Abstract

The refractive index n(λ) and the extinction coefficient k(λ) of a TiO2 film prepared by electron-beam evaporation are determined in the spectral region 1.5–5.5 eV. The transmission spectrum of the TiO2 film on a vitreous silica specimen is inverted to get the k(λ) of TiO2 in its interband transition region. Above 3.5 eV, k(λ) is used to get the coefficients of the quantum mechanically derived dispersion relation of an amorphous TiO2. These coefficients and n are used to determine n(λ). The modeling procedure is applied to spectroscopic ellipsometry data of a TiO2 film on a c-Si specimen, and the void distribution of the film is revealed. With spectroscopic ellipsometry data above the fundamental band gap, valuable information about surface roughness is obtained. The effective thickness of this rough surface layer is confirmed by an atomic force microscopy measurement.

© 1996 Optical Society of America

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References

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  1. H. A. Macleod, Thin-Film Optical Filters (Hilger, Bristol, 1986) 391–393.
  2. E. Pelletier, “Methods for determining optical parameters of thin films,” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, Toronto, 1991), Chap. 3.
  3. J. M. Bennett, E. Pelletier, G. Albrand, J. P. Borgogno, B. Lazarides, C. K. Carniglia, R. A. Schmell, T. H. Allen, T. Tuttle-Hart, K. H. Guenther, A. Saxer, “Comparison of the properties of titanium dioxide films prepared by various techniques,” Appl. Opt. 28, 3303–3317 (1989).
    [CrossRef] [PubMed]
  4. J. P. Borgogno, B. Lazarides, E. Pelletier, “Automatic determination of the optical constants of inhomogeneous films,” Appl. Opt. 21, 4020–4029 (1982).
    [CrossRef] [PubMed]
  5. F. Abeles, “Methods for determining optical parameters of thin films,” in Progress in Optics II, E. Wolf, ed. (North-Holland, Amsterdam, 1963), chap. 7.
    [CrossRef]
  6. J. E. Nestell, R. W. Christy, “Derivation of optical constants of metals from thin-film measurements at oblique incidence,” Appl. Opt. 11, 643–651 (1972).
    [CrossRef] [PubMed]
  7. M. Malin, K. Vedam, “Generalized ellipsometric method for the determination of all the optical constants of the system: optically absorbing film on an absorbing substrate,” Surf. Sci. 56, 49–63 (1976).
    [CrossRef]
  8. J. Joseph, A. Gagnaire, “Ellipsometric study of anodic oxide growth: application to the titanium oxide film,” Thin Solid Films 103, 257–265 (1983).
    [CrossRef]
  9. A. R. Forouhi, I. Bloomer, “Calculation of Optical Constants, n and k, in the Interband Region,” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, Toronto1991), chap. 7.
  10. S. Y. Kim, J. H. Shin, “Fabrication of a spectroscopic ellipsometer and characterization of optical thin films,” Proceedings of Seventh Optics and Quantum Electronics Workshop (Korean Optical Society, Yong Pyung, 1990), pp. 45–56.
  11. S. Y. Kim, K. Vedam, “Simultaneous determination of dispersion relation and depth profile of thorium fluoride thin film by spectroscopic ellipsometry,” Thin Solid Films 166, 325–334 (1988); S. Y. Kim, K. Vedam, “Simultaneous determination of refractive index, its dispersion and depth-profile of magnesium oxide thin film by spectroscopic ellipsometry,” Appl. Opt. 28, 2691–2694 (1989).
    [CrossRef] [PubMed]
  12. W. L. Wolfe, “Properties of optical materials,” in Handbook of Optics, W. G. Driscoll, ed. (McGraw-Hill, New York1978), Chap. 7.
  13. D. E. Aspnes, “Optical characterization by ellipsometry—a perspective,” J. Phys. C 10, 3–12 (1983).

1989 (1)

1988 (1)

S. Y. Kim, K. Vedam, “Simultaneous determination of dispersion relation and depth profile of thorium fluoride thin film by spectroscopic ellipsometry,” Thin Solid Films 166, 325–334 (1988); S. Y. Kim, K. Vedam, “Simultaneous determination of refractive index, its dispersion and depth-profile of magnesium oxide thin film by spectroscopic ellipsometry,” Appl. Opt. 28, 2691–2694 (1989).
[CrossRef] [PubMed]

1983 (2)

D. E. Aspnes, “Optical characterization by ellipsometry—a perspective,” J. Phys. C 10, 3–12 (1983).

J. Joseph, A. Gagnaire, “Ellipsometric study of anodic oxide growth: application to the titanium oxide film,” Thin Solid Films 103, 257–265 (1983).
[CrossRef]

1982 (1)

1976 (1)

M. Malin, K. Vedam, “Generalized ellipsometric method for the determination of all the optical constants of the system: optically absorbing film on an absorbing substrate,” Surf. Sci. 56, 49–63 (1976).
[CrossRef]

1972 (1)

Abeles, F.

