Abstract

Fast and efficient metrology tools are required in microelectronics for control of ever-decreasing feature sizes. Optical techniques such as spectroscopic ellipsometry (SE) and normal incidence reflectometry are widely used for this task. In this work we investigate the potential of spectral Mueller polarimetry in conical diffraction for the characterization of 1D gratings, with particular emphasis on small critical dimensions (CDs). Mueller matrix spectra were taken in the visible (450700  nm) wavelength range on a photoresist grating on a Si substrate with 70/240  nm CD/period nominal values, set at nine different azimuthal angles. These spectra were fitted with a rigorous coupled-wave analysis (RCWA) algorithm by using different models for the grating profile (rectangular and trapezoidal, with or without rounded corners). A detailed study of the stability and consistency of the optimal CD values, together with the variation of the merit function (the mean square deviation D2) around these values, clearly showed that for a given wavelength range, this technique can decouple some critical parameters (e.g., top and bottom CDs, left and right sidewall projections) much more efficiently than the usual SE.

© 2006 Optical Society of America

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  1. B. K. Minhas, S. A. Coulombe, S. Sohail, H. Naqvi, and J. R. McNeil, "Ellipsometric scatterometry for the metrology of sub-0.1-μm-linewidth structures," Appl. Opt. 37, 5112-5115 (1998).
    [CrossRef]
  2. X.-T. Huang and F. L. Terry, Jr., Erratum to "Spectroscopic ellipsometry and reflectometry from grating (scatterometry) for critical dimension measurement and in situ, real-time process monitoring," [Thin Solid Films 455-456, 828-836 (2004)], Thin Solid Films 486, 339-346 (2004).
    [CrossRef]
  3. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, 1986).
  4. P. C. Logofatu, S. A. Coulombe, B. K. Minhas, and J. R. McNeil, "Identity of the cross-reflection coefficients for symmetric surface-relief gratings," J. Opt. Soc. Am. A 16, 1108-1114 (1999).
    [CrossRef]
  5. L. Li, "Symmetries of cross-polarization diffraction coefficients of gratings," J. Opt. Soc. Am. A 17, 881-887 (2000).
    [CrossRef]
  6. T. Novikova, A. De Martino, R. Ossikovski, and B. Drévillon, "Metrological applications of Mueller polarimetry in conical diffraction for overlay characterization in microelectronics," Eur. Phys. J. Appl. Phys. 31, 63-69 (2005).
    [CrossRef]
  7. E. Garcia-Caurel, A. De Martino, and B. Drévillon, "Spectroscopic Mueller polarimeter based on liquid crystal devices," Thin Solid Films 455-456, 120-123 (2004).
    [CrossRef]
  8. E. Compain and B. Drévillon, "High frequency modulation of the four states of polarization of light with a single phase modulator," Rev. Sci. Instrum. 69, 1574-1580 (1998).
    [CrossRef]
  9. J. S. Tyo, "Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error," Appl. Opt. 41, 619-630 (2002).
    [CrossRef] [PubMed]
  10. A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, "General methods for optimized design and calibration of Mueller polarimeters," Thin Solid Films 455-456, 112-119 (2004).
    [CrossRef]
  11. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, "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]
  12. L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. A 13, 1024-1035 (1996).
    [CrossRef]
  13. B. Kaplan, T. Novikova, A. De Martino, and B. Drévillon, "Characterization of bidimensional gratings by spectroscopic ellipsometry and angle-resolved Mueller polarimetry," Appl. Opt. 43, 1233-1240 (2004).
    [CrossRef] [PubMed]
  14. K. Narahari Rao, Molecular Spectroscopy: Modern Research, Vol. II (Academic, 1976).
  15. V. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).
  16. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077-1086 (1995).
    [CrossRef]
  17. A. Weidner, M. Slodowski, C. Halm, C. Schneider, and L. Pfizner, "Effective-medium model for fast evaluation of scatterometric measurements on grating," in Metrology, Inspection, and Process Control for Microlithography XVIII, R. M. Silver, ed., Proc. SPIE 5375, 232-243 (2004).
    [CrossRef]
  18. M. Schubert, "Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems," Phys. Rev. B 53, 4265-4274 (1996).
    [CrossRef]
  19. G. E. Jellison, Jr., "Data analysis for spectroscopic ellipsometry," Thin Solid Films 234, 416-422 (1993).
    [CrossRef]

