Abstract

Amorphous and nanocrystalline TiO2 thin films coated on a vitreous silica substrate by a solgel dip coating method are investigated for optical properties by spectroscopic ellipsometry (SE) together with transmission spectroscopy. A method of analysis of SE data to determine the degree of inhomogeneity of TiO2 films has also been presented. Instead of the refractive index, the volume fraction of void has been assumed to vary along the thickness of the films and an excellent agreement between the experimental and calculated data of SE below the fundamental band gap has been obtained. The transmission spectrum of these samples is inverted to obtain the extinction coefficient k spectrum in the wavelength range of 300–1600 nm by using the refractive indices and parameters of structure determined by SE. The nonzero extinction coefficient below the fundamental band-gap energy (3.2 eV) has been obtained for the nanocrystalline TiO2 and shows the presence of optical scattering in the film.

© 1998 Optical Society of America

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References

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  1. M. Gratzel, “Nanocrystalline electronic junctions,” in Semiconductor Nanoclusters–Physical, Chemical and Catalytic Aspects, P. V. Kamat, D. Meisel, eds. (Elsevier, The Netherlands, 1997), pp. 353–461.
    [CrossRef]
  2. 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, 3303–3316 (1989).
    [CrossRef] [PubMed]
  3. G. Parjadis de Lariviere, J. M. Frigerio, J. Rivory, F. Abeles, “Estimate of the degree of inhomogeneity of the refractive index of dielectric films from spectroscopic ellipsometry,” Appl. Opt. 31, 6059–6061 (1992).
  4. J. P. Borgogno, F. Flory, P. Roche, B. Schmitt, G. Albrand, E. Pelletier, H. A. Macleod, “Refractive index and inhomogeneity of thin films,” Appl. Opt. 23, 3567–3570 (1984).
    [CrossRef] [PubMed]
  5. 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, Toronto, 1991), Chap. 7.
  6. S. Y. Kim, “Simultaneous determination of refractive index, extinction coefficient, and void distribution of titanium dioxide thin film by optical methods,” Appl. Opt. 35, 6703–6707 (1996).
    [CrossRef] [PubMed]
  7. M. M. Rahman, T. Miki, K. M. Krishna, T. Soga, K. Igarashi, S. Tanemura, M. Umeno, “Structural and optical characterization of PbxTi1-xO2 film prepared by solgel method,” Mater. Sci. Eng. B 41, 67–71 (1996).
    [CrossRef]
  8. C. K. Carniglia, “Ellipsometric calculations for nonabsorbing thin films with linear refractive-index gradients,” J. Opt. Soc. Am. A 7, 848–856 (1990).
    [CrossRef]
  9. D. E. Aspnes, J. B. Theeten, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phy. Rev. B 20, 3292–3302 (1979).
    [CrossRef]
  10. T. Gerfin, M. Gratzel, “Optical properties of tin-doped indium oxide determined by spectroscopic ellipsometry,” J. Appl. Phys. 79, 1722–1729 (1996).
    [CrossRef]
  11. K. A. Vorotilov, E. V. Orlova, V. I. Petrovsky, “Solgel TiO2 films on silicon substrates,” Thin Solid Films 207, 180–184 (1992).
    [CrossRef]
  12. T. M. Susan, J. Chen, K. Vedam, R. E. Newnham, “In situ annealing studies of solgel ferroelectric thin films by spectroscopic ellipsometry,” J. Am. Ceram. Soc. 78, 1907–1913 (1995).
    [CrossRef]
  13. Y. Mishima, M. Takei, T. Uematsu, N. Matsumoto, T. Kakehi, U. Wakino, M. Okabe, “Polycrystalline silicon formed by ultrahigh-vacuum sputtering system,” J. Appl. Phys. 78, 217–223 (1995).
    [CrossRef]
  14. H. A. Macleod, Thin-Film Optical Filters (Adam Hilger, Bristol, UK, 1986).
    [CrossRef]
  15. M. H. Suhail, G. M. Rao, S. Mohan, “dc reactive magnetron sputtering of titanium-structural and optical characterization of TiO2 films,” J. Appl. Phys. 71, 1421–1427 (1992).
    [CrossRef]

1996 (3)

M. M. Rahman, T. Miki, K. M. Krishna, T. Soga, K. Igarashi, S. Tanemura, M. Umeno, “Structural and optical characterization of PbxTi1-xO2 film prepared by solgel method,” Mater. Sci. Eng. B 41, 67–71 (1996).
[CrossRef]

