Abstract

We describe a new and unique method for simultaneous determination of the groove depth and duty cycle of binary diffraction gratings. For a near-normal angle of incidence, the +1 and -1 diffracted orders will behave nearly the same as the duty cycle is varied for a fixed grating depth. The difference in their behavior, quantified as the ratio of their respective diffraction efficiencies, is compared to a look-up table generated by rigorous coupled-wave theory, and the duty cycle of the grating is thus obtained as a function of grating depth. Performing the same analysis for the orthogonal probe-light polarization results in a different functional dependence of the duty cycle on the grating depth. By use of both TE and TM polarizations, the depth and duty cycle for the grating are obtained by the intersection of the functions generated by the individual polarizations. These measurements can also be used to assess qualitatively both the uniformity of the grating and the symmetry of the grating profile. Comparison with scanning electron microscope images shows excellent agreement. This method is advantageous since it can be carried out rapidly, is accurate and repeatable, does not damage the sample, and uses low-cost, commonly available equipment. Since this method consists of only four fixed simple measurements, it is highly suitable for quality control in a manufacturing environment.

© 2003 Optical Society of America

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  1. The complete vector formula can be found in G. H. Spencer, M. V. R. K. Murty, “General raytracing procedure,” J. Opt. Soc. Am. 52, 672–678 (1962).
  2. S. D. Bennett, J. T. Lindow, I. R. Smith, “Integrated circuit metrology with confocal optical microscopy,” Philos. Trans. R. Soc. London Ser. A 320, 307–312 (1986).
    [CrossRef]
  3. C. J. Raymond, M. R. Murane, 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]
  4. 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]
  5. E. W. Conrad, D. P. Paul, “Method and apparatus for measuring the profile of small repeating lines,” U.S. Patent5,963,329 (5October1999).
  6. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1285–1392 (1982).
    [CrossRef]
  7. E. M. Drege, J. A. Reed, D. M. Byrne, “Linearized inversion of scatterometric data to obtain surface profile information,” Opt. Eng. 41, 225–236 (2002).
    [CrossRef]
  8. H. P. Kleinknecht, H. Meier, “Linewidth measurement on IC masks and wafers by grating test patterns,” Appl. Opt. 19, 525–533 (1980).
    [CrossRef] [PubMed]

2002

E. M. Drege, J. A. Reed, D. M. Byrne, “Linearized inversion of scatterometric data to obtain surface profile information,” Opt. Eng. 41, 225–236 (2002).
[CrossRef]

1998

1995

C. J. Raymond, M. R. Murane, 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]

1986

S. D. Bennett, J. T. Lindow, I. R. Smith, “Integrated circuit metrology with confocal optical microscopy,” Philos. Trans. R. Soc. London Ser. A 320, 307–312 (1986).
[CrossRef]

1982

M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1285–1392 (1982).
[CrossRef]

1980

1962

Bennett, S. D.

S. D. Bennett, J. T. Lindow, I. R. Smith, “Integrated circuit metrology with confocal optical microscopy,” Philos. Trans. R. Soc. London Ser. A 320, 307–312 (1986).
[CrossRef]

Byrne, D. M.

E. M. Drege, J. A. Reed, D. M. Byrne, “Linearized inversion of scatterometric data to obtain surface profile information,” Opt. Eng. 41, 225–236 (2002).
[CrossRef]

Conrad, E. W.

E. W. Conrad, D. P. Paul, “Method and apparatus for measuring the profile of small repeating lines,” U.S. Patent5,963,329 (5October1999).

Coulombe, S. A.

Drege, E. M.

E. M. Drege, J. A. Reed, D. M. Byrne, “Linearized inversion of scatterometric data to obtain surface profile information,” Opt. Eng. 41, 225–236 (2002).
[CrossRef]

Gaylord, T. K.

M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1285–1392 (1982).
[CrossRef]

Kleinknecht, H. P.

Lindow, J. T.

S. D. Bennett, J. T. Lindow, I. R. Smith, “Integrated circuit metrology with confocal optical microscopy,” Philos. Trans. R. Soc. London Ser. A 320, 307–312 (1986).
[CrossRef]

McNeil, J. R.

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. Murane, 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]

Meier, H.

Minhas, B. K.

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1285–1392 (1982).
[CrossRef]

Murane, M. R.

C. J. Raymond, M. R. Murane, 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]

Murty, M. V. R. K.

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]

C. J. Raymond, M. R. Murane, 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]

Paul, D. P.

E. W. Conrad, D. P. Paul, “Method and apparatus for measuring the profile of small repeating lines,” U.S. Patent5,963,329 (5October1999).

Raymond, C. J.

C. J. Raymond, M. R. Murane, 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]

Reed, J. A.

E. M. Drege, J. A. Reed, D. M. Byrne, “Linearized inversion of scatterometric data to obtain surface profile information,” Opt. Eng. 41, 225–236 (2002).
[CrossRef]

Smith, I. R.

