Abstract

Small nonlinearity (~2%) of the light-flux detection system is shown to have appreciable effects on the accuracy of calibration and data analysis in rotating-analyzer ellipsometers. Procedures for detecting and correcting these effects are presented.

© 1976 Optical Society of America

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References

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  1. B. D. Cahan and R. F. Spanier, Surf. Sci. 16, 166 (1969).
    [Crossref]
  2. R. Greef, Rev. Sci. Instrum. 41, 532 (1970).
    [Crossref]
  3. P. S. Hauge and F. H. Dill, IBM J. Res. Dev. 17, 472 (1973).
    [Crossref]
  4. D. E. Aspnes, Opt. Commun. 8, 222 (1973).
    [Crossref]
  5. Y. J. van der Meulen and N. C. Hien, J. Opt. Soc. Am. 64, 804 (1974).
    [Crossref]
  6. D. E. Aspnes, J. Opt. Soc. Am. 64, 812 (1974).
    [Crossref]
  7. R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 64, 1459 (1974).
    [Crossref]
  8. R. H. Muller, Surf. Sci. 16, 14 (1969).
    [Crossref]
  9. Actually, the first, third, and fourth coefficients, which indicate errors, are also calculated.
  10. Previous measurements indicated that A0 = 0 was appropriate for this particular instrument. However, small changes of A0 (even with A2 = 0) can appreciably affect F.
  11. D. E. Aspnes, J. Opt. Soc. Am. 64, 639 (1974).
    [Crossref]
  12. W. G. Oldham, J. Opt. Soc. Am. 57, 57 (1967).

1974 (4)

1973 (2)

P. S. Hauge and F. H. Dill, IBM J. Res. Dev. 17, 472 (1973).
[Crossref]

D. E. Aspnes, Opt. Commun. 8, 222 (1973).
[Crossref]

1970 (1)

R. Greef, Rev. Sci. Instrum. 41, 532 (1970).
[Crossref]

1969 (2)

B. D. Cahan and R. F. Spanier, Surf. Sci. 16, 166 (1969).
[Crossref]

R. H. Muller, Surf. Sci. 16, 14 (1969).
[Crossref]

1967 (1)

W. G. Oldham, J. Opt. Soc. Am. 57, 57 (1967).

Aspnes, D. E.

Azzam, R. M. A.

Bashara, N. M.

Cahan, B. D.

B. D. Cahan and R. F. Spanier, Surf. Sci. 16, 166 (1969).
[Crossref]

Dill, F. H.

P. S. Hauge and F. H. Dill, IBM J. Res. Dev. 17, 472 (1973).
[Crossref]

Greef, R.

R. Greef, Rev. Sci. Instrum. 41, 532 (1970).
[Crossref]

Hauge, P. S.

P. S. Hauge and F. H. Dill, IBM J. Res. Dev. 17, 472 (1973).
[Crossref]

Hien, N. C.

Muller, R. H.

R. H. Muller, Surf. Sci. 16, 14 (1969).
[Crossref]

Oldham, W. G.

W. G. Oldham, J. Opt. Soc. Am. 57, 57 (1967).

Spanier, R. F.

B. D. Cahan and R. F. Spanier, Surf. Sci. 16, 166 (1969).
[Crossref]

van der Meulen, Y. J.

IBM J. Res. Dev. (1)

P. S. Hauge and F. H. Dill, IBM J. Res. Dev. 17, 472 (1973).
[Crossref]

J. Opt. Soc. Am. (5)

Opt. Commun. (1)

D. E. Aspnes, Opt. Commun. 8, 222 (1973).
[Crossref]

Rev. Sci. Instrum. (1)

R. Greef, Rev. Sci. Instrum. 41, 532 (1970).
[Crossref]

Surf. Sci. (2)

B. D. Cahan and R. F. Spanier, Surf. Sci. 16, 166 (1969).
[Crossref]

R. H. Muller, Surf. Sci. 16, 14 (1969).
[Crossref]

Other (2)

Actually, the first, third, and fourth coefficients, which indicate errors, are also calculated.

Previous measurements indicated that A0 = 0 was appropriate for this particular instrument. However, small changes of A0 (even with A2 = 0) can appreciably affect F.

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Figures (2)

FIG. 1
FIG. 1

FPCA and the compensator parameters δC (in degrees) and TC obtained in P-C-A are plotted against the polarizer azimuth P (in degrees) for no nonlinearity correction [A0 = 0, A2 = 0 in Eq. (2)], shown with (x), and with nonlinearity correction (A0 = 0, A2 = 1 × 10−5) shown with (+). For the uncorrected case (x), δC were too close to corrected (+) to be plotted. The compensator was set at C = 90.00°.

FIG. 2
FIG. 2

FPSA and the calculated SiO2 film index and thickness, nf and df (in Å) obtained in P-S-A are plotted against polarizer azimuth P (in degrees) for no nonlinearity correction [A0 = 0, A2 = 0 in Eq. (2)], shown with (x), and with nonlinearity correction (A0 = 0, A2 = 1.28 × 10−5), shown with (+).

Equations (16)

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P = P S + δ P ,
C = C S + δ C + δ P ,
A = A S + δ A + δ P ,
I r = A 0 + I c + A 2 I c 2 ,
I c = a 0 + a 2 cos 2 A S + b 2 sin 2 A S .
2 A SMIN = 360° u ( b 2 ) - sgn ( b 2 ) cos - 1 - a 2 [ ( a 2 ) 2 + ( b 2 ) 2 ] 1 / 2 ,
δ A = P S + 90 - A SMIN .
δ P = - P S ,             P S 0
δ P = 90° - P S ,             P S 90° ,
δ C = P S - C S ,             P S C S
δ C = P S - ( C S + 90° ) ,             P S C S + 90° .
I C = a 0 + a 2 cos 2 ( A - C ) + b 2 sin 2 ( A - C ) ,
a 2 = a 2 cos 2 θ - b 2 sin 2 θ ,
b 2 = a 2 sin 2 θ + b 2 cos 2 θ ,
T C 2 = ( a 0 - a 2 ) cos 2 ( C - P ) ( a 0 + a 2 ) sin 2 ( C - P ) ,             T C 0
cos Δ C = b 2 cos ( C - P ) T C ( a 0 + a 2 ) sin ( C - P ) ,             Δ C 90° .