2005 (1)

T. Novikova, A. De Martino, R. Ossikovski, and B. Drévillon, "Metrological applications of Mueller polarimetry in conical diffraction for overlay characterization in microelectronics," Eur. Phys. J. Appl. Phys. 31, 63-69 (2005).
[CrossRef]

2004 (5)

E. Garcia-Caurel, A. De Martino, and B. Drévillon, "Spectroscopic Mueller polarimeter based on liquid crystal devices," Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

X.-T. Huang and F. L. Terry, Jr., Erratum to "Spectroscopic ellipsometry and reflectometry from grating (scatterometry) for critical dimension measurement and in situ, real-time process monitoring," [Thin Solid Films 455-456, 828-836 (2004)], Thin Solid Films 486, 339-346 (2004).
[CrossRef]

B. Kaplan, T. Novikova, A. De Martino, and B. Drévillon, "Characterization of bidimensional gratings by spectroscopic ellipsometry and angle-resolved Mueller polarimetry," Appl. Opt. 43, 1233-1240 (2004).
[CrossRef] [PubMed]

A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, "General methods for optimized design and calibration of Mueller polarimeters," Thin Solid Films 455-456, 112-119 (2004).
[CrossRef]

A. Weidner, M. Slodowski, C. Halm, C. Schneider, and L. Pfizner, "Effective-medium model for fast evaluation of scatterometric measurements on grating," in Metrology, Inspection, and Process Control for Microlithography XVIII, R. M. Silver, ed., Proc. SPIE 5375, 232-243 (2004).
[CrossRef]

2002 (1)

2000 (1)

1999 (1)

1998 (2)

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

E. Compain and B. Drévillon, "High frequency modulation of the four states of polarization of light with a single phase modulator," Rev. Sci. Instrum. 69, 1574-1580 (1998).
[CrossRef]

1996 (2)

L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. A 13, 1024-1035 (1996).
[CrossRef]

M. Schubert, "Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems," Phys. Rev. B 53, 4265-4274 (1996).
[CrossRef]

1995 (2)

1993 (1)

G. E. Jellison, Jr., "Data analysis for spectroscopic ellipsometry," Thin Solid Films 234, 416-422 (1993).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, 1986).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, 1986).

Compain, E.

E. Compain and B. Drévillon, "High frequency modulation of the four states of polarization of light with a single phase modulator," Rev. Sci. Instrum. 69, 1574-1580 (1998).
[CrossRef]

Coulombe, S. A.

De Martino, A.

T. Novikova, A. De Martino, R. Ossikovski, and B. Drévillon, "Metrological applications of Mueller polarimetry in conical diffraction for overlay characterization in microelectronics," Eur. Phys. J. Appl. Phys. 31, 63-69 (2005).
[CrossRef]

B. Kaplan, T. Novikova, A. De Martino, and B. Drévillon, "Characterization of bidimensional gratings by spectroscopic ellipsometry and angle-resolved Mueller polarimetry," Appl. Opt. 43, 1233-1240 (2004).
[CrossRef] [PubMed]

A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, "General methods for optimized design and calibration of Mueller polarimeters," Thin Solid Films 455-456, 112-119 (2004).
[CrossRef]

E. Garcia-Caurel, A. De Martino, and B. Drévillon, "Spectroscopic Mueller polarimeter based on liquid crystal devices," Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

Drévillon, B.

