Abstract

In rotating-analyzer ellipsometry, an improved measurement method that does not need the accurate adjustment of the optical components before measurement is described. By carrying out the measurements at two 90°-different azimuths of the polarizer, we can determine the orientation of the optical components to the plane of incidence and the ellipsometric parameters of the specimen at the same time. The method is also applicable to a new adjustment procedure that is simpler and more convenient than the usual methods. The versatility of this improved measurement method has been confirmed experimentally.

© 1984 Optical Society of America

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References

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  1. P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96, 108–140 (1980).
    [CrossRef]
  2. M. J. Dignam, M. Moskovits, “Azimuthal misalignment and surface anisotropy as sources of error in ellipsometry,” Appl. Opt. 9, 1868–1873 (1970).
    [PubMed]
  3. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1980), Chap. 5, pp. 380–385.
  4. D. E. Aspnes, “Effect of component optical activity in data reduction and calibration of rotating-analyzer ellipsometers,” J. Opt. Soc. Am. 64, 812–819 (1974).
    [CrossRef]
  5. D. E. Aspnes, A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975).
    [PubMed]
  6. R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizer and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25, 137–140 (1978).
    [CrossRef]
  7. P. S. Haug, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–487 (1973).
    [CrossRef]
  8. F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. Sect. A 67, 363–377 (1963).
    [CrossRef]
  9. S. Kawabata, H. Inose, “Photometric ellipsometer combined with microcomputer,” Acad. Rep. Tokyo Inst. Polytech. 4(1), 9–17 (1981) (in Japanese).
  10. D. E. Aspnes, “Optimizing precision of rotating-analyzer ellipsometers,” J. Opt. Soc. Am. 64, 639–646 (1974).
    [CrossRef]

1981 (1)

S. Kawabata, H. Inose, “Photometric ellipsometer combined with microcomputer,” Acad. Rep. Tokyo Inst. Polytech. 4(1), 9–17 (1981) (in Japanese).

1980 (1)

P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96, 108–140 (1980).
[CrossRef]

1978 (1)

R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizer and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25, 137–140 (1978).
[CrossRef]

1975 (1)

1974 (2)

1973 (1)

P. S. Haug, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–487 (1973).
[CrossRef]

1970 (1)

1963 (1)

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. Sect. A 67, 363–377 (1963).
[CrossRef]

Aspnes, D. E.

Azzam, R. M. A.

R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizer and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25, 137–140 (1978).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1980), Chap. 5, pp. 380–385.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1980), Chap. 5, pp. 380–385.

Dignam, M. J.

Dill, F. H.

P. S. Haug, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–487 (1973).
[CrossRef]

Haug, P. S.

P. S. Haug, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–487 (1973).
[CrossRef]

Hauge, P. S.

P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96, 108–140 (1980).
[CrossRef]

Inose, H.

S. Kawabata, H. Inose, “Photometric ellipsometer combined with microcomputer,” Acad. Rep. Tokyo Inst. Polytech. 4(1), 9–17 (1981) (in Japanese).

Kawabata, S.

S. Kawabata, H. Inose, “Photometric ellipsometer combined with microcomputer,” Acad. Rep. Tokyo Inst. Polytech. 4(1), 9–17 (1981) (in Japanese).

McCrackin, F. L.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. Sect. A 67, 363–377 (1963).
[CrossRef]

Moskovits, M.

Passaglia, E.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. Sect. A 67, 363–377 (1963).
[CrossRef]

Steinberg, H. L.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. Sect. A 67, 363–377 (1963).
[CrossRef]

Stromberg, R. R.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. Sect. A 67, 363–377 (1963).
[CrossRef]

Studna, A. A.

Acad. Rep. Tokyo Inst. Polytech. (1)

S. Kawabata, H. Inose, “Photometric ellipsometer combined with microcomputer,” Acad. Rep. Tokyo Inst. Polytech. 4(1), 9–17 (1981) (in Japanese).

Appl. Opt. (2)

IBM J. Res. Dev. (1)

P. S. Haug, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–487 (1973).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Res. Natl. Bur. Stand. Sect. A (1)

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. Sect. A 67, 363–377 (1963).
[CrossRef]

Opt. Commun. (1)

R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizer and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25, 137–140 (1978).
[CrossRef]

Surf. Sci. (1)

P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96, 108–140 (1980).
[CrossRef]

Other (1)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1980), Chap. 5, pp. 380–385.

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the rotating-analyzer ellipsometer. P, polarizer; S, specimen; RA, rotating analyzer.

