Abstract

We describe a technique for studying scattering from subwavelength features. A simple scatterometer was developed to measure the scattering from the single-submicrometer, subwavelength features generated with a focused ion beam system. A model that can describe diffraction from subwavelength features with arbitrary profiles is also presented and shown to agree quite well with the experimental measurements. The model is used to demonstrate ways in which the aspect ratios of subwavelength ridges and trenches can be obtained from scattering data and how ridges can be distinguished from trenches over a wide range of aspect ratios. We show that some earlier results of studies on distinguishing pits from particles do not extend to low-aspect-ratio features.

© 2001 Optical Society of America

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References

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    [CrossRef]
  7. H. Haidner, D. Dias, L. L. Wang, T. Tschudi, “Binary subwavelength structures/resonance gratings as polarization elements,” Pure Appl. Opt. 7, 1347–1361 (1998).
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    [CrossRef]
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1999 (1)

Y. A. Eremin, J. C. Stover, N. V. Orlov, “Modeling scatter from silicon wafer features based on discrete sources method,” Opt. Eng. 38, 1296–1304 (1999).
[CrossRef]

1998 (3)

1997 (2)

1995 (1)

D. Levy, L. Shingher, J. Shamir, Y. Leviatan, “Step height determination by a focused Gaussian beam,” Opt. Eng. 34, 3303–3319 (1995).
[CrossRef]

1991 (1)

Bernt, M.

J. C. Stover, M. Bernt, “A multiple particle technique for determination of differential scattering cross-section of very small surface bound particles,” in Optical Scattering in the Optics, Semiconductor, and Computer Disk Industries, J. C. Stover, ed., Proc. SPIE2541, 108–112 (1995).
[CrossRef]

Cronin, N. J.

N. J. Cronin, Microwave and Optical Waveguides (Institute of Physics, London, 1995).

De Hoop, A. T.

A. T. De Hoop, Modern Topics in Electromagnetics and Antennas, PPL Conference Publication, Vol. 13, Peter Peregrinus Ltd., Stevenage, England (1977).

Dias, D.

H. Haidner, D. Dias, L. L. Wang, T. Tschudi, “Binary subwavelength structures/resonance gratings as polarization elements,” Pure Appl. Opt. 7, 1347–1361 (1998).
[CrossRef]

Eremin, Y. A.

Y. A. Eremin, J. C. Stover, N. V. Orlov, “Modeling scatter from silicon wafer features based on discrete sources method,” Opt. Eng. 38, 1296–1304 (1999).
[CrossRef]

Greffet, J.-J.

Haidner, H.

H. Haidner, D. Dias, L. L. Wang, T. Tschudi, “Binary subwavelength structures/resonance gratings as polarization elements,” Pure Appl. Opt. 7, 1347–1361 (1998).
[CrossRef]

Ivahknenko, V. I.

C. A. Scheer, J. C. Stover, V. I. Ivahknenko, “Comparison of models and measurements of scatter from surface bound particles,” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, J. C. Stover, ed., Proc. SPIE3275, 102–111 (1998).
[CrossRef]

Kowarz, M. W.

Ladan, F.-R.

Leviatan, Y.

D. Levy, L. Shingher, J. Shamir, Y. Leviatan, “Step height determination by a focused Gaussian beam,” Opt. Eng. 34, 3303–3319 (1995).
[CrossRef]

Levy, D.

D. Levy, L. Shingher, J. Shamir, Y. Leviatan, “Step height determination by a focused Gaussian beam,” Opt. Eng. 34, 3303–3319 (1995).
[CrossRef]

Li, L.

Liu, W.-C.

Mansuripur, M.

Marx, D. S.

Orlov, N. V.

Y. A. Eremin, J. C. Stover, N. V. Orlov, “Modeling scatter from silicon wafer features based on discrete sources method,” Opt. Eng. 38, 1296–1304 (1999).
[CrossRef]

Psaltis, D.

Scheer, C. A.

C. A. Scheer, J. C. Stover, V. I. Ivahknenko, “Comparison of models and measurements of scatter from surface bound particles,” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, J. C. Stover, ed., Proc. SPIE3275, 102–111 (1998).
[CrossRef]

Shamir, J.

D. Levy, L. Shingher, J. Shamir, Y. Leviatan, “Step height determination by a focused Gaussian beam,” Opt. Eng. 34, 3303–3319 (1995).
[CrossRef]

Shingher, L.

D. Levy, L. Shingher, J. Shamir, Y. Leviatan, “Step height determination by a focused Gaussian beam,” Opt. Eng. 34, 3303–3319 (1995).
[CrossRef]

Stover, J. C.