T. Novikova, A. De Martino, R. Ossikovski, and B. Drévillon, "Metrological applications of Mueller polarimetry in conical diffraction for overlay characterization in microelectronics," Eur. Phys. J. Appl. Phys. 31, 63-69 (2005).
[CrossRef]

B. Kaplan, T. Novikova, A. De Martino, and B. Drévillon, "Characterization of bidimensional gratings by spectroscopic ellipsometry and angle-resolved Mueller polarimetry," Appl. Opt. 43, 1233-1240 (2004).
[CrossRef] [PubMed]

A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, "General methods for optimized design and calibration of Mueller polarimeters," Thin Solid Films 455-456, 112-119 (2004).
[CrossRef]

E. Garcia-Caurel, A. De Martino, and B. Drévillon, "Spectroscopic Mueller polarimeter based on liquid crystal devices," Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

E. Compain and B. Drévillon, "High frequency modulation of the four states of polarization of light with a single phase modulator," Rev. Sci. Instrum. 69, 1574-1580 (1998).
[CrossRef]

Flannery, B. P.

V. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).

Garcia-Caurel, E.

E. Garcia-Caurel, A. De Martino, and B. Drévillon, "Spectroscopic Mueller polarimeter based on liquid crystal devices," Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, "General methods for optimized design and calibration of Mueller polarimeters," Thin Solid Films 455-456, 112-119 (2004).
[CrossRef]

Gaylord, T. K.

Grann, E. B.

Halm, C.

A. Weidner, M. Slodowski, C. Halm, C. Schneider, and L. Pfizner, "Effective-medium model for fast evaluation of scatterometric measurements on grating," in Metrology, Inspection, and Process Control for Microlithography XVIII, R. M. Silver, ed., Proc. SPIE 5375, 232-243 (2004).
[CrossRef]

Huang, X.-T.

X.-T. Huang and F. L. Terry, Jr., Erratum to "Spectroscopic ellipsometry and reflectometry from grating (scatterometry) for critical dimension measurement and in situ, real-time process monitoring," [Thin Solid Films 455-456, 828-836 (2004)], Thin Solid Films 486, 339-346 (2004).
[CrossRef]

Jellison, G. E.

G. E. Jellison, Jr., "Data analysis for spectroscopic ellipsometry," Thin Solid Films 234, 416-422 (1993).
[CrossRef]

Kaplan, B.

Laude, B.

A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, "General methods for optimized design and calibration of Mueller polarimeters," Thin Solid Films 455-456, 112-119 (2004).
[CrossRef]

Li, L.

Logofatu, P. C.

McNeil, J. R.

Minhas, B. K.

Moharam, M. G.

Naqvi, H.

Novikova, T.

T. Novikova, A. De Martino, R. Ossikovski, and B. Drévillon, "Metrological applications of Mueller polarimetry in conical diffraction for overlay characterization in microelectronics," Eur. Phys. J. Appl. Phys. 31, 63-69 (2005).
[CrossRef]

B. Kaplan, T. Novikova, A. De Martino, and B. Drévillon, "Characterization of bidimensional gratings by spectroscopic ellipsometry and angle-resolved Mueller polarimetry," Appl. Opt. 43, 1233-1240 (2004).
[CrossRef] [PubMed]

Ossikovski, R.

T. Novikova, A. De Martino, R. Ossikovski, and B. Drévillon, "Metrological applications of Mueller polarimetry in conical diffraction for overlay characterization in microelectronics," Eur. Phys. J. Appl. Phys. 31, 63-69 (2005).
[CrossRef]

Pfizner, L.

A. Weidner, M. Slodowski, C. Halm, C. Schneider, and L. Pfizner, "Effective-medium model for fast evaluation of scatterometric measurements on grating," in Metrology, Inspection, and Process Control for Microlithography XVIII, R. M. Silver, ed., Proc. SPIE 5375, 232-243 (2004).
[CrossRef]

Pommet, D. A.

Press, V. H.

V. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).

Rao, K. Narahari

K. Narahari Rao, Molecular Spectroscopy: Modern Research, Vol. II (Academic, 1976).

Schneider, C.