T. Gerfin, M. Gratzel, “Optical properties of tin-doped indium oxide determined by spectroscopic ellipsometry,” J. Appl. Phys. 79, 1722–1729 (1996).
[CrossRef]

S. Y. Kim, “Simultaneous determination of refractive index, extinction coefficient, and void distribution of titanium dioxide thin film by optical methods,” Appl. Opt. 35, 6703–6707 (1996).
[CrossRef] [PubMed]

1995 (2)

T. M. Susan, J. Chen, K. Vedam, R. E. Newnham, “In situ annealing studies of solgel ferroelectric thin films by spectroscopic ellipsometry,” J. Am. Ceram. Soc. 78, 1907–1913 (1995).
[CrossRef]

Y. Mishima, M. Takei, T. Uematsu, N. Matsumoto, T. Kakehi, U. Wakino, M. Okabe, “Polycrystalline silicon formed by ultrahigh-vacuum sputtering system,” J. Appl. Phys. 78, 217–223 (1995).
[CrossRef]

1992 (3)

M. H. Suhail, G. M. Rao, S. Mohan, “dc reactive magnetron sputtering of titanium-structural and optical characterization of TiO2 films,” J. Appl. Phys. 71, 1421–1427 (1992).
[CrossRef]

K. A. Vorotilov, E. V. Orlova, V. I. Petrovsky, “Solgel TiO2 films on silicon substrates,” Thin Solid Films 207, 180–184 (1992).
[CrossRef]

G. Parjadis de Lariviere, J. M. Frigerio, J. Rivory, F. Abeles, “Estimate of the degree of inhomogeneity of the refractive index of dielectric films from spectroscopic ellipsometry,” Appl. Opt. 31, 6059–6061 (1992).

1990 (1)

1989 (1)

1984 (1)

1979 (1)

D. E. Aspnes, J. B. Theeten, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phy. Rev. B 20, 3292–3302 (1979).
[CrossRef]

Abeles, F.

G. Parjadis de Lariviere, J. M. Frigerio, J. Rivory, F. Abeles, “Estimate of the degree of inhomogeneity of the refractive index of dielectric films from spectroscopic ellipsometry,” Appl. Opt. 31, 6059–6061 (1992).

Albrand, G.

Allen, T. H.

Aspnes, D. E.

D. E. Aspnes, J. B. Theeten, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phy. Rev. B 20, 3292–3302 (1979).
[CrossRef]

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, Toronto, 1991), Chap. 7.

Borgogno, J. P.

Carniglia, C. K.

Chen, J.

T. M. Susan, J. Chen, K. Vedam, R. E. Newnham, “In situ annealing studies of solgel ferroelectric thin films by spectroscopic ellipsometry,” J. Am. Ceram. Soc. 78, 1907–1913 (1995).
[CrossRef]

Flory, F.

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, Toronto, 1991), Chap. 7.

Frigerio, J. M.

G. Parjadis de Lariviere, J. M. Frigerio, J. Rivory, F. Abeles, “Estimate of the degree of inhomogeneity of the refractive index of dielectric films from spectroscopic ellipsometry,” Appl. Opt. 31, 6059–6061 (1992).

Gerfin, T.

T. Gerfin, M. Gratzel, “Optical properties of tin-doped indium oxide determined by spectroscopic ellipsometry,” J. Appl. Phys. 79, 1722–1729 (1996).
[CrossRef]

Gratzel, M.

T. Gerfin, M. Gratzel, “Optical properties of tin-doped indium oxide determined by spectroscopic ellipsometry,” J. Appl. Phys. 79, 1722–1729 (1996).
[CrossRef]

M. Gratzel, “Nanocrystalline electronic junctions,” in Semiconductor Nanoclusters–Physical, Chemical and Catalytic Aspects, P. V. Kamat, D. Meisel, eds. (Elsevier, The Netherlands, 1997), pp. 353–461.
[CrossRef]

Guenther, K. H.

Igarashi, K.

M. M. Rahman, T. Miki, K. M. Krishna, T. Soga, K. Igarashi, S. Tanemura, M. Umeno, “Structural and optical characterization of PbxTi1-xO2 film prepared by solgel method,” Mater. Sci. Eng. B 41, 67–71 (1996).
[CrossRef]

Kakehi, T.

