Abstract

We present a novel and nondestructive method for measuring the duty cycles (ratio of ridge width to period) of submicrometer rectangular photoresist gratings made on top of multilayer dielectric stacks. The method exploits the fact that the effective index of the leaky mode that has a strong evanescent tail in the cladding changes with the duty cycle of the grating situated at the interface between the top dielectric layer and the cladding. By comparing measured coupling angles of the leaky mode with a theoretical or experimentally calibrated relationship between coupling angles and duty cycle, one can determine the duty cycle of the grating. This method is applicable even when the grating period is less than the measurement wavelength. It is simple because it does not require any power measurement. Most importantly, it is virtually independent of groove depth. The physical principle of the method and the results of experimental verification are presented.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2004

H.-T. Huang, F. L. Terry, “Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455–456, 828–836 (2004).
[CrossRef]

2003

2002

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

1999

1997

1995

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]

M. D. Perry, R. D. Boyd, J. A. Britten, D. Decker, B. W. Shore, C. Shannon, E. Shults, L. Li, “High-efficiency multilayer dielectric diffraction gratings,” Opt. Lett. 20, 940–942 (1995); erratum 20, 1513 (1995).
[CrossRef] [PubMed]

1994

1986

T. Tamir, F. Y. Kou, “Varieties of leaky waves and their excitation along multilayered structures,” IEEE J. Quantum Electron. 22, 544–551 (1986).
[CrossRef]

1980

1975

T. Tamir, “Leaky waves in planar optical waveguides,” Nouv. Rev. Opt. 6, 273–284 (1975).
[CrossRef]

1973

T. Tamir, “Inhomogeneous wave types at planar interfaces. III. Leaky waves,” Optik 38, 269–297 (1973).

1965

Bischoff, J.

Bödefeld, R.

Boyd, R. D.

Breidne, M.

Britten, J. A.

Byrne, D. M.

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

Chow, R.

Decker, D.

Drège, E. M.

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

Evans, M. S.

Farmiga, N. O.

Feit, M. D.

Hehl, K.

Hessel, A.

Heyer, H.

Hirsh, J. I.

Hosch, J. W.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997).
[CrossRef]

Huang, H.-T.

H.-T. Huang, F. L. Terry, “Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455–456, 828–836 (2004).
[CrossRef]

Kou, F. Y.

T. Tamir, F. Y. Kou, “Varieties of leaky waves and their excitation along multilayered structures,” IEEE J. Quantum Electron. 22, 544–551 (1986).
[CrossRef]

Li, L.

Loomis, G.

Marciante, J. R.

Maystre, D.

McNeil, J. R.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997).
[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]

Mohaupt, U.

Murnane, M. R.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997).
[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]

Naqvi, S. S. H.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997).
[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]

Nevière, M.

M. Nevière, “The homogeneous problem,” in Electromagnetic Theory of Gratings,R. Petit, ed. (Springer-Verlag, 1980), pp. 123–157.
[CrossRef]

Nguyen, H.

Oliner, A. A.

Palme, M.

Perry, M. D.

Prins, S. L.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997).
[CrossRef]

Raymond, C. J.

C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997).
[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]

Reed, J. A.

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

Sauerbrey, R.

Schnabel, B.

Shannon, C.

Shore, B. W.

Shults, E.

Ta, H. T.

Tamir, T.

T. Tamir, S. Zhang, “Resonant scattering by multilayered dielectric gratings,” J. Opt. Soc. Am. A 14, 1607–1616 (1997).
[CrossRef]

T. Tamir, F. Y. Kou, “Varieties of leaky waves and their excitation along multilayered structures,” IEEE J. Quantum Electron. 22, 544–551 (1986).
[CrossRef]

T. Tamir, “Leaky waves in planar optical waveguides,” Nouv. Rev. Opt. 6, 273–284 (1975).
[CrossRef]

T. Tamir, “Inhomogeneous wave types at planar interfaces. III. Leaky waves,” Optik 38, 269–297 (1973).

Terry, F. L.

H.-T. Huang, F. L. Terry, “Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455–456, 828–836 (2004).
[CrossRef]

Theobald, W.

Welsch, E.

Wenke, L.

Zhang, S.

Appl. Opt.

IEEE J. Quantum Electron.

T. Tamir, F. Y. Kou, “Varieties of leaky waves and their excitation along multilayered structures,” IEEE J. Quantum Electron. 22, 544–551 (1986).
[CrossRef]

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

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]

C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, J. W. Hosch, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997).
[CrossRef]

Nouv. Rev. Opt.

T. Tamir, “Leaky waves in planar optical waveguides,” Nouv. Rev. Opt. 6, 273–284 (1975).
[CrossRef]

Opt. Eng.

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

Opt. Lett.

Optik

T. Tamir, “Inhomogeneous wave types at planar interfaces. III. Leaky waves,” Optik 38, 269–297 (1973).

Thin Solid Films

H.-T. Huang, F. L. Terry, “Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455–456, 828–836 (2004).
[CrossRef]

Other

M. Nevière, “The homogeneous problem,” in Electromagnetic Theory of Gratings,R. Petit, ed. (Springer-Verlag, 1980), pp. 123–157.
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Refractive-index distribution of a three-layer planar waveguide and electric field distributions of its two TE bound modes.

Fig. 2
Fig. 2

Coupling angles of the two modes of the waveguide shown in Fig. 1 as functions of the duty cycles of photoresist gratings of different groove depths. The gratings are made on top of the waveguide.

Fig. 3
Fig. 3

Dependence of the coupling angle of mode 1 on groove depth for the waveguide shown in Fig. 1. Here Δ denotes the duty cycle.

Fig. 4
Fig. 4

Refractive-index distribution of the multilayer dielectric stacks that were used as substrates of the photoresist gratings and electric field distributions of three selected TE bound modes.

Fig. 5
Fig. 5

Coupling angles of the 11th mode of the grating sample shown in Fig. 4 as functions of the duty cycles of photoresist gratings of different groove depths.

Fig. 6
Fig. 6

Schematic diagram of the experimental setup for measuring coupling angles.

Fig. 7
Fig. 7

Theoretical prediction of diffraction efficiencies of the −1st reflected and transmitted orders as functions of incident angle in the neighborhood of the −1st-order Littrow angle (28.44°).

Fig. 8
Fig. 8

Correlation between the signals measured experimentally by detectors D1 and D2.

Fig. 9
Fig. 9

SEM picture of a typical photoresist grating used in the duty-cycle measurement experiment.

Fig. 10
Fig. 10

Experimentally measured differences between the two coupling angles for the 11th bound mode of the multilayer waveguide versus duty cycles of photoresist gratings measured from SEM pictures. Filled circles, experimental data points; straight line, linear fit.

Equations (1)

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sin θ m ( i ) = N ( i ) + m λ d ,

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