A. Weidner, M. Slodowski, C. Halm, C. Schneider, and L. Pfizner, "Effective-medium model for fast evaluation of scatterometric measurements on grating," in Metrology, Inspection, and Process Control for Microlithography XVIII, R. M. Silver, ed., Proc. SPIE 5375, 232-243 (2004).
[CrossRef]

Schubert, M.

M. Schubert, "Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems," Phys. Rev. B 53, 4265-4274 (1996).
[CrossRef]

Slodowski, M.

A. Weidner, M. Slodowski, C. Halm, C. Schneider, and L. Pfizner, "Effective-medium model for fast evaluation of scatterometric measurements on grating," in Metrology, Inspection, and Process Control for Microlithography XVIII, R. M. Silver, ed., Proc. SPIE 5375, 232-243 (2004).
[CrossRef]

Sohail, S.

Terry, F. L.

X.-T. Huang and F. L. Terry, Jr., Erratum to "Spectroscopic ellipsometry and reflectometry from grating (scatterometry) for critical dimension measurement and in situ, real-time process monitoring," [Thin Solid Films 455-456, 828-836 (2004)], Thin Solid Films 486, 339-346 (2004).
[CrossRef]

Teukolsky, S. A.

V. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).

Tyo, J. S.

Vetterling, W. T.

V. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).

Weidner, A.

A. Weidner, M. Slodowski, C. Halm, C. Schneider, and L. Pfizner, "Effective-medium model for fast evaluation of scatterometric measurements on grating," in Metrology, Inspection, and Process Control for Microlithography XVIII, R. M. Silver, ed., Proc. SPIE 5375, 232-243 (2004).
[CrossRef]

Appl. Opt. (3)

Eur. Phys. J. Appl. Phys. (1)

T. Novikova, A. De Martino, R. Ossikovski, and B. Drévillon, "Metrological applications of Mueller polarimetry in conical diffraction for overlay characterization in microelectronics," Eur. Phys. J. Appl. Phys. 31, 63-69 (2005).
[CrossRef]

J. Opt. Soc. Am. A (5)

Phys. Rev. B (1)

M. Schubert, "Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems," Phys. Rev. B 53, 4265-4274 (1996).
[CrossRef]

Proc. SPIE (1)

A. Weidner, M. Slodowski, C. Halm, C. Schneider, and L. Pfizner, "Effective-medium model for fast evaluation of scatterometric measurements on grating," in Metrology, Inspection, and Process Control for Microlithography XVIII, R. M. Silver, ed., Proc. SPIE 5375, 232-243 (2004).
[CrossRef]

Rev. Sci. Instrum. (1)

E. Compain and B. Drévillon, "High frequency modulation of the four states of polarization of light with a single phase modulator," Rev. Sci. Instrum. 69, 1574-1580 (1998).
[CrossRef]

Thin Solid Films (4)

A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drévillon, "General methods for optimized design and calibration of Mueller polarimeters," Thin Solid Films 455-456, 112-119 (2004).
[CrossRef]

E. Garcia-Caurel, A. De Martino, and B. Drévillon, "Spectroscopic Mueller polarimeter based on liquid crystal devices," Thin Solid Films 455-456, 120-123 (2004).
[CrossRef]

X.-T. Huang and F. L. Terry, Jr., Erratum to "Spectroscopic ellipsometry and reflectometry from grating (scatterometry) for critical dimension measurement and in situ, real-time process monitoring," [Thin Solid Films 455-456, 828-836 (2004)], Thin Solid Films 486, 339-346 (2004).
[CrossRef]

G. E. Jellison, Jr., "Data analysis for spectroscopic ellipsometry," Thin Solid Films 234, 416-422 (1993).
[CrossRef]

Other (3)

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, 1986).

K. Narahari Rao, Molecular Spectroscopy: Modern Research, Vol. II (Academic, 1976).

V. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: the Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).

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Figures (11)

Fig. 1
Fig. 1

Representation of conical light incidence for a 1D grating.

Fig. 2
Fig. 2

SEM image of the sample. White bar length: 200 nm. Thin black curve: profile provided by fitting polarimetric spectra with a symmetric trapezoidal model (see text).

