Abstract

Two methods are described which provide in-process calibration of ellipsometer divided circles. Both methods (a residual method and a nonlinear least-squares estimation procedure) utilize multiple measurements on any arbitrary specimen to compute the azimuth angle corrections for the polarizer, compensator, and analyzer divided circles. The results of an experimental comparison of the two methods show (1) the confidence limits on the calibration constants are greater than is generally assumed, (2) that within experimental uncertainties both methods yield the same set of calibration constants, but one method may be more appropriate than the other for a given set of data, (3) the calibration constants can be a function of the wavelength of the light used for measurements, (4) other factors being equal, the maximum accuracy in a conventional ellipsometer system would be obtained by using a fixed-polarizer nulling scheme with the compensator set after reflection.

© 1976 Optical Society of America

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References

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  1. R. M. A. Azzam, N. M. Bashara, J. Opt. Soc. Am. 61, 600 (1971).
    [CrossRef]
  2. R. M. A. Azzam, N. M. Bashara, J. Opt. Soc. Am. 61, 1118 (1971).
    [CrossRef]
  3. D. E. Aspnes, J. Opt. Soc. Am. 61, 1077 (1970) and references therein.
    [CrossRef]
  4. F. L. McCrackin, J. Opt. Soc. Am. 60, 57 (1970).
    [CrossRef]
  5. J. A. Johnson, N. M. Bashara, J. Opt. Soc. Am. 60, 221 (1970) and references therein.
    [CrossRef]
  6. D. G. Schueler, Surf. Sci. 16, 104 (1969).
    [CrossRef]
  7. W. G. Oldham, J. Opt. Soc. Am. 57, 617 (1966).
    [CrossRef]
  8. W. H. Hunter, J. Opt. Soc. Am. 63, 951 (1973).
    [CrossRef]
  9. J. R. Zeidler, R. B. Kohles, N. M. Bashara, Appl. Opt. 13, 1115 (1974).
    [CrossRef] [PubMed]
  10. R. H. Muller, Surf. Sci. 16, 14 (1969).
    [CrossRef]
  11. W. A. Shurcliff, Polarized Light (Harvard U.P., Cambridge, 1962).
  12. Assume that ψ1 = ψ3 and Δ1 = Δ3 or ψ2 = ψ4 and Δ2 = Δ4.

1974 (1)

1973 (1)

1971 (2)

1970 (3)

1969 (2)

D. G. Schueler, Surf. Sci. 16, 104 (1969).
[CrossRef]

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

1966 (1)

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Figures (1)

Fig. 1
Fig. 1

The error in the computed compensator retardation, as a function of the Δ of the sample, which occurs when the divided circle calibration constants for the polarizer, compensator, and analyzer are assumed to be zero when in fact they are approximately −0.33, −0.26, and −0.55, respectively.

Tables (2)

Tables Icon

Table I Divided-Circle Calibration Constants from Averaged Measurements on Gold, Silver, and Silicon at Angles-of-Incidence of 55°, 60°, 65°, and 70°; Δ varied between 17° and 179°

Tables Icon

Table II Divided-Circle Calibration Constants from Averaged Measurements on Two Specimens of Silicon at Angles-of-lncidence of 57.5°, 60.0°, 62.5°, and 65.0°; Δ Varied Between 160° and 179°

Equations (27)

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Res A ± = t 1 c sin 2 ψ sin Δ + 2 sin 2 ψ cos Δ δ C - 2 δ A ,
Res A + = A 2 + A 4 - π , Res A - = A 1 + A 3 .
( Res A ± ± t 1 c ± sin 2 ψ sin Δ ) / 2.0
T c = [ 1 0 0 ρ c ] ,
ρ c = ρ c exp ( - j δ c ) ,
ρ c = ρ c cos δ c - j ρ c sin δ c .
ρ c = ρ c 0 + δ ρ c
δ ρ c = t 1 c + j t 2 c ,
ρ c 0 = - j .
ρ c = t 1 c - j ( 1 - t 2 c ) ;
t 1 c = ρ c cos δ c , t 2 c = ρ c ( 1.0 - sin δ c ) .
ρ c = 1.0 / [ - tan ( p ) tan ( p ) ] 1 / 2 ,
cos δ c = sin ( p - p ) sin ( A + A ) + cos 2 C sin ( p + p ) sin ( A - A ) 2 ρ c sin 2 C cos p cos p sin ( A - A ) ,
Res 1 P = P 1 + P 2 + P 3 + P 4 - 360.0 = - 4 δ P + 4 δ C - 4 t 1 p .
δ P = δ C - ¼ Res 1 P .
δ P = δ C - ¼ Res 1 P av ,
Δ Z A = ( P 1 + P 3 ) = - ( P 2 + P 4 ) ,
Δ Z A ± = Δ 0 ± ( 2 t 1 p + 2 δ P - 2 δ C ) ,
δ P = δ C ± ( Δ Z A ± - Δ 0 ) / 2.0 ,
ρ c i = f ( p , c , a ) ψ = f ( p , c , α ) ,
δ c i = f ( p , c , a ) Δ = f ( p , c , a ) ,
f ( ρ c ) = i = 1 n - 1 j = i n ρ c i - ρ c j ,
f ( δ c ) = i = 1 n - 1 j = i n δ c i - δ c j .
R 2 = f 2 ( ρ c ) + f 2 ( δ c )
f ( ψ ) = i = 1 n ψ i + - ψ i - ,
f ( Δ ) = i = 1 n Δ i + - Δ i - ,
R 2 = f 2 ( ρ c + ) + f 2 ( δ c + ) + f 2 ( ρ c - ) + f 2 ( δ c - ) + f 2 ( ψ ) + f 2 ( Δ )

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