Abstract

Dynamic imaging microellipsometry (DIM) is a new rapid full-field imaging technique for high spatial resolution studies of thin films. The DIM concept is based on radiometric polarizer, compensator, specimen, and analyzer ellipsometry combined with video and image processing techniques. The theoretical basis for this approach is developed using the Jones vector and matrix formalisms. Basic systems design is presented with error model predictions of ellipsometric accuracies better than 0.1° for full-field Δ and ψ images captured in a few seconds with spatial resolution under 10 μm. Initial feasibility tests have demonstrated interframe discriminations of 0.36° for Δ and 0.082° for ψ.

© 1988 Optical Society of America

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References

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  1. R. F. Cohn, J. W. Wagner, J. Kruger, “Dynamic Imaging Microellipsometry: Proof of Concept Test Results,” J. Electrochem. Soc. 135, 1033 (Apr.1988).
    [CrossRef]
  2. J. Kruger, “Application of Ellipsometry to Electrochemistry,” in Advances in Electrochemistry and Electrochemical Engineering, Vol. 9, P. Delahay, C. W. Tobias (Wiley, New York, 1973).
  3. C. L. McBee, J. Kruger, “Events Leading to the Initiation of the Pitting of Iron,” Localized Corrosion NACE-3, 252 (1974).
  4. C. L. McBee, J. Kruger, “Ellipsometric-Spectroscopy of Films Formed on Metals in Solution,” Surf. Sci. 16, 340 (1969).
    [CrossRef]
  5. K. Sugimoto, S. Matsuda, Y. Ogiwara, K. Kitamura, “Microscopic Ellipsometric Observation of the Change in Passive Film on 18Cr-8Ni Stainless Steel with the Initiation and Growth of Pitt,” J. Electrochem. Soc. 132, 1791 (Aug.1985).
    [CrossRef]
  6. K. Sugimoto, S. Matsuda, “Analysis of Passive Films on Austeno-Ferritic Stainless Steel by Microscopic Ellipsometry,” J. Electrochem. Soc. 130, 2323 (Dec.1983).
    [CrossRef]
  7. R. H. Muller, “Principles of Ellipsometry,” in Advances in Electrochemistry and Electrochemical Engineering, Vol. 9, P. Delahay, C. W. Tobias, Eds. (Wiley, New York, 1973).
  8. R. M. N. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987).
  9. M. Erman, J. B. Theeten, “Spatially Resolved Ellipsometry,” J. Appl. Phys. 60, 859 (1986).
    [CrossRef]
  10. D. J. Dunlavy, R. B. Hammond, R. K. Ahrenkiel, “Scanning Microellipsometer for the Spatial Characterization of Thin Films,” Los Alamos National Laboratory Report LA-UR-81-1806 (1981).
  11. “Auto Gain Ellipsometers,” Bulletin EE, Gaertner Scientific Corp., p. 13.
  12. A. J. Hurd, C. J. Brinker, “Optical Sol-Gel Coatings: Ellipsometry of Film Formation,” J. Physique 49, 1017 (1988).
    [CrossRef]
  13. P. Hauge, F. Dill, “Design and Operation of ETA, An Automated Ellipsometer,” IBM J. Res. Dev. 472 (Nov.1973).
  14. G. Dahlquist, A. Bjorck, N. Anderson, Numerical Methods (Prentice-Hall, Englewood Cliffs, NJ, 1974), p. 30.

1988 (2)

R. F. Cohn, J. W. Wagner, J. Kruger, “Dynamic Imaging Microellipsometry: Proof of Concept Test Results,” J. Electrochem. Soc. 135, 1033 (Apr.1988).
[CrossRef]

A. J. Hurd, C. J. Brinker, “Optical Sol-Gel Coatings: Ellipsometry of Film Formation,” J. Physique 49, 1017 (1988).
[CrossRef]

1986 (1)

M. Erman, J. B. Theeten, “Spatially Resolved Ellipsometry,” J. Appl. Phys. 60, 859 (1986).
[CrossRef]

1985 (1)

K. Sugimoto, S. Matsuda, Y. Ogiwara, K. Kitamura, “Microscopic Ellipsometric Observation of the Change in Passive Film on 18Cr-8Ni Stainless Steel with the Initiation and Growth of Pitt,” J. Electrochem. Soc. 132, 1791 (Aug.1985).
[CrossRef]

1983 (1)

K. Sugimoto, S. Matsuda, “Analysis of Passive Films on Austeno-Ferritic Stainless Steel by Microscopic Ellipsometry,” J. Electrochem. Soc. 130, 2323 (Dec.1983).
[CrossRef]

1974 (1)

C. L. McBee, J. Kruger, “Events Leading to the Initiation of the Pitting of Iron,” Localized Corrosion NACE-3, 252 (1974).