Y. Mishima, M. Takei, T. Uematsu, N. Matsumoto, T. Kakehi, U. Wakino, M. Okabe, “Polycrystalline silicon formed by ultrahigh-vacuum sputtering system,” J. Appl. Phys. 78, 217–223 (1995).
[CrossRef]

Kim, S. Y.

Krishna, K. M.

M. M. Rahman, T. Miki, K. M. Krishna, T. Soga, K. Igarashi, S. Tanemura, M. Umeno, “Structural and optical characterization of PbxTi1-xO2 film prepared by solgel method,” Mater. Sci. Eng. B 41, 67–71 (1996).
[CrossRef]

Lazarides, B.

Macleod, H. A.

Matsumoto, N.

Y. Mishima, M. Takei, T. Uematsu, N. Matsumoto, T. Kakehi, U. Wakino, M. Okabe, “Polycrystalline silicon formed by ultrahigh-vacuum sputtering system,” J. Appl. Phys. 78, 217–223 (1995).
[CrossRef]

Miki, T.

M. M. Rahman, T. Miki, K. M. Krishna, T. Soga, K. Igarashi, S. Tanemura, M. Umeno, “Structural and optical characterization of PbxTi1-xO2 film prepared by solgel method,” Mater. Sci. Eng. B 41, 67–71 (1996).
[CrossRef]

Mishima, Y.

Y. Mishima, M. Takei, T. Uematsu, N. Matsumoto, T. Kakehi, U. Wakino, M. Okabe, “Polycrystalline silicon formed by ultrahigh-vacuum sputtering system,” J. Appl. Phys. 78, 217–223 (1995).
[CrossRef]

Mohan, S.

M. H. Suhail, G. M. Rao, S. Mohan, “dc reactive magnetron sputtering of titanium-structural and optical characterization of TiO2 films,” J. Appl. Phys. 71, 1421–1427 (1992).
[CrossRef]

Newnham, R. E.

T. M. Susan, J. Chen, K. Vedam, R. E. Newnham, “In situ annealing studies of solgel ferroelectric thin films by spectroscopic ellipsometry,” J. Am. Ceram. Soc. 78, 1907–1913 (1995).
[CrossRef]

Okabe, M.

Y. Mishima, M. Takei, T. Uematsu, N. Matsumoto, T. Kakehi, U. Wakino, M. Okabe, “Polycrystalline silicon formed by ultrahigh-vacuum sputtering system,” J. Appl. Phys. 78, 217–223 (1995).
[CrossRef]

Orlova, E. V.

K. A. Vorotilov, E. V. Orlova, V. I. Petrovsky, “Solgel TiO2 films on silicon substrates,” Thin Solid Films 207, 180–184 (1992).
[CrossRef]

Parjadis de Lariviere, G.

G. Parjadis de Lariviere, J. M. Frigerio, J. Rivory, F. Abeles, “Estimate of the degree of inhomogeneity of the refractive index of dielectric films from spectroscopic ellipsometry,” Appl. Opt. 31, 6059–6061 (1992).

Pelletier, E.

Petrovsky, V. I.

K. A. Vorotilov, E. V. Orlova, V. I. Petrovsky, “Solgel TiO2 films on silicon substrates,” Thin Solid Films 207, 180–184 (1992).
[CrossRef]

Rahman, M. M.

M. M. Rahman, T. Miki, K. M. Krishna, T. Soga, K. Igarashi, S. Tanemura, M. Umeno, “Structural and optical characterization of PbxTi1-xO2 film prepared by solgel method,” Mater. Sci. Eng. B 41, 67–71 (1996).
[CrossRef]

Rao, G. M.

M. H. Suhail, G. M. Rao, S. Mohan, “dc reactive magnetron sputtering of titanium-structural and optical characterization of TiO2 films,” J. Appl. Phys. 71, 1421–1427 (1992).
[CrossRef]

Rivory, J.

G. Parjadis de Lariviere, J. M. Frigerio, J. Rivory, F. Abeles, “Estimate of the degree of inhomogeneity of the refractive index of dielectric films from spectroscopic ellipsometry,” Appl. Opt. 31, 6059–6061 (1992).

Roche, P.

Saxer, A.

Schmell, R. A.

Schmitt, B.

Soga, T.

M. M. Rahman, T. Miki, K. M. Krishna, T. Soga, K. Igarashi, S. Tanemura, M. Umeno, “Structural and optical characterization of PbxTi1-xO2 film prepared by solgel method,” Mater. Sci. Eng. B 41, 67–71 (1996).
[CrossRef]

Suhail, M. H.

