Abstract

A three-intensity measurement technique has been employed in polarizer–sample–analyzer imaging ellipsometry to measure the two-dimensional ellipsometric parameters of a coated cylindrical lens. Since azimuth deviation α of a polarizer can also be measured with this three-intensity measurement technique, we tilted a well-calibrated thin-film wafer to identify the orientation of the measured α with respect to the incident plane. Using the analytic property of this measurement technique, we can correct the deviation and determine the thickness profile of the thin film coated on a cylindrical lens.

© 2009 Optical Society of America

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References

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  1. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1992), Chap. 4, p. 274.
  2. C. L. Tien, C. C. Lee, and C. C. Jaing,” The measurement of thin film stress using phase shifting interferometry,” J. Mod. Opt. 47, 839-849 (2000).
  3. Y. F. Chao, C. S. Wei, W. C. Lee, S. C. Lin, and T. S. Chao,” Ellipsometric measurements and its alignment: using the intensity ratio technique,” Jpn. J. Appl. Phys. 34, 5016-5019(1995).
    [CrossRef]
  4. Y. F. Chao and K. Y. Lee, “Index profile of radial gradient index lens measured by imaging ellipsometric technique,” Jpn. J. Appl. Phys. 44, 1111-1114 (2005).
    [CrossRef]
  5. K. Y. Lee and Y. F. Chao, “The ellipsometric measurements of a curved surface,” Jpn. J. Appl. Phys. 44, L1015-L1018 (2005).
    [CrossRef]
  6. Y. F. Chao, K. Y. Lee, and Y. D. Lin,” Analytical solutions of the azimuthal deviation of a polarizer and an analyzer by polarizer-sample-analyzer ellipsometry,” Appl. Opt. 45, 3935-3939 (2006).
    [CrossRef] [PubMed]
  7. E. Meyer, H. Frede and H. Knof, “Optical effects in metals: application of a least-squares method to measurements on gold and silver,” J. Appl. Phys. 38, 3682-3684 (1967).
    [CrossRef]

2006 (1)

2005 (2)

Y. F. Chao and K. Y. Lee, “Index profile of radial gradient index lens measured by imaging ellipsometric technique,” Jpn. J. Appl. Phys. 44, 1111-1114 (2005).
[CrossRef]

K. Y. Lee and Y. F. Chao, “The ellipsometric measurements of a curved surface,” Jpn. J. Appl. Phys. 44, L1015-L1018 (2005).
[CrossRef]

2000 (1)

C. L. Tien, C. C. Lee, and C. C. Jaing,” The measurement of thin film stress using phase shifting interferometry,” J. Mod. Opt. 47, 839-849 (2000).

1995 (1)

Y. F. Chao, C. S. Wei, W. C. Lee, S. C. Lin, and T. S. Chao,” Ellipsometric measurements and its alignment: using the intensity ratio technique,” Jpn. J. Appl. Phys. 34, 5016-5019(1995).
[CrossRef]

1967 (1)

E. Meyer, H. Frede and H. Knof, “Optical effects in metals: application of a least-squares method to measurements on gold and silver,” J. Appl. Phys. 38, 3682-3684 (1967).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1992), Chap. 4, p. 274.

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1992), Chap. 4, p. 274.

Chao, T. S.

Y. F. Chao, C. S. Wei, W. C. Lee, S. C. Lin, and T. S. Chao,” Ellipsometric measurements and its alignment: using the intensity ratio technique,” Jpn. J. Appl. Phys. 34, 5016-5019(1995).
[CrossRef]

Chao, Y. F.

