Abstract

The multiple-angle-of-incidence ellipsometric study of polycrystalline Si deposited on oxidized single-crystal Si is presented. The complex index of refraction of polycrystalline Si, 3.936 + i.040 at 632.8 nm, and the film thicknesses are obtained with high precision for the optimum thicknesses of a SiO2 layer predicted numerically.

© 1985 Optical Society of America

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References

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  1. E. A. Irene, D. W. Dong, “Ellipsometry measurements of poly-crystalline silicon films,”J. Electrochem. Soc. 129, 1347–1353 (1982).
    [CrossRef]
  2. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  3. J. Humlíček, “Sensitivity extrema in multiple-angle ellipsometry,” J. Opt. Soc. Am. A 2, 713–722 (1985).
    [CrossRef]
  4. D. E. Aspnes, A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 905–1009 (1983).
    [CrossRef]
  5. E. Taft, L. Cordes, “Optical evidence for silicon–silicon oxide interlayer,”J. Electrochem. Soc. 126, 131–134 (1979).
    [CrossRef]
  6. J. Humlíček, “Evaluation of derivatives of reflectance and transmittance by stratified structures and solution of the reverse problem of ellipsometry,” Opt. Acta 30, 97–105 (1983).
    [CrossRef]
  7. W. T. Eadie, E. Dryard, F. E. James, M. Roos, B. Sadoulet, Statistical Methods in Experimental Physics (North-Holland, Amsterdam, 1971).

1985 (1)

1983 (2)

D. E. Aspnes, A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 905–1009 (1983).
[CrossRef]

J. Humlíček, “Evaluation of derivatives of reflectance and transmittance by stratified structures and solution of the reverse problem of ellipsometry,” Opt. Acta 30, 97–105 (1983).
[CrossRef]

1982 (1)

E. A. Irene, D. W. Dong, “Ellipsometry measurements of poly-crystalline silicon films,”J. Electrochem. Soc. 129, 1347–1353 (1982).
[CrossRef]

1979 (1)

E. Taft, L. Cordes, “Optical evidence for silicon–silicon oxide interlayer,”J. Electrochem. Soc. 126, 131–134 (1979).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 905–1009 (1983).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Cordes, L.

E. Taft, L. Cordes, “Optical evidence for silicon–silicon oxide interlayer,”J. Electrochem. Soc. 126, 131–134 (1979).
[CrossRef]

Dong, D. W.

E. A. Irene, D. W. Dong, “Ellipsometry measurements of poly-crystalline silicon films,”J. Electrochem. Soc. 129, 1347–1353 (1982).
[CrossRef]

Dryard, E.

W. T. Eadie, E. Dryard, F. E. James, M. Roos, B. Sadoulet, Statistical Methods in Experimental Physics (North-Holland, Amsterdam, 1971).

Eadie, W. T.

W. T. Eadie, E. Dryard, F. E. James, M. Roos, B. Sadoulet, Statistical Methods in Experimental Physics (North-Holland, Amsterdam, 1971).

Humlícek, J.

J. Humlíček, “Sensitivity extrema in multiple-angle ellipsometry,” J. Opt. Soc. Am. A 2, 713–722 (1985).
[CrossRef]

J. Humlíček, “Evaluation of derivatives of reflectance and transmittance by stratified structures and solution of the reverse problem of ellipsometry,” Opt. Acta 30, 97–105 (1983).
[CrossRef]

Irene, E. A.

E. A. Irene, D. W. Dong, “Ellipsometry measurements of poly-crystalline silicon films,”J. Electrochem. Soc. 129, 1347–1353 (1982).
[CrossRef]

James, F. E.

W. T. Eadie, E. Dryard, F. E. James, M. Roos, B. Sadoulet, Statistical Methods in Experimental Physics (North-Holland, Amsterdam, 1971).

Roos, M.

W. T. Eadie, E. Dryard, F. E. James, M. Roos, B. Sadoulet, Statistical Methods in Experimental Physics (North-Holland, Amsterdam, 1971).

Sadoulet, B.

W. T. Eadie, E. Dryard, F. E. James, M. Roos, B. Sadoulet, Statistical Methods in Experimental Physics (North-Holland, Amsterdam, 1971).

Studna, A. A.

D. E. Aspnes, A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 905–1009 (1983).
[CrossRef]

Taft, E.

E. Taft, L. Cordes, “Optical evidence for silicon–silicon oxide interlayer,”J. Electrochem. Soc. 126, 131–134 (1979).
[CrossRef]

J. Electrochem. Soc. (2)

E. Taft, L. Cordes, “Optical evidence for silicon–silicon oxide interlayer,”J. Electrochem. Soc. 126, 131–134 (1979).
[CrossRef]

E. A. Irene, D. W. Dong, “Ellipsometry measurements of poly-crystalline silicon films,”J. Electrochem. Soc. 129, 1347–1353 (1982).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

J. Humlíček, “Evaluation of derivatives of reflectance and transmittance by stratified structures and solution of the reverse problem of ellipsometry,” Opt. Acta 30, 97–105 (1983).
[CrossRef]

Phys. Rev. B (1)

D. E. Aspnes, A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 905–1009 (1983).
[CrossRef]

Other (2)

W. T. Eadie, E. Dryard, F. E. James, M. Roos, B. Sadoulet, Statistical Methods in Experimental Physics (North-Holland, Amsterdam, 1971).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the studied system.

Fig. 2
Fig. 2

Prediction of the parameter errors as functions of the thickness d1 of SiO2 layer for different thicknesses d2 of poly-Si film: ——, 100 nm;– – –, 120 nm;–·– ·–, 140 nm;–-–-–, 160 nm.

Fig. 3
Fig. 3

Resulting parameters and 68% confidence intervals for samples of different SiO2 thickness d1. The refractive index of SiO2 fixed at n = 1.46 (circles) and determined (crosses). One half of the actual error bars of the leftmost crosses are drawn.

Tables (3)

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Table 1 Retrieved Parameters

Tables Icon

Table 2 Errors Resulting from Incorrect Fixing of the Parameters

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Table 3 Test of the Linear Approximation

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

ψ k = ψ ( N 0 , d 1 , N 1 , d 2 , N 2 , d 3 , N 3 , n a , λ , φ k ) , Δ k = Δ ( N 0 , d 1 , N 1 , d 2 , N 2 , d 3 , N 3 , n a , λ , φ k ) ,
S = k = 1 N [ ( ψ e k - ψ k δ ψ k ) 2 + ( Δ e k - Δ k δ Δ k ) 2 ] ,
N 2 = 3.936 + i 0.040.
q j - q 0 j = ρ j L ( D j j D L L ) 1 / 2 ( q - q 0 ) ,             j = 1 , , L - 1.
S l ( q j - q 0 j ) = S 0 + H j j ( q j + q 0 j ) 2 ,
α = ( S - S l ) / S ,

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