M. H. Suhail, G. M. Rao, S. Mohan, “dc reactive magnetron sputtering of titanium-structural and optical characterization of TiO2 films,” J. Appl. Phys. 71, 1421–1427 (1992).
[CrossRef]

Susan, T. M.

T. M. Susan, J. Chen, K. Vedam, R. E. Newnham, “In situ annealing studies of solgel ferroelectric thin films by spectroscopic ellipsometry,” J. Am. Ceram. Soc. 78, 1907–1913 (1995).
[CrossRef]

Takei, M.

Y. Mishima, M. Takei, T. Uematsu, N. Matsumoto, T. Kakehi, U. Wakino, M. Okabe, “Polycrystalline silicon formed by ultrahigh-vacuum sputtering system,” J. Appl. Phys. 78, 217–223 (1995).
[CrossRef]

Tanemura, S.

M. M. Rahman, T. Miki, K. M. Krishna, T. Soga, K. Igarashi, S. Tanemura, M. Umeno, “Structural and optical characterization of PbxTi1-xO2 film prepared by solgel method,” Mater. Sci. Eng. B 41, 67–71 (1996).
[CrossRef]

Theeten, J. B.

D. E. Aspnes, J. B. Theeten, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phy. Rev. B 20, 3292–3302 (1979).
[CrossRef]

Tuttle-Hart, T.

Uematsu, T.

Y. Mishima, M. Takei, T. Uematsu, N. Matsumoto, T. Kakehi, U. Wakino, M. Okabe, “Polycrystalline silicon formed by ultrahigh-vacuum sputtering system,” J. Appl. Phys. 78, 217–223 (1995).
[CrossRef]

Umeno, M.

M. M. Rahman, T. Miki, K. M. Krishna, T. Soga, K. Igarashi, S. Tanemura, M. Umeno, “Structural and optical characterization of PbxTi1-xO2 film prepared by solgel method,” Mater. Sci. Eng. B 41, 67–71 (1996).
[CrossRef]

Vedam, K.

T. M. Susan, J. Chen, K. Vedam, R. E. Newnham, “In situ annealing studies of solgel ferroelectric thin films by spectroscopic ellipsometry,” J. Am. Ceram. Soc. 78, 1907–1913 (1995).
[CrossRef]

Vorotilov, K. A.

K. A. Vorotilov, E. V. Orlova, V. I. Petrovsky, “Solgel TiO2 films on silicon substrates,” Thin Solid Films 207, 180–184 (1992).
[CrossRef]

Wakino, U.

Y. Mishima, M. Takei, T. Uematsu, N. Matsumoto, T. Kakehi, U. Wakino, M. Okabe, “Polycrystalline silicon formed by ultrahigh-vacuum sputtering system,” J. Appl. Phys. 78, 217–223 (1995).
[CrossRef]

Appl. Opt. (4)

J. Am. Ceram. Soc. (1)

T. M. Susan, J. Chen, K. Vedam, R. E. Newnham, “In situ annealing studies of solgel ferroelectric thin films by spectroscopic ellipsometry,” J. Am. Ceram. Soc. 78, 1907–1913 (1995).
[CrossRef]

J. Appl. Phys. (3)

Y. Mishima, M. Takei, T. Uematsu, N. Matsumoto, T. Kakehi, U. Wakino, M. Okabe, “Polycrystalline silicon formed by ultrahigh-vacuum sputtering system,” J. Appl. Phys. 78, 217–223 (1995).
[CrossRef]

T. Gerfin, M. Gratzel, “Optical properties of tin-doped indium oxide determined by spectroscopic ellipsometry,” J. Appl. Phys. 79, 1722–1729 (1996).
[CrossRef]

M. H. Suhail, G. M. Rao, S. Mohan, “dc reactive magnetron sputtering of titanium-structural and optical characterization of TiO2 films,” J. Appl. Phys. 71, 1421–1427 (1992).
[CrossRef]

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

Mater. Sci. Eng. B (1)

M. M. Rahman, T. Miki, K. M. Krishna, T. Soga, K. Igarashi, S. Tanemura, M. Umeno, “Structural and optical characterization of PbxTi1-xO2 film prepared by solgel method,” Mater. Sci. Eng. B 41, 67–71 (1996).
[CrossRef]

Phy. Rev. B (1)

D. E. Aspnes, J. B. Theeten, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phy. Rev. B 20, 3292–3302 (1979).
[CrossRef]

Thin Solid Films (1)

K. A. Vorotilov, E. V. Orlova, V. I. Petrovsky, “Solgel TiO2 films on silicon substrates,” Thin Solid Films 207, 180–184 (1992).
[CrossRef]

Other (3)

H. A. Macleod, Thin-Film Optical Filters (Adam Hilger, Bristol, UK, 1986).
[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, Toronto, 1991), Chap. 7.