Y. F. Chao, K. Y. Lee, and Y. D. Lin,” Analytical solutions of the azimuthal deviation of a polarizer and an analyzer by polarizer-sample-analyzer ellipsometry,” Appl. Opt. 45, 3935-3939 (2006).
[CrossRef] [PubMed]

Y. F. Chao and K. Y. Lee, “Index profile of radial gradient index lens measured by imaging ellipsometric technique,” Jpn. J. Appl. Phys. 44, 1111-1114 (2005).
[CrossRef]

K. Y. Lee and Y. F. Chao, “The ellipsometric measurements of a curved surface,” Jpn. J. Appl. Phys. 44, L1015-L1018 (2005).
[CrossRef]

Y. F. Chao, C. S. Wei, W. C. Lee, S. C. Lin, and T. S. Chao,” Ellipsometric measurements and its alignment: using the intensity ratio technique,” Jpn. J. Appl. Phys. 34, 5016-5019(1995).
[CrossRef]

Frede, H.

E. Meyer, H. Frede and H. Knof, “Optical effects in metals: application of a least-squares method to measurements on gold and silver,” J. Appl. Phys. 38, 3682-3684 (1967).
[CrossRef]

Jaing, C. C.

C. L. Tien, C. C. Lee, and C. C. Jaing,” The measurement of thin film stress using phase shifting interferometry,” J. Mod. Opt. 47, 839-849 (2000).

Knof, H.

E. Meyer, H. Frede and H. Knof, “Optical effects in metals: application of a least-squares method to measurements on gold and silver,” J. Appl. Phys. 38, 3682-3684 (1967).
[CrossRef]

Lee, C. C.

C. L. Tien, C. C. Lee, and C. C. Jaing,” The measurement of thin film stress using phase shifting interferometry,” J. Mod. Opt. 47, 839-849 (2000).

Lee, K. Y.

Y. F. Chao, K. Y. Lee, and Y. D. Lin,” Analytical solutions of the azimuthal deviation of a polarizer and an analyzer by polarizer-sample-analyzer ellipsometry,” Appl. Opt. 45, 3935-3939 (2006).
[CrossRef] [PubMed]

Y. F. Chao and K. Y. Lee, “Index profile of radial gradient index lens measured by imaging ellipsometric technique,” Jpn. J. Appl. Phys. 44, 1111-1114 (2005).
[CrossRef]

K. Y. Lee and Y. F. Chao, “The ellipsometric measurements of a curved surface,” Jpn. J. Appl. Phys. 44, L1015-L1018 (2005).
[CrossRef]

Lee, W. C.

Y. F. Chao, C. S. Wei, W. C. Lee, S. C. Lin, and T. S. Chao,” Ellipsometric measurements and its alignment: using the intensity ratio technique,” Jpn. J. Appl. Phys. 34, 5016-5019(1995).
[CrossRef]

Lin, S. C.

Y. F. Chao, C. S. Wei, W. C. Lee, S. C. Lin, and T. S. Chao,” Ellipsometric measurements and its alignment: using the intensity ratio technique,” Jpn. J. Appl. Phys. 34, 5016-5019(1995).
[CrossRef]

Lin, Y. D.

Meyer, E.

E. Meyer, H. Frede and H. Knof, “Optical effects in metals: application of a least-squares method to measurements on gold and silver,” J. Appl. Phys. 38, 3682-3684 (1967).
[CrossRef]

Tien, C. L.

C. L. Tien, C. C. Lee, and C. C. Jaing,” The measurement of thin film stress using phase shifting interferometry,” J. Mod. Opt. 47, 839-849 (2000).

Wei, C. S.

Y. F. Chao, C. S. Wei, W. C. Lee, S. C. Lin, and T. S. Chao,” Ellipsometric measurements and its alignment: using the intensity ratio technique,” Jpn. J. Appl. Phys. 34, 5016-5019(1995).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (1)

E. Meyer, H. Frede and H. Knof, “Optical effects in metals: application of a least-squares method to measurements on gold and silver,” J. Appl. Phys. 38, 3682-3684 (1967).
[CrossRef]

J. Mod. Opt. (1)

C. L. Tien, C. C. Lee, and C. C. Jaing,” The measurement of thin film stress using phase shifting interferometry,” J. Mod. Opt. 47, 839-849 (2000).