Fig. 2
Fig. 2

The relations between correct and apparent coordinate systems on the Poincaré sphere in the rotating-analyzer ellipsometry whose initial azimuth is χA.

Fig. 3
Fig. 3

The great circle that passes through the two measured apparent polarization states on the Poincaré sphere. P and Q represent the measured apparent polarization states for the azimuths of the polarizer χP and χP + π/2, respectively.

Tables (2)

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Table 1 Improved Rotating-Analyzer Ellipsometry for a Thick Evaporated Au Film on a Glass Substratea

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Table 2 Adjustment of the Azimuth of the Analyzer

Equations (18)

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I = ( I 0 / 2 ) { 1 + S 1 cos [ 2 ( ω t + χ A ) ] + S 2 sin [ 2 ( ω t + χ A ) ] } ,
S 1 = 2 0 2 π / ω I cos ( 2 ω t ) d t / 0 2 π / ω I d t = S 1 cos ( 2 χ A ) + S 2 sin ( 2 χ A ) , S 2 = 2 0 2 π / ω I sin ( 2 ω t ) d t / 0 2 π / ω I d t = - S 1 sin ( 2 χ A ) + S 2 cos ( 2 χ A ) .
S 3 = ± [ 1 - ( S 1 ) 2 - ( S 2 ) 2 ] 1 / 2 = ± ( 1 - S 1 2 - S 2 2 ) 1 / 2 = ± S 3 .
( S 1 S 2 S 3 ) = [ cos ( 2 χ A ) sin ( 2 χ A ) 0 - sin ( 2 χ A ) cos ( 2 χ A ) 0 0 0 1 ] ( S 1 S 2 S 3 ) .
tan Ψ cot χ P = [ ( 1 + P 1 ) / ( 1 - P 1 ) ] 1 / 2 , tan Δ = P 2 / P 3 ,
P 1 = P 1 cos ( 2 χ A ) + P 2 sin ( 2 χ A ) , P 2 = - P 1 sin ( 2 χ A ) + P 2 cos ( 2 χ A ) , P 3 = [ 1 - ( P 1 ) 2 - ( P 2 ) 2 ] 1 / 2 = P 3 ,
Q 1 = Q 1 cos ( 2 χ A ) + Q 2 sin ( 2 χ A ) , Q 2 = - Q 1 sin ( 2 χ A ) + Q 2 cos ( 2 χ A ) , Q 3 = - [ 1 - ( Q 1 ) 2 - ( Q 2 ) 2 ] 1 / 2 = Q 3 ( < 0 ) ,
tan Ψ tan χ P = [ ( 1 + Q 1 ) / ( 1 - Q 1 ) ] 1 / 2 , tan Δ = Q 2 / Q 3 .
P 1 = P 1 cos ( 2 χ A ) - P 2 sin ( 2 χ A ) , P 2 = P 1 sin ( 2 χ A ) + P 2 cos ( 2 χ A ) , P 3 = P 3
Q 1 = Q 1 cos ( 2 χ A ) - Q 2 sin ( 2 χ A ) , Q 2 = Q 1 sin ( 2 χ A ) + Q 2 cos ( 2 χ A ) , Q 3 = Q 3 .
( A B 0 ) = ( 1 0 0 0 cos Δ sin Δ 0 - sin Δ cos Δ ) ( S 1 S 2 S 3 ) ,
( A B 0 ) = ( 1 0 0 0 cos Δ sin Δ 0 - sin Δ cos Δ ) [ cos ( 2 χ A ) - sin ( 2 χ A ) 0 sin ( 2 χ A ) cos ( 2 χ A ) 0 0 0 1 ] ( S 1 S 2 S 3 ) ,
- [ P 1 sin ( 2 χ A ) + P 2 cos ( 2 χ A ) ] sin Δ + P 3 cos Δ = 0 ,
- [ Q 1 sin ( 2 χ A ) + Q 2 cos ( 2 χ A ) ] sin Δ + Q 3 cos Δ = 0.
tan ( 2 χ A ) = - ( P 2 Q 3 - P 3 Q 2 ) / ( P 1 Q 3 - P 3 Q 1 ) .
tan 2 χ P = [ ( 1 - P 1 ) ( 1 + Q 1 ) / ( 1 + P 1 ) ( 1 - Q 1 ) ] 1 / 2 ,
tan 2 Ψ = [ ( 1 + P 1 ) ( 1 + Q 1 ) / ( 1 - P 1 ) ( 1 - Q 1 ) ] 1 / 2 ,
tan Δ = P 2 / P 3 .

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