry,” in Encyclopedia of Materials Characterization, C. A. Evans, C. R. Brundle, S. Wilson, eds. (Manning, Boston, 1992).

Appl. Opt. (2)

Appl. Phys. Lett. (1)

L. E. Ocola, D. S. Fryer, G. Reynolds, A. Krasnoperova, F. Cerina, “Scanning force microscopy measurements of latent image topography in chemically amplified resists,” Appl. Phys. Lett. 68, 717–719 (1996).
[CrossRef]

J. Opt. Soc. Am (1)

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]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Res. Natl. Bur. Stand. (1)

M. Postek, D. Joy, “Submicrometer microelectronics dimensional metrology: scanning electron microscopy,” J. Res. Natl. Bur. Stand. 92, 205–228 (1987).
[CrossRef]

Microlithogr. World (1)

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,” Microlithogr. World 1, 16–22 (1992).

Opt. Eng. (1)

S. Hava, M. Auslender, “Optical scatterometry evaluation of groove depth in lamellar silicon grating structures,” Opt. Eng. 40, 1244–1248 (2001).
[CrossRef]

Phys. Rev. B (1)

R. M. A. Azzam, N. M. Bashara, “Polarization characteristics of scattered radiation from a diffraction grating by ellipsometry with applications to surface roughness,” Phys. Rev. B 5, 4721–4729 (1972).
[CrossRef]

Scanning (1)

A. Sicignano, M. Vaez-Iravani, “Precision metrology of integrated circuit critical dimensions using in situ differential scanning electron microscopy,” Scanning 10, 201–206 (1988).
[CrossRef]

Other (9)

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, S. R. Wilson, “Optical scatterometry,” in Encyclopedia of Materials Characterization, C. A. Evans, C. R. Brundle, S. Wilson, eds. (Manning, Boston, 1992).

C. J. Raymond, J. R. McNeil, S. S. H. Naqvi, “Scatterometry for CD measurements of etched structures,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 720–728 (1996).

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).

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

P. C. Logofatu, J. R. McNeil, “Sensitivity analysis of fitting for scatterometry,” in Metrology, Inspection, and Process Control for Microlithography XIII, B. Singh, ed., Proc. SPIE3677, 177–183 (1999).

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, New York, 1993).

P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, Boston, 1992).

G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists (Academic, San Diego, Calif., 2001).

P. C. Logofatu, “Sensitivity-optimized scatterometry,” Ph.D. dissertation (University of New Mexico, Albuquerque, N. Mex., 2000).

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Figures (7)

Fig. 1
Fig. 1

Experimental arrangement of the ellipsometric scatterometer.

Fig. 2
Fig. 2

Example of a test structure for scatterometry studies. A unidimensional grating is placed on top of a stack of thin films ending with a silicon substrate. The materials in the figure are common for microelectronics samples. ARC, ●●●.

Fig. 3
Fig. 3

Map of a sensitivity (σ) scan of the whole range of polarization angles illustrating the redundancy of the measurement configurations. The redundancy occurs no matter what particular sample and azimuth correspond to the map.

Fig. 4
Fig. 4

Measurement precision (dots) fitted by the empirical error function for the ellipsometric scatterometer (solid curve). In the figure are shown the coefficients for the empirical error function, which here are the coefficients of the best fit. The dots are the average values for a batch of 50 measurement sets in the configuration ϕ = 90°, P = 0°, and A = 0° at λ = 632.8 nm.

Fig. 5
Fig. 5

Example of the fitting of a curve measured by the ellipsometric scatterometer in the configuration ϕ = 24°, P = -63°, and A = 63° at λ = 632.8 nm. In the plot the geometric parameters of the sample (parameters of the best fit) are shown.

Fig. 6
Fig. 6

Illustration of the sensitivity (σ) scan for the sample XL6 at λ = 632.8 nm. In the figure is a section of the investigated domain for ϕ = 24°. The optimum measurement configuration is ϕ = 24°, P = 63°, and A = 117°.

Fig. 7
Fig. 7

Illustration of the sensitivity (σ) scan for the sample P200 at λ = 632.8 nm. In the figure is a section of the investigated domain for ϕ = 0°. The optimum measurement configuration is ϕ = 0°, P = -78°, and A = 102°. The lower corners of the plot correspond to the conventional measurement configurations 1 and 2 from Table 3.

Tables (3)

Tables Icon

Table 1 Geometric and Optical Parameters of the Samples Referred to in Section 5

Tables Icon

Table 2 Numerical Results for the Sensitivity Analysis of the Sample XL6 for Ellipsometric Scatterometer Measurements at λ = 632.8 nm

Tables Icon

Table 3 Numerical Results for the Sensitivity Analysis of the Sample P200 for Ellipsometric Scatterometer Measurements at λ = 632.8 nm

Equations (17)

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

qi=qipgeo, popt, pscan, pexp, i=1N,
Eout=ÂrˆPˆEin,
EpoutEsout=cos2 Acos A sin Asin A cos Asin2 A rpprpsrsprss×cos2 Pcos P sin Psin P cos Psin2 PEpinEsin.
EpoutEsout=rEPcos Asin A,
r=rpp cos A cos P+rps cos A sin P+rsp sin A cos P+rss sin A sin P,
EP=Epin cos P+Esin sin P.
R=|r|2.
σpgeom=Amm-1 ΔχN,
Ak,l=i=1N1σi2qipkqipl,
PΔχN=ΓM/2, 0, ΔχN2/2ΓM/2,
σmoptimumpexpoptimum=MinpexpMaxpgeoσmpgeo, pexp,
r=rpp cos A cos P+rps sinP-A+rss sin A sin P.
P-A, A-P.
P+A0°, 180°, P-A0°, 180°,
σ2=σres2+σpow2R2+σvib2R/θ2.
σ2=1.0×10-8+1.3×10-5R2.
ϕ=const of Maxpgeoσmpgeo, pexp

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