Jpn. J. Appl. Phys. (3)

Y. F. Chao, C. S. Wei, W. C. Lee, S. C. Lin, and T. S. Chao,” Ellipsometric measurements and its alignment: using the intensity ratio technique,” Jpn. J. Appl. Phys. 34, 5016-5019(1995).
[CrossRef]

Y. F. Chao and K. Y. Lee, “Index profile of radial gradient index lens measured by imaging ellipsometric technique,” Jpn. J. Appl. Phys. 44, 1111-1114 (2005).
[CrossRef]

K. Y. Lee and Y. F. Chao, “The ellipsometric measurements of a curved surface,” Jpn. J. Appl. Phys. 44, L1015-L1018 (2005).
[CrossRef]

Other (1)

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1992), Chap. 4, p. 274.

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Figures (5)

Fig. 1
Fig. 1

Schematic setup of the PSA ellipsometer.

Fig. 2
Fig. 2

Schematic configuration of a tilted sample: (a) side view and (b) top view that indicates the motion of its surface normal: Θ, the tilted angle by spacer; Δ θ , the component that contributes to the incident angle variation; α, the component measured in the deviation of the polarizer.

Fig. 3
Fig. 3

Deviation angle of the surface normal across the vertex of a cylindrical lens: open circles, measured α across the vertex of the lens; solid line, its best linear fit; inset, intersection of the measured line on the cylindrical lens.

Fig. 4
Fig. 4

Ellipsometric parameters and thickness profile of the cylindrical lens: (a) Ψ and (b) Δ measured when P = + 45 ° ; (c) Ψ and (d) Δ measured when P = 45 ° ; (e) Ψ and (f) Δ after correction.

Fig. 5
Fig. 5

Thickness profiles (a) of coated thin film on a cylindrical lens and (b) on flat glass that was coated with a cylindrical lens.

Tables (1)

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Table 1 Ellipsometric Measurements of Tilted and Untilted Samples

Equations (13)

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tan Ψ e i Δ = r p r s ,
I = I 0 ( sin 2 P sin 2 A + tan 2 Ψ cos 2 P cos 2 A + 0.5 tan Ψ cos Δ sin 2 P sin 2 A ) ,
I ( A ) = L 2 cos 2 ( A γ ) + T 2 sin 2 ( A γ ) ,
tan 2 γ = cos Δ sin 2 P sin 2 Ψ cos 2 P cos 2 Ψ ,
( L T ) 2 4 L T sin 2 ( 2 γ ) = cot 2 Δ .
I ( A ) = B ( 1 + C cos 2 A + D sin 2 A ) ,
B = 1 3 [ I ( 0 ° ) + I ( 60 ° ) + I ( 120 ° ) ] , C = 2 1 B [ I ( 60 ° ) + I ( 120 ° ) ] , D = I ( 60 ° ) I ( 120 ° ) ,
tan 2 γ = D C , L = D B sin 2 γ + B , T = 2 B L .
tan 2 Ψ = 1 + C 1 C tan 2 P .
P = + 45 ° tan 2 Ψ = ( 1 + C 1 ) ( 1 + sin 2 α ) ( 1 C 1 ) ( 1 sin 2 α ) , P = 45 ° tan 2 Ψ = ( 1 + C 2 ) ( 1 + sin 2 α ) ( 1 C 2 ) ( 1 sin 2 α ) ,
sin 2 α = 1 ( 1 + C 1 ) ( 1 C 1 ) ( 1 C 2 ) ( 1 + C 2 ) 1 + ( 1 + C 1 ) ( 1 C 1 ) ( 1 C 2 ) ( 1 + C 2 ) ,
tan Ψ = [ ( 1 + C 1 ) ( 1 C 1 ) ( 1 C 2 ) ( 1 + C 2 ) ] 1 4 .
γ = 1 4 ( tan 1 D 1 C 1 tan 1 D 2 C 2 ) ,

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