1973 (1)

P. Hauge, F. Dill, “Design and Operation of ETA, An Automated Ellipsometer,” IBM J. Res. Dev. 472 (Nov.1973).

1969 (1)

C. L. McBee, J. Kruger, “Ellipsometric-Spectroscopy of Films Formed on Metals in Solution,” Surf. Sci. 16, 340 (1969).
[CrossRef]

Ahrenkiel, R. K.

D. J. Dunlavy, R. B. Hammond, R. K. Ahrenkiel, “Scanning Microellipsometer for the Spatial Characterization of Thin Films,” Los Alamos National Laboratory Report LA-UR-81-1806 (1981).

Anderson, N.

G. Dahlquist, A. Bjorck, N. Anderson, Numerical Methods (Prentice-Hall, Englewood Cliffs, NJ, 1974), p. 30.

Azzam, R. M. N.

R. M. N. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987).

Bashara, N. M.

R. M. N. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987).

Bjorck, A.

G. Dahlquist, A. Bjorck, N. Anderson, Numerical Methods (Prentice-Hall, Englewood Cliffs, NJ, 1974), p. 30.

Brinker, C. J.

A. J. Hurd, C. J. Brinker, “Optical Sol-Gel Coatings: Ellipsometry of Film Formation,” J. Physique 49, 1017 (1988).
[CrossRef]

Cohn, R. F.

R. F. Cohn, J. W. Wagner, J. Kruger, “Dynamic Imaging Microellipsometry: Proof of Concept Test Results,” J. Electrochem. Soc. 135, 1033 (Apr.1988).
[CrossRef]

Dahlquist, G.

G. Dahlquist, A. Bjorck, N. Anderson, Numerical Methods (Prentice-Hall, Englewood Cliffs, NJ, 1974), p. 30.

Dill, F.

P. Hauge, F. Dill, “Design and Operation of ETA, An Automated Ellipsometer,” IBM J. Res. Dev. 472 (Nov.1973).

Dunlavy, D. J.

D. J. Dunlavy, R. B. Hammond, R. K. Ahrenkiel, “Scanning Microellipsometer for the Spatial Characterization of Thin Films,” Los Alamos National Laboratory Report LA-UR-81-1806 (1981).

Erman, M.

M. Erman, J. B. Theeten, “Spatially Resolved Ellipsometry,” J. Appl. Phys. 60, 859 (1986).
[CrossRef]

Hammond, R. B.

D. J. Dunlavy, R. B. Hammond, R. K. Ahrenkiel, “Scanning Microellipsometer for the Spatial Characterization of Thin Films,” Los Alamos National Laboratory Report LA-UR-81-1806 (1981).

Hauge, P.

P. Hauge, F. Dill, “Design and Operation of ETA, An Automated Ellipsometer,” IBM J. Res. Dev. 472 (Nov.1973).

Hurd, A. J.

A. J. Hurd, C. J. Brinker, “Optical Sol-Gel Coatings: Ellipsometry of Film Formation,” J. Physique 49, 1017 (1988).
[CrossRef]

Kitamura, K.

K. Sugimoto, S. Matsuda, Y. Ogiwara, K. Kitamura, “Microscopic Ellipsometric Observation of the Change in Passive Film on 18Cr-8Ni Stainless Steel with the Initiation and Growth of Pitt,” J. Electrochem. Soc. 132, 1791 (Aug.1985).
[CrossRef]

Kruger, J.

R. F. Cohn, J. W. Wagner, J. Kruger, “Dynamic Imaging Microellipsometry: Proof of Concept Test Results,” J. Electrochem. Soc. 135, 1033 (Apr.1988).
[CrossRef]

C. L. McBee, J. Kruger, “Events Leading to the Initiation of the Pitting of Iron,” Localized Corrosion NACE-3, 252 (1974).

C. L. McBee, J. Kruger, “Ellipsometric-Spectroscopy of Films Formed on Metals in Solution,” Surf. Sci. 16, 340 (1969).
[CrossRef]

J. Kruger, “Application of Ellipsometry to Electrochemistry,” in Advances in Electrochemistry and Electrochemical Engineering, Vol. 9, P. Delahay, C. W. Tobias (Wiley, New York, 1973).

Matsuda, S.