Fig. 3
Fig. 3

Geometric models of diffraction grating and corresponding sets of fitting parameters: (I) rectangular (H, L); (II) symmetric trapezoid (H, L, A); (III) rectangular with top corner rounding (H, L, R); (IV) symmetric trapezoid with top corner rounding (H, L, A, R); (V) asymmetric trapezoid (H, L, A, B).

Fig. 4
Fig. 4

Normalized Mueller matrix spectra at different azimuthal angles. Symbols: measured values. Thin curves: fits with model (II) (symmetric trapezoid).

Fig. 5
Fig. 5

Optimal values of the fitting parameters with different geometric models versus azimuthal angle. (a) Solid symbols: model (I); open symbols: model (III); dotted lines: height and width of the nominal rectangular profile. (b) Solid symbols: model (II); open symbols: model (IV); thin solid lines: fit of data taken at only three wavelengths and all azimuths; crosses: fit of standard SE spectra (see text). (c) Open symbols: model (II); solid symbols: model (V); (d) radius of curvature, solid symbols: model (III); open symbols: model (IV).

Fig. 6
Fig. 6

Minimal values of D 2 obtained with geometric models (I)–(V) versus azimuthal angle.

Fig. 7
Fig. 7

Maps of D 2 calculated versus A and L, with model (II) and whole Mueller matrices measured at different azimuthal angles φ (H = 220 nm). The interval between the contour lines is 2.2 × 10−4.

Fig. 8
Fig. 8

Map of D 2 calculated with the EMA for φ = 0 (H = 220 nm). The interval between the contour lines is 2.2 × 10−4.

Fig. 9
Fig. 9

Analogous to Fig. 7, but with partial Mueller matrices [I s and I c ; see Eqs. (3)–(5)]. The interval between the contour lines is 6.7 × 10−4.

Fig. 10
Fig. 10

Angular dependence of the variance of the parameters H, L and A (open symbols) for model (II), calculated with ellipsometric data I s and I c (a) and with full Mueller matrices (b). Bottom lines: parameter variances obtained with data taken at all azimuthal angles.

Fig. 11
Fig. 11

Maps of D 2 calculated as a function of A and B [model (V)] with complete Mueller matrices (H = 220 nm; L = 46 nm). The interval between the contour lines is 8 × 10−5.

Equations (6)

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( E p r E s r ) = ( J 11 J 12 J 21 J 22 ) ( E p i E s i ).
M = [ 1 2 ( | J 11 | 2 + | J 22 | 2 + | J 12 | 2 + | J 21 | 2 ) 1 2 ( | J 11 | 2 - | J 22 | 2 - | J 12 | 2 + | J 21 | 2 ) Re ( J 11 * J 12 + J 21 * J 22 ) - Im ( J 11 * J 12 + J 21 * J 22 ) 1 2 ( | J 11 | 2 - | J 22 | 2 + | J 12 | 2 - | J 21 | 2 ) 1 2 ( ( | J 11 | 2 + | J 22 | 2 - | J 12 | 2 - | J 21 | 2 ) Re ( J 11 * J 12 - J 21 * J 22 ) Im ( - J 11 * J 12 + J 21 * J 22 ) Re ( J 11 * J 21 + J 12 * J 22 ) Re ( J 11 * J 21 - J 12 * J 22 ) Re ( J 11 * J 22 + J 12 * J 21 ) Im ( - J 11 * J 22 + J 12 * J 21 ) Im ( J 11 * J 21 + J 12 * J 22 ) Im ( J 11 * J 21 - J 12 * J 22 ) Im ( J 11 * J 22 + J 12 * J 21 ) Re ( J 11 * J 22 - J 12 * J 21 ) ]
I s = M 41 + ε A M 43 ,
I c = ε M ( M 31 + ε A M 33 ) ,
ε A , M = { + 1      A , M = 0 ° , + 45 ° 1      A , M = 90 ° , 45 ° ,
D 2 = 1 N k = 1 N [ 1 15 i . j ( M ij , exp * - M ij , the * ) 2 ]

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