M. Gratzel, “Nanocrystalline electronic junctions,” in Semiconductor Nanoclusters–Physical, Chemical and Catalytic Aspects, P. V. Kamat, D. Meisel, eds. (Elsevier, The Netherlands, 1997), pp. 353–461.
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Typical refractive-index profile of an inhomogeneous film of thickness d on a nonabsorbing substrate with refractive index n 3 in a medium with refractive index n 0. The refractive index of the film varies from n 1 at the outer surface of the film to n 2 at the inner surface.

Fig. 2
Fig. 2

Calculated tan Ψ spectrum (solid curves) for films together with the tan Ψ s spectrum (dashed line) for the substrate with Δn/ varying from -15% to +15% in steps of 7.5% for an angle of incidence of 75°. The average refractive index of the film is assumed to be 2.3 and that of the substrate to be 1.5.

Fig. 3
Fig. 3

Calculated tan Ψ spectrum (solid curves) for films together with the tan Ψ s spectrum (dashed line) for the substrate, with the average refractive index varying from 1.7 to 2.5. The degree of inhomogeneity Δn/ for all the films is considered to be constant (-15%).

Fig. 4
Fig. 4

Schematic diagram of the film structure used in SE fitting.

Fig. 5
Fig. 5

Measured (solid circles and plus sign) and fitted (solid curves) cos Δ (top) and tan Ψ (bottom) spectra of Samples 1 and 2 together with the calculated data of the bare substrate (dashed lines).

Fig. 6
Fig. 6

Graphic determination of the high-frequency dielectric constant of the two samples.

Fig. 7
Fig. 7

Depth profile of the refractive indices at a 500-nm wavelength for the two samples.

Fig. 8
Fig. 8

Variation of the degree of inhomogeneity Δn/ with photon energy for both samples.

Fig. 9
Fig. 9

Measured (solid circles and plus sign) and calculated (solid curves) transmission spectra of both samples in the wavelength range of 300–1600 nm. The solid curves are obtained by using the extrapolated optical constants and thicknesses determined by SE. The dashed line shows the measured transmission spectrum of the bare substrate.

Fig. 10
Fig. 10

Refractive index n and extinction coefficient k spectra of Samples 1 (dotted curves) and 2 (solid curves).

Tables (1)

Tables Icon

Table 1 Best-Fit Model Parameters of the Solgel-Derived TiO2 Thin Films on Vitreous Silica Substrate Determined by Spectroscopic Ellipsometrya

Equations (12)

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

ρ = r p r s = | r p | | r s |   exp i δ p - δ s = tan   Ψ   exp i Δ .
tan   Ψ HW = n p 0 n p 2 - n p 1 n p 3 n p 0 n p 2 + n p 1 n p 3 n s 0 n s 2 - n s 1 n s 3 n s 0 n s 2 + n s 1 n s 3 ,
n si = n i 2 - n 0 2 sin 2   θ 0 1 / 2 , n pi = n i 2 / n i 2 - n 0 2 sin 2   θ 0 1 / 2 .
tan   Ψ HW = n p 0 - n p 3 n p 0 + n p 3 n s 0 - n s 3 n s 0 + n s 3 = tan   Ψ s ,
t = t 10 t 23 exp - i δ 1 + r 10 r 23 exp - i 2 δ ,
t 10 = 2 n 0 n 0 + n 1 ,     t 23 = 2 n 2 n 2 + n 3 ,   r 10 = n 0 - n 1 n 0 + n 1 ,   r 23 = n 2 - n 3 n 2 + n 3 .
δ = 2 π λ 0 d   n z d z .
T = n 1 n 3 n 0 n 2   tt * .
1 - f ν ε m - ε ε m + 2 ε + f ν 1 - ε 1 + 2 ε = 0 ,
ε = ε + ε s - ε ω t 2 ω t 2 - ω 2 + i Γ 0 ω ,
δ 2 = 1 2 N - P i N tan   Ψ i exp - tan   Ψ i cal 2 + cos   Δ i exp - cos   Δ i cal 2 ,
Ψ = T 1 - R = i T i 1 - R i ,

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