Abstract

The amplitude and the phase of the diffracted far field depends on polarization when the diffracting structure is comparable to or less than the wavelength. When the far-field amplitude and the phase of one polarization with respect to the orthogonal polarization is measured, small changes in the structure can be measured. To make the far-field polarization measurements, we design a detector that measures the relative polarization amplitude and the phase in quadrature. We predict numerically and verify experimentally the polarization amplitude and the phase for an optical disc and a set of gratings with varying depth. Our results show that this measurement technique is sensitive to small variations in the diffracting structure and that it can be useful in applications such as critical dimension and overlay metrology in microelectronics fabrication.

© 1997 Optical Society of America

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References

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  1. C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, J. W. Hosch, “Multi-parameter CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, pp. 698–709 (1996).
    [CrossRef]
  2. C. J. Raymond, S. S. H. Naqvi, J. R. McNeil, “Scatterometry for CD measurements of etched structures,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, pp. 720–728 (1996).
    [CrossRef]
  3. Toshiba Digital Video Disc Brochure (Toshiba Corporation, 1995).
  4. J. G. Dil, B. A. Jacobs, “Apparent size of reflecting polygonal obstacles of the order of one wavelength,” J. Opt. Soc. Am. 69, 950–960 (1979).
    [CrossRef]
  5. Y. Kok, N. C. Gallagher, “Relative phases of electromagnetic waves diffracted by a perfectly conducting rectangular-grooved grating,” J. Opt. Soc. Am. A 5, 65–73 (1988).
    [CrossRef]
  6. D. S. Marx, D. Psaltis, “Optical diffraction of focused spots and subwavelength structures,” J. Opt. Soc. Am. A 14, 1268–1278 (1997).
    [CrossRef]
  7. J. Pasman, “Vector theory of diffraction,” in Principles of Optical Disc Systems (Hilger, London, 1985), Chap. 3.
  8. H. Haidner, J. T. Sheridan, J. Schwider, N. Streibl, “Design of a blazed grating consisting of metallic subwavelength binary grooves,” Opt. Commun. 98, 5–10 (1993).
    [CrossRef]
  9. G. Sirat, D. Psaltis, “Conoscopic holography,” Opt. Lett. 10, 4–6 (1985).
    [CrossRef]
  10. G. Sirat, D. Psaltis, “Conoscopic holograms,” Opt. Commun. 65, 243–249 (1988).
    [CrossRef]
  11. J. P. Wu, J. L. White, “Study of birefringence character of injection and compression-molded polycarbonate and its interpretation,” Polym. Eng. Sci. 31, 652–660 (1991).
    [CrossRef]

1997 (1)

1993 (1)

H. Haidner, J. T. Sheridan, J. Schwider, N. Streibl, “Design of a blazed grating consisting of metallic subwavelength binary grooves,” Opt. Commun. 98, 5–10 (1993).
[CrossRef]

1991 (1)

J. P. Wu, J. L. White, “Study of birefringence character of injection and compression-molded polycarbonate and its interpretation,” Polym. Eng. Sci. 31, 652–660 (1991).
[CrossRef]

1988 (2)

1985 (1)

1979 (1)

Dil, J. G.

Gallagher, N. C.

Haidner, H.

H. Haidner, J. T. Sheridan, J. Schwider, N. Streibl, “Design of a blazed grating consisting of metallic subwavelength binary grooves,” Opt. Commun. 98, 5–10 (1993).
[CrossRef]

Hosch, J. W.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, J. W. Hosch, “Multi-parameter CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, pp. 698–709 (1996).
[CrossRef]

Jacobs, B. A.

Kok, Y.

Marx, D. S.

McNeil, J. R.

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

C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, J. W. Hosch, “Multi-parameter CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, pp. 698–709 (1996).
[CrossRef]

Murnane, M. R.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, J. W. Hosch, “Multi-parameter CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, pp. 698–709 (1996).
[CrossRef]

Naqvi, S. S. H.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, J. W. Hosch, “Multi-parameter CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, pp. 698–709 (1996).
[CrossRef]

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

Pasman, J.

J. Pasman, “Vector theory of diffraction,” in Principles of Optical Disc Systems (Hilger, London, 1985), Chap. 3.

Prins, S. L.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, J. W. Hosch, “Multi-parameter CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, pp. 698–709 (1996).
[CrossRef]

Psaltis, D.

Raymond, C. J.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, J. W. Hosch, “Multi-parameter CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, pp. 698–709 (1996).
[CrossRef]

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

Schwider, J.