F. Abeles, “Methods for determining optical parameters of thin films,” in Progress in Optics II, E. Wolf, ed. (North-Holland, Amsterdam, 1963), chap. 7.
[CrossRef]

Albrand, G.

Allen, T. H.

Aspnes, D. E.

D. E. Aspnes, “Optical characterization by ellipsometry—a perspective,” J. Phys. C 10, 3–12 (1983).

Bennett, J. M.

Bloomer, I.

A. R. Forouhi, I. Bloomer, “Calculation of Optical Constants, n and k, in the Interband Region,” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, Toronto1991), chap. 7.

Borgogno, J. P.

Carniglia, C. K.

Christy, R. W.

Forouhi, A. R.

A. R. Forouhi, I. Bloomer, “Calculation of Optical Constants, n and k, in the Interband Region,” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, Toronto1991), chap. 7.

Gagnaire, A.

J. Joseph, A. Gagnaire, “Ellipsometric study of anodic oxide growth: application to the titanium oxide film,” Thin Solid Films 103, 257–265 (1983).
[CrossRef]

Guenther, K. H.

Joseph, J.

J. Joseph, A. Gagnaire, “Ellipsometric study of anodic oxide growth: application to the titanium oxide film,” Thin Solid Films 103, 257–265 (1983).
[CrossRef]

Kim, S. Y.

S. Y. Kim, K. Vedam, “Simultaneous determination of dispersion relation and depth profile of thorium fluoride thin film by spectroscopic ellipsometry,” Thin Solid Films 166, 325–334 (1988); S. Y. Kim, K. Vedam, “Simultaneous determination of refractive index, its dispersion and depth-profile of magnesium oxide thin film by spectroscopic ellipsometry,” Appl. Opt. 28, 2691–2694 (1989).
[CrossRef] [PubMed]

S. Y. Kim, J. H. Shin, “Fabrication of a spectroscopic ellipsometer and characterization of optical thin films,” Proceedings of Seventh Optics and Quantum Electronics Workshop (Korean Optical Society, Yong Pyung, 1990), pp. 45–56.

Lazarides, B.

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (Hilger, Bristol, 1986) 391–393.

Malin, M.

M. Malin, K. Vedam, “Generalized ellipsometric method for the determination of all the optical constants of the system: optically absorbing film on an absorbing substrate,” Surf. Sci. 56, 49–63 (1976).
[CrossRef]

Nestell, J. E.

Pelletier, E.

Saxer, A.

Schmell, R. A.

Shin, J. H.

S. Y. Kim, J. H. Shin, “Fabrication of a spectroscopic ellipsometer and characterization of optical thin films,” Proceedings of Seventh Optics and Quantum Electronics Workshop (Korean Optical Society, Yong Pyung, 1990), pp. 45–56.

Tuttle-Hart, T.

Vedam, K.

S. Y. Kim, K. Vedam, “Simultaneous determination of dispersion relation and depth profile of thorium fluoride thin film by spectroscopic ellipsometry,” Thin Solid Films 166, 325–334 (1988); S. Y. Kim, K. Vedam, “Simultaneous determination of refractive index, its dispersion and depth-profile of magnesium oxide thin film by spectroscopic ellipsometry,” Appl. Opt. 28, 2691–2694 (1989).
[CrossRef] [PubMed]

M. Malin, K. Vedam, “Generalized ellipsometric method for the determination of all the optical constants of the system: optically absorbing film on an absorbing substrate,” Surf. Sci. 56, 49–63 (1976).
[CrossRef]

Wolfe, W. L.

W. L. Wolfe, “Properties of optical materials,” in Handbook of Optics, W. G. Driscoll, ed. (McGraw-Hill, New York1978), Chap. 7.