K. Sugimoto, S. Matsuda, Y. Ogiwara, K. Kitamura, “Microscopic Ellipsometric Observation of the Change in Passive Film on 18Cr-8Ni Stainless Steel with the Initiation and Growth of Pitt,” J. Electrochem. Soc. 132, 1791 (Aug.1985).
[CrossRef]

K. Sugimoto, S. Matsuda, “Analysis of Passive Films on Austeno-Ferritic Stainless Steel by Microscopic Ellipsometry,” J. Electrochem. Soc. 130, 2323 (Dec.1983).
[CrossRef]

McBee, C. L.

C. L. McBee, J. Kruger, “Events Leading to the Initiation of the Pitting of Iron,” Localized Corrosion NACE-3, 252 (1974).

C. L. McBee, J. Kruger, “Ellipsometric-Spectroscopy of Films Formed on Metals in Solution,” Surf. Sci. 16, 340 (1969).
[CrossRef]

Muller, R. H.

R. H. Muller, “Principles of Ellipsometry,” in Advances in Electrochemistry and Electrochemical Engineering, Vol. 9, P. Delahay, C. W. Tobias, Eds. (Wiley, New York, 1973).

Ogiwara, Y.

K. Sugimoto, S. Matsuda, Y. Ogiwara, K. Kitamura, “Microscopic Ellipsometric Observation of the Change in Passive Film on 18Cr-8Ni Stainless Steel with the Initiation and Growth of Pitt,” J. Electrochem. Soc. 132, 1791 (Aug.1985).
[CrossRef]

Sugimoto, K.

K. Sugimoto, S. Matsuda, Y. Ogiwara, K. Kitamura, “Microscopic Ellipsometric Observation of the Change in Passive Film on 18Cr-8Ni Stainless Steel with the Initiation and Growth of Pitt,” J. Electrochem. Soc. 132, 1791 (Aug.1985).
[CrossRef]

K. Sugimoto, S. Matsuda, “Analysis of Passive Films on Austeno-Ferritic Stainless Steel by Microscopic Ellipsometry,” J. Electrochem. Soc. 130, 2323 (Dec.1983).
[CrossRef]

Theeten, J. B.

M. Erman, J. B. Theeten, “Spatially Resolved Ellipsometry,” J. Appl. Phys. 60, 859 (1986).
[CrossRef]

Wagner, J. W.

R. F. Cohn, J. W. Wagner, J. Kruger, “Dynamic Imaging Microellipsometry: Proof of Concept Test Results,” J. Electrochem. Soc. 135, 1033 (Apr.1988).
[CrossRef]

IBM J. Res. Dev. (1)

P. Hauge, F. Dill, “Design and Operation of ETA, An Automated Ellipsometer,” IBM J. Res. Dev. 472 (Nov.1973).

J. Appl. Phys. (1)

M. Erman, J. B. Theeten, “Spatially Resolved Ellipsometry,” J. Appl. Phys. 60, 859 (1986).
[CrossRef]

J. Electrochem. Soc. (3)

R. F. Cohn, J. W. Wagner, J. Kruger, “Dynamic Imaging Microellipsometry: Proof of Concept Test Results,” J. Electrochem. Soc. 135, 1033 (Apr.1988).
[CrossRef]

K. Sugimoto, S. Matsuda, Y. Ogiwara, K. Kitamura, “Microscopic Ellipsometric Observation of the Change in Passive Film on 18Cr-8Ni Stainless Steel with the Initiation and Growth of Pitt,” J. Electrochem. Soc. 132, 1791 (Aug.1985).
[CrossRef]

K. Sugimoto, S. Matsuda, “Analysis of Passive Films on Austeno-Ferritic Stainless Steel by Microscopic Ellipsometry,” J. Electrochem. Soc. 130, 2323 (Dec.1983).
[CrossRef]

J. Physique (1)

A. J. Hurd, C. J. Brinker, “Optical Sol-Gel Coatings: Ellipsometry of Film Formation,” J. Physique 49, 1017 (1988).
[CrossRef]

Localized Corrosion (1)

C. L. McBee, J. Kruger, “Events Leading to the Initiation of the Pitting of Iron,” Localized Corrosion NACE-3, 252 (1974).

Surf. Sci. (1)

C. L. McBee, J. Kruger, “Ellipsometric-Spectroscopy of Films Formed on Metals in Solution,” Surf. Sci. 16, 340 (1969).
[CrossRef]

Other (6)

J. Kruger, “Application of Ellipsometry to Electrochemistry,” in Advances in Electrochemistry and Electrochemical Engineering, Vol. 9, P. Delahay, C. W. Tobias (Wiley, New York, 1973).