H. Haidner, J. T. Sheridan, J. Schwider, N. Streibl, “Design of a blazed grating consisting of metallic subwavelength binary grooves,” Opt. Commun. 98, 5–10 (1993).
[CrossRef]

Sheridan, J. T.

H. Haidner, J. T. Sheridan, J. Schwider, N. Streibl, “Design of a blazed grating consisting of metallic subwavelength binary grooves,” Opt. Commun. 98, 5–10 (1993).
[CrossRef]

Sirat, G.

G. Sirat, D. Psaltis, “Conoscopic holograms,” Opt. Commun. 65, 243–249 (1988).
[CrossRef]

G. Sirat, D. Psaltis, “Conoscopic holography,” Opt. Lett. 10, 4–6 (1985).
[CrossRef]

Streibl, N.

H. Haidner, J. T. Sheridan, J. Schwider, N. Streibl, “Design of a blazed grating consisting of metallic subwavelength binary grooves,” Opt. Commun. 98, 5–10 (1993).
[CrossRef]

White, J. L.

J. P. Wu, J. L. White, “Study of birefringence character of injection and compression-molded polycarbonate and its interpretation,” Polym. Eng. Sci. 31, 652–660 (1991).
[CrossRef]

Wu, J. P.

J. P. Wu, J. L. White, “Study of birefringence character of injection and compression-molded polycarbonate and its interpretation,” Polym. Eng. Sci. 31, 652–660 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (2)

H. Haidner, J. T. Sheridan, J. Schwider, N. Streibl, “Design of a blazed grating consisting of metallic subwavelength binary grooves,” Opt. Commun. 98, 5–10 (1993).
[CrossRef]

G. Sirat, D. Psaltis, “Conoscopic holograms,” Opt. Commun. 65, 243–249 (1988).
[CrossRef]

Opt. Lett. (1)

Polym. Eng. Sci. (1)

J. P. Wu, J. L. White, “Study of birefringence character of injection and compression-molded polycarbonate and its interpretation,” Polym. Eng. Sci. 31, 652–660 (1991).
[CrossRef]

Other (4)

C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, J. W. Hosch, “Multi-parameter CD measurements using scatterometry,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, pp. 698–709 (1996).
[CrossRef]

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

Toshiba Digital Video Disc Brochure (Toshiba Corporation, 1995).

J. Pasman, “Vector theory of diffraction,” in Principles of Optical Disc Systems (Hilger, London, 1985), Chap. 3.

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Figures (6)

Fig. 1
Fig. 1

Calculated pit phase depth and far-field intensity for the DVD format. The dashed vertical lines indicate which pit depths can be used to represent four logical states.

Fig. 2
Fig. 2

Pit phase depth for different pit widths with the pit depth equal to a quarter wave. In the region where the pit width is betweenλ/2 (λ is adjusted for the index of refraction of the incident medium) and λ, the phase depth for TE illumination varies almost a quarter wave, but it remains fairly constant for TM illumination.

Fig. 3
Fig. 3

Inphase and quadrature detection of the TM far field. The TE field was used as a reference.

Fig. 4
Fig. 4

Experimental setup. The He–Ne laser output polarization is set to be 45° with respect to the grating direction of the sample. When the quarter-wave plate is set to 0°, the detector outputVa andVb, givesVi. When the quarter-wave plate is rotated 45°, the output isVq.

Fig. 5
Fig. 5

Polarization in quadrature response for the DVD. The arrow points to the response for a planar aluminum–polycarbonate interface (planar surface), and the locus of points is the polarization response as the illumination spot moves from a region of flat aluminum to a region where recorded data tracks are present.

Fig. 6
Fig. 6

Polarization in quadrature response for a 1-µm sinusoidal aluminum grating. The arrows point to the response for a planar aluminum–air interface, and each data point, calculated or measured, is labeled with its corresponding grating depth.

Equations (9)

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E x , z = sin p π x / d exp jk z z ,   k z = k 2 - p π d 2 1 / 2 ,
H x , z = cos p π x / d exp jk z z ,   k z = k 2 - p π d 2 1 / 2 .
E 1 = a e   exp j ϕ e x ˆ + a m   exp j ϕ m y ˆ ,
E 2 = a e   exp j ϕ e + π / 2 x ˆ + a m   exp j ϕ m y ˆ .
V A , C 1 2 E 1 , 2 · x ˆ + y ˆ 2
V B , D 1 2 E 1 , 2 · - x ˆ + y ˆ 2 .
V I = V A - V B = 2 a e a m   cos ϕ e - ϕ m ,
V Q = V C - V D = 2 a e a m   sin ϕ e - ϕ m .
A Σ i - Σ q Σ i + Σ q < 1

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