Appl. Opt. (3)

J. Phys. C (1)

D. E. Aspnes, “Optical characterization by ellipsometry—a perspective,” J. Phys. C 10, 3–12 (1983).

Surf. Sci. (1)

M. Malin, K. Vedam, “Generalized ellipsometric method for the determination of all the optical constants of the system: optically absorbing film on an absorbing substrate,” Surf. Sci. 56, 49–63 (1976).
[CrossRef]

Thin Solid Films (2)

J. Joseph, A. Gagnaire, “Ellipsometric study of anodic oxide growth: application to the titanium oxide film,” Thin Solid Films 103, 257–265 (1983).
[CrossRef]

S. Y. Kim, K. Vedam, “Simultaneous determination of dispersion relation and depth profile of thorium fluoride thin film by spectroscopic ellipsometry,” Thin Solid Films 166, 325–334 (1988); S. Y. Kim, K. Vedam, “Simultaneous determination of refractive index, its dispersion and depth-profile of magnesium oxide thin film by spectroscopic ellipsometry,” Appl. Opt. 28, 2691–2694 (1989).
[CrossRef] [PubMed]

Other (6)

W. L. Wolfe, “Properties of optical materials,” in Handbook of Optics, W. G. Driscoll, ed. (McGraw-Hill, New York1978), Chap. 7.

H. A. Macleod, Thin-Film Optical Filters (Hilger, Bristol, 1986) 391–393.

E. Pelletier, “Methods for determining optical parameters of thin films,” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, Toronto, 1991), Chap. 3.

F. Abeles, “Methods for determining optical parameters of thin films,” in Progress in Optics II, E. Wolf, ed. (North-Holland, Amsterdam, 1963), chap. 7.
[CrossRef]

A. R. Forouhi, I. Bloomer, “Calculation of Optical Constants, n and k, in the Interband Region,” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, Toronto1991), chap. 7.

S. Y. Kim, J. H. Shin, “Fabrication of a spectroscopic ellipsometer and characterization of optical thin films,” Proceedings of Seventh Optics and Quantum Electronics Workshop (Korean Optical Society, Yong Pyung, 1990), pp. 45–56.

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Figures (4)

Fig. 1
Fig. 1

Transmission spectra of the bare vitreous silica substrate (circle) and the sample with electron-beam-evaporated TiO2 film on vitreous silica (solid curve).

Fig. 2
Fig. 2

Diagrams showing quantities used in calculations of the optical constants of TiO2 film. r 1, r 2, and r 3 are the Fresnel reflection coefficients at the interfaces air–film, film–substrate, and substrate–air, respectively, and t 1 and t 2 are the Fresnel transmission coefficients at the interfaces air–film and film–substrate, respectively.

Fig. 3
Fig. 3

Spectra of the refractive index n(λ) and the extinction coefficient k(λ) of the electron-beam-evaporated TiO2 film (solid curves) and those of void-free TiO2 film (open circles, see text). The refractive index of anatase (dashed curve) and rutile (dotted curve) are also shown for comparison.

Fig. 4
Fig. 4

Spectroscopic ellipsometry constants Δ and ψ of the electron-beam-evaporated TiO2 film on c-Si substrate (open circles) and the best-fit spectra with (solid curves) and without (dashed curves) surface roughness. The best-fit model parameters are summarized in Tables 1 and 2.

Tables (2)

Tables Icon

Table 1 Coefficients of Eqs. (4) and (5) for an Electron-Beam Grown TiO2 Film on a Vitreous Silica Substrate a

Tables Icon

Table 2 Best-Fit Model Parameters of the Electron-Beam-Evaporated TiO2 Thin Film on c-Si Determined by Spectroscopic Ellipsometry a

Equations (7)

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T = n 0 | E t | 2 ( 1 r 3 2 ) ( 1 | r 2 r 3 | 2 ) ,
E t = t 1 t 2 exp ( i δ ) 1 + r 1 r 2 exp ( 2 i δ ) ,
k ( λ ) = λ 4 π d { ln ( T / n 0 ) + ln ( 1 | r 2 r 3 | 2 ) / ( 1 r 3 2 ) + ln | [ 1 + r 1 r 2 exp ( 2 i δ ) ] / t 1 t 2 | 2 } .
k ( E ) = A ( E E g ) 2 E 2 B E + C .
n ( E ) = n + B E + C E 2 B E + C ,
B = A ( B 2 + 2 E g B 2 E g 2 + 2 C ) ( 4 C B 2 ) 1 / 2 ,
C = A [ B ( E g 2 + C ) 4 E g C ] ( 4 C B 2 ) 1 / 2 .

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