R. H. Muller, “Principles of Ellipsometry,” in Advances in Electrochemistry and Electrochemical Engineering, Vol. 9, P. Delahay, C. W. Tobias, Eds. (Wiley, New York, 1973).

R. M. N. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987).

D. J. Dunlavy, R. B. Hammond, R. K. Ahrenkiel, “Scanning Microellipsometer for the Spatial Characterization of Thin Films,” Los Alamos National Laboratory Report LA-UR-81-1806 (1981).

“Auto Gain Ellipsometers,” Bulletin EE, Gaertner Scientific Corp., p. 13.

G. Dahlquist, A. Bjorck, N. Anderson, Numerical Methods (Prentice-Hall, Englewood Cliffs, NJ, 1974), p. 30.

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Figures (10)

Fig. 1
Fig. 1

Basic PCSA system and CCD detector.

Fig. 2
Fig. 2

DIM PSA system Δ and ψ error plot.

Fig. 3
Fig. 3

Optimum polarizer and compensator settings for silicon samples are defined at the intersection.

Fig. 4
Fig. 4

Silicon tuned PCSA system error plots using P = 10.0 and C = −1.0°.

Fig. 5
Fig. 5

DIM prototype system block diagram.

Fig. 6
Fig. 6

Δ and ψ plots from silicon wafer ellipsogram line 196.

Fig. 7
Fig. 7

Copper/aluminum specimen ellipsogram.

Fig. 8
Fig. 8

Copper/aluminum specimen Δ and ψ plots from ellipsogram line 250.

Fig. 9
Fig. 9

Steel/copper specimen ellipsogram.

Fig. 10
Fig. 10

Steel/copper specimen Δ and ψ plots from ellipsogram line 250.

Tables (1)

Tables Icon

Table I Results from Copper/Aluminum and Steel/Copper Specimens

Equations (23)

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r p = r p exp ( j δ p ) ;
r s = r s exp ( j δ s ) .
Δ = δ p - δ s
ψ = arctan r p / r s .
E A O t e = T A t e R ( A ) T S x y R ( - C ) C C f s R ( C - P ) E P O t e ,
E P O t e = K p [ 1 0 ] ;
T C f s = K c [ 1 0 0 ρ c ] ;
T S x , y = [ V ex 0 0 V ey ] ;
T A t e = K A [ 1 0 0 0 ] ;
R ( α ) = [ cos α sin α - sin α cos α ] .
E A O t e = K p K A K c V ey { cos A tan ψ exp ( j Δ ) [ cos C cos ( P - C ) - ρ c sin C sin ( P - C ) ] + sin A [ sin C cos ( P - C ) + ρ c cos C sin ( P - C ) ] ,
V ex / V ey = tan ψ exp ( j Δ ) .
ρ c = exp ( - j π / 2 ) = - j
G = K p K A K c V ey ,
I ( A ) = E A O t e ( E A O t e ) * = ( G 2 / 2 ) { [ 1 + cos 2 C cos 2 ( P - C ) ] cos 2 A × tan 2 ψ + [ 1 - cos 2 C cos 2 ( P - C ) ] sin 2 A + [ sin 2 C cos 2 ( P - C ) cos Δ - sin 2 ( P - C ) sin Δ ] sin 2 A tan ψ } .
ψ = tan - 1 [ 1 - cos 2 C cos 2 ( P - C ) 1 + cos 2 C cos 2 ( P - C ) I ( 0 ° ) I ( 90 ° ) ] ;
Δ = cos - 1 [ I ( 45 ° ) - I ( - 45 ° ) 2 I ( 0 ° ) I ( 90 ° ) ] - tan - 1 [ tan 2 ( P - C ) sin 2 C ] .
σ I ( A ) { i = 1 n [ I ( A ) x i ] 2 σ x i 2 } 1 / 2 .
δ y A | y I ( A ) | · δ I ( A ) ,
E S O x y = [ V ex [ cos C cos ( P - C ) + j sin C sin ( P - C ) ] V ey [ sin C cos ( P - C ) - j cos C sin ( P - C ) ] ] ,
χ S O = exp ( j π / 2 ) = tan ψ exp ( j Δ ) × [ cos C cos ( P - C ) + j sin C sin ( P - C ) sin C cos ( P - C ) - j cos C sin ( P - C ) ] ,
P = 1 2 cos - 1 ( cos 2 ψ cos 2 C ) + C .
P = - 1 / 2 tan - 1 [ sin 2 C tan ( Δ - π / 2 ) ] + C .

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