Abstract

We present a numerical method for spectroscopic ellipsometry of thick transparent films. When an analytical expression for the dispersion of the refractive index (which contains several unknown coefficients) is assumed, the procedure is based on fitting the coefficients at a fixed thickness. Then the thickness is varied within a range (according to its approximate value). The final result given by our method is as follows: The sample thickness is considered to be the one that gives the best fitting. The refractive index is defined by the coefficients obtained for this thickness.

© 1998 Optical Society of America

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References

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  1. S. Guo, G. Gustafsson, O. J. Hagel, H. Arwin, “Determination of refractive index and thickness of thick transparent films by variable-angle spectroscopic ellipsometry: application to beczocyclobutene films,” Appl. Opt. 35, 1693–1699 (1996).
    [CrossRef] [PubMed]
  2. S. Bosch, F. Monzonís, E. Masetti, “Ellipsometric methods for absorbing layers: a modified downhill simplex algorithm,” Thin Solid Films 289, 54–58 (1996).
    [CrossRef]
  3. W. H. Press, S. A. Teukolsky, W. T. Wetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1992), Chaps. 10 and 15.

1996 (2)

Arwin, H.

Bosch, S.

S. Bosch, F. Monzonís, E. Masetti, “Ellipsometric methods for absorbing layers: a modified downhill simplex algorithm,” Thin Solid Films 289, 54–58 (1996).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Wetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1992), Chaps. 10 and 15.

Guo, S.

Gustafsson, G.

Hagel, O. J.

Masetti, E.

S. Bosch, F. Monzonís, E. Masetti, “Ellipsometric methods for absorbing layers: a modified downhill simplex algorithm,” Thin Solid Films 289, 54–58 (1996).
[CrossRef]

Monzonís, F.

S. Bosch, F. Monzonís, E. Masetti, “Ellipsometric methods for absorbing layers: a modified downhill simplex algorithm,” Thin Solid Films 289, 54–58 (1996).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Wetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1992), Chaps. 10 and 15.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Wetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1992), Chaps. 10 and 15.

Wetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Wetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1992), Chaps. 10 and 15.

Appl. Opt. (1)

Thin Solid Films (1)

S. Bosch, F. Monzonís, E. Masetti, “Ellipsometric methods for absorbing layers: a modified downhill simplex algorithm,” Thin Solid Films 289, 54–58 (1996).
[CrossRef]

Other (1)

W. H. Press, S. A. Teukolsky, W. T. Wetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, England, 1992), Chaps. 10 and 15.

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Figures (2)

Fig. 1
Fig. 1

Refractive-index values and best fittings to the Cauchy model corresponding to assumed thicknesses, 9.0 and 9.05 μm, for the data with σ = 1.0° noise added.

Fig. 2
Fig. 2

Plots of χ2 versus layer thickness for three data sets corresponding to noise levels σ = 0°, 0.3°, 1.0°.

Equations (2)

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n λ = A + B / λ 2 + C / λ 4
d = m λ 2 n 2 - sin 2   ϕ   m = 0 ,   1 ,   2

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