S. D. Bennett, J. T. Lindow, I. R. Smith, “Integrated circuit metrology with confocal optical microscopy,” Philos. Trans. R. Soc. London Ser. A 320, 307–312 (1986).
[CrossRef]

Spencer, G. H.

Appl. Opt.

J. Opt. Soc. Am.

The complete vector formula can be found in G. H. Spencer, M. V. R. K. Murty, “General raytracing procedure,” J. Opt. Soc. Am. 52, 672–678 (1962).

M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1285–1392 (1982).
[CrossRef]

J. Vac. Sci. Technol. B

C. J. Raymond, M. R. Murane, 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]

Opt. Eng.

E. M. Drege, J. A. Reed, D. M. Byrne, “Linearized inversion of scatterometric data to obtain surface profile information,” Opt. Eng. 41, 225–236 (2002).
[CrossRef]

Philos. Trans. R. Soc. London Ser. A

S. D. Bennett, J. T. Lindow, I. R. Smith, “Integrated circuit metrology with confocal optical microscopy,” Philos. Trans. R. Soc. London Ser. A 320, 307–312 (1986).
[CrossRef]

Other

E. W. Conrad, D. P. Paul, “Method and apparatus for measuring the profile of small repeating lines,” U.S. Patent5,963,329 (5October1999).

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Figures (12)

Fig. 1
Fig. 1

Depiction of a binary grating: n 1 and n 2 are the refractive indices of the media that share the periodic boundary, which generally consists of materials of indices n 3 and n 4; d is the grating depth; Λ is the grating period; and a/Λ is the duty cycle of the material with refractive index n 3.

Fig. 2
Fig. 2

Experimental configuration of the SOER method shown in the transmission mode. The TE and TM polarizations required for the measurements are indicated in gray.

Fig. 3
Fig. 3

Diffraction efficiencies of the m = +1 and m = -1 transmitted orders as a function of duty cycle. The grating under investigation is a fused-silica binary grating, such that n 1 = n 4 = 1 (air) and n 2 = n 3 = 1.457 (fused silica at 632.8 nm). The probe light is TM polarized with a wavelength of 632.8 nm and is incident on the grating at 8 degs from normal. The grating pitch is 750 nm, and the grating depth is 220 nm.

Fig. 4
Fig. 4

Ratio of diffraction efficiencies of the m = +1 and m = -1 transmitted orders (black curve) and the m = +1 and m = 0 orders (gray curve) as a function of duty cycle. The grating under investigation and the probe technique used are identical to that used in Fig. 3.

Fig. 5
Fig. 5

Precent deviation of duty cycle prediction as a function of sidewall tilt for the T +1/T -1 SOER method (black line) and T +1/T 0 method (gray curve). The grating under investigation and the probe technique used are identical to that used in Figs. 3 and 4.

Fig. 6
Fig. 6

Ratio of diffraction efficiencies of the m = +1 and m = -1 transmitted orders as a function of duty cycle for various grating depths, as labeled in the figure. Otherwise, the grating under investigation and the probe technique used are identical to that used in Figs. 3 5.

Fig. 7
Fig. 7

T +1/T -1 ratio versus duty cycle for various He-Ne laser wavelengths, as labeled in the figure. The grating under investigation is a binary photoresist-air layer 550 nm deep with a 750-nm pitch on a fused-silica substrate. The probe technique used is identical to that used in Figs. 3 6 except for the incident wavelength.

Fig. 8
Fig. 8

T +1/T -1 ratio versus duty cycle by use of TE-polarized light for the fused-silica and photoresist gratings used in Figs. 3 7. The probe technique used is identical to that used in Figs. 3 7 except for the incident wavelength and polarization.

Fig. 9
Fig. 9

R +1/R -1 ratio versus duty cycle by use of TM-polarized light for the fused-silica and photoresist gratings used in Figs. 3 7. The probe technique used is identical to that in Figs. 3 7 except for the incident wavelength and use of reflected rather than transmitted orders.

Fig. 10
Fig. 10

SEM image of a photoresist grating on a fused-silica substrate with similar parameters as those used in Fig. 7.

Fig. 11
Fig. 11

Calculated duty cycle versus depth curves for orthogonal polarizations by use of a TM SOER value of 0.95 and a TE SOER value of 1.00. The probe light has a wavelength of 632.8 nm, and is incident on the grating at 7.5 deg from normal. The binary grating has a grating pitch of 760 nm and is made of fused silica [n 1 = n 4 = 1 (air) and n 2 = n 3 = 1.457 (fused silica at 632.8 nm)].

Fig. 12
Fig. 12

Calculated duty cycle versus depth curves for orthogonal polarizations and various values of the TE and TM SOER. The probe configuration and grating are identical to those used in Fig. 11.

Tables (1)

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Table 1 Refractive-Index Values Used in Numerical Calculations for Fused Silica and Photoresist at Various Optical Wavelengths

Equations (1)

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n1 sinθ1+no sinθm+mλΛ=0,

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