Y. A. Eremin, J. C. Stover, N. V. Orlov, “Modeling scatter from silicon wafer features based on discrete sources method,” Opt. Eng. 38, 1296–1304 (1999).
[CrossRef]

C. A. Scheer, J. C. Stover, V. I. Ivahknenko, “Comparison of models and measurements of scatter from surface bound particles,” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, J. C. Stover, ed., Proc. SPIE3275, 102–111 (1998).
[CrossRef]

J. C. Stover, M. Bernt, “A multiple particle technique for determination of differential scattering cross-section of very small surface bound particles,” in Optical Scattering in the Optics, Semiconductor, and Computer Disk Industries, J. C. Stover, ed., Proc. SPIE2541, 108–112 (1995).
[CrossRef]

Tschudi, T.

H. Haidner, D. Dias, L. L. Wang, T. Tschudi, “Binary subwavelength structures/resonance gratings as polarization elements,” Pure Appl. Opt. 7, 1347–1361 (1998).
[CrossRef]

Wang, L. L.

H. Haidner, D. Dias, L. L. Wang, T. Tschudi, “Binary subwavelength structures/resonance gratings as polarization elements,” Pure Appl. Opt. 7, 1347–1361 (1998).
[CrossRef]

Yeh, W. H.

Appl. Opt. (2)

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

Opt. Eng. (2)

D. Levy, L. Shingher, J. Shamir, Y. Leviatan, “Step height determination by a focused Gaussian beam,” Opt. Eng. 34, 3303–3319 (1995).
[CrossRef]

Y. A. Eremin, J. C. Stover, N. V. Orlov, “Modeling scatter from silicon wafer features based on discrete sources method,” Opt. Eng. 38, 1296–1304 (1999).
[CrossRef]

Opt. Express (1)

Pure Appl. Opt. (1)

H. Haidner, D. Dias, L. L. Wang, T. Tschudi, “Binary subwavelength structures/resonance gratings as polarization elements,” Pure Appl. Opt. 7, 1347–1361 (1998).
[CrossRef]

Other (4)

C. A. Scheer, J. C. Stover, V. I. Ivahknenko, “Comparison of models and measurements of scatter from surface bound particles,” in Flatness, Roughness, and Discrete Defects Characterization for Computer Disks, Wafers, and Flat Panel Displays II, J. C. Stover, ed., Proc. SPIE3275, 102–111 (1998).
[CrossRef]

J. C. Stover, M. Bernt, “A multiple particle technique for determination of differential scattering cross-section of very small surface bound particles,” in Optical Scattering in the Optics, Semiconductor, and Computer Disk Industries, J. C. Stover, ed., Proc. SPIE2541, 108–112 (1995).
[CrossRef]

A. T. De Hoop, Modern Topics in Electromagnetics and Antennas, PPL Conference Publication, Vol. 13, Peter Peregrinus Ltd., Stevenage, England (1977).

N. J. Cronin, Microwave and Optical Waveguides (Institute of Physics, London, 1995).

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Figures (10)

Fig. 1
Fig. 1

Average AFM cross sections of FIB-produced trenches.

Fig. 2
Fig. 2

(a) Schematic diagram of the experimental setup used to measure the diffracted far field from subwavelength linear trenches. (b) Coordinate system for the far-field measurements. The trenches are aligned along the y axis, and the PMT rotates about the y axis in the x–z plane.

Fig. 3
Fig. 3

Far-field diffraction comparison of rectangular versus Gaussian-shaped incident beams.

Fig. 4
Fig. 4

Specular beam with no feature present, p polarization. θi=15°.

Fig. 5
Fig. 5

Modeled and experimental scattering data from four trenches. Figures a-d are for p polarization and e-h are the corresponding plots for s polarization. The incidence angle is 5° for all cases. The solid curve is the modeling result, and the diamonds are the experimental data.

Fig. 6
Fig. 6

Same as Fig. 5 for a 15° angle of incidence. Figures a-d are for p polarization and e-h are the corresponding plots for s polarization.

Fig. 7
Fig. 7

Cross-sectional profiles of four different trenches, all having the same cross-sectional area but different aspect ratios. The aspect ratios range from approximately 1:4 (depth to width) to approximately 1:1.

Fig. 8
Fig. 8

Scattering for trenches versus ridges. The illumination is at 60°, and is p polarized: (a) for feature with an aspect ratio of 1:1, (b) for feature with an aspect ratio of 1:4 (depth to width).

Fig. 9
Fig. 9

Computed scattering from the four trenches of Fig. 7 at normal-incidence illumination. (a) Polarization perpendicular to the trench (p polarization), (b) polarization parallel to the trench (s polarization), (c) zooming in on the dip in (a).

Fig. 10
Fig. 10

Ratio of the scattering of light polarized parallel versus perpendicular to the trench axis as a function of the aspect ratio of the feature.

Tables (1)

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Table 1 Summary of AFM Data for FIB-Produced Trenches a

Equations (4)

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k=sin θs-sin θiλ.
B(u)=1ifu<NA0ifu>NA,
B(u)=exp(-u2/NA2).
B(u)=exp[-(u-sin θi)2/NA2].

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