Abstract

An optical method to determine the nanostructure and the morphology of porous thin films is presented. This procedure is based on the response of a side-polished optical fiber with the film under study, when an adsorption-desorption cycle is carried out. Spectroscopic ellipsometry provides additional information about the optical properties and adsorption behavior of the film. Pore size distribution, anisotropy, and inhomogeneity of films can be determined by use of these two complementary techniques. To check the performances and suitability of the optical method, we have characterized a typical porous material: a TiO2 film deposited by evaporation. Water vapor has been used for the adsorption cycles. The well-known columnar structure of the evaporated TiO2 has been evidenced, and the relation between the nanostructure and the optical properties of the film is showed.

© 2002 Optical Society of America

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References

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  1. 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]
  2. J. S. Chen, S. Chao, J. S. Kao, G. R. Lai, W. H. Wang, “Substrate-dependent optical absorption characteristics of titanium dioxide thin films,” Appl. Opt. 36, 4403–4408 (1997).
    [CrossRef] [PubMed]
  3. B. A. Movchan, A. V. Demchishin, “Study of the structure and properties of thick vacuum condensates of nickel, titanium, tungsten, aluminium oxide and zirconium dioxide,” Phys. Met. Metallogr. (USSR) 28, 83–90 (1969).
  4. J. A. Thornton, “High rate thick film growth,” Annu. Rev. Mater. Sci. 7, 239–260 (1977).
    [CrossRef]
  5. R. Messier, A. P. Giri, R. A. Roy, “Revised structure zone model for thin film physical structure,” J. Vac. Sci. Technol. A 2, 500–503 (1984).
    [CrossRef]
  6. A. G. Dirks, H. J. Leamy, “Columnar nanostructure in vapor deposited thin films,” Thin Solid Films 45, 219–323 (1977).
    [CrossRef]
  7. P. Ramanlal, L. M. Sander, “Theory of ballistic aggregation,” Phys. Rev. Lett. 54, 1828–1831 (1985).
    [CrossRef] [PubMed]
  8. I. Hodgkinson, Q. H. Wu, J. Hazel, “Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide,” Appl. Opt. 37, 2653–2659 (1998).
    [CrossRef]
  9. F. Flory, D. Endelema, E. Pelletier, I. Hodgkinson, “Anisotropy in thin films: modeling and measurement of guided and nonguided optical properties: application to TiO2 films,” Appl. Opt. 32, 5649–5659 (1993).
    [CrossRef] [PubMed]
  10. I. Hodgkinson, J. Hazel, Q. H. Wu, “In situ measurement of principal refractive indices of thin films by two-angle ellipsometry,” Thin Solid Films 313–314, 368–372 (1998).
    [CrossRef]
  11. C. K. Carniglia, “Ellipsometric calculation for nonabsorbing thin films with linear refractive-index gradients,” J. Opt. Soc. Am. A 7, 848–856 (1990).
    [CrossRef]
  12. Md. Mosaddeq-ur-Rahman, G. Yu, K. M. Krishna, T. Soga, J. Watanabe, T. Jimbo, M. Umeno, “Determination of optical constants of solgel-derived inhomogeneous TiO2 films by spectroscopic ellipsometry and transmission spectroscopy,” Appl. Opt. 37, 691–697 (1998).
    [CrossRef]
  13. G. Parjadis de Lariviére, J. M. Frigerio, F. Bridou, J. Rivory, “Modelling of ellipsometric data of inhomogeneous TiO2 films,” Thin Solid Films 233–234, 458–462 (1993).
    [CrossRef]
  14. 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]
  15. A. Alvarez-Herrero, A. J. Fort, H. Guerrero, E. Bernabeu, “Ellipsometric characterization and influence of relative humidity on TiO2 layers optical properties,” Thin Solid Films 349, 212–219 (1999).
    [CrossRef]
  16. A. Álvarez-Herrero, R. L. Heredero, E. Bernabeu, D. Levy, “Adsorption of water on porous Vycor glass studied by ellipsometry,” Appl. Opt. 40, 527–532 (2001).
    [CrossRef]
  17. B. P. Pal, G. R. Chakravarty, “All-fiber wavelength selective components for optical communication,” Commun. Instr. 5, 181–208 (1997).
  18. S. J. Gregg, K. S. W. Sing, Adsorption, Surface Area and Porosity (Academic, New York, 1997).
  19. R. M. A. Azzam, N. N. Bashara, Ellipsometry and Polarized Light (North Holland, Amsterdam, 1977).
  20. R. W. Collins, D. E. Aspnes, E. A. Irene, “Proceedings of the Second International Conference on Spectroscopic Ellipsometry,” Thin Solid Films 313–314 (1998).
  21. V. A. Tolmachev, “Adsorption-ellipsometry method of studying the optical profile, thickness, and porosity of thin films,” J. Opt. Technol. 66, 596–607 (1999).
    [CrossRef]
  22. V. A. Tolmachev, “Determination of the porosity of uniform films by adsorption-ellipsometric method,” Opt. Spectrosc. 84, 584–588 (1998).
  23. P. K. Tien, “Light waves in thin films and integrated optics,” Appl. Opt. 10, 2395–2413 (1971).
    [CrossRef] [PubMed]
  24. D. E. Aspnes, A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975).
    [CrossRef]
  25. H. K. Pulker, Coatings on Glass (Elsevier, Amsterdam, 1999).
  26. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993).

2001 (1)

1999 (2)

A. Alvarez-Herrero, A. J. Fort, H. Guerrero, E. Bernabeu, “Ellipsometric characterization and influence of relative humidity on TiO2 layers optical properties,” Thin Solid Films 349, 212–219 (1999).
[CrossRef]

V. A. Tolmachev, “Adsorption-ellipsometry method of studying the optical profile, thickness, and porosity of thin films,” J. Opt. Technol. 66, 596–607 (1999).
[CrossRef]

1998 (5)

V. A. Tolmachev, “Determination of the porosity of uniform films by adsorption-ellipsometric method,” Opt. Spectrosc. 84, 584–588 (1998).

R. W. Collins, D. E. Aspnes, E. A. Irene, “Proceedings of the Second International Conference on Spectroscopic Ellipsometry,” Thin Solid Films 313–314 (1998).

I. Hodgkinson, J. Hazel, Q. H. Wu, “In situ measurement of principal refractive indices of thin films by two-angle ellipsometry,” Thin Solid Films 313–314, 368–372 (1998).
[CrossRef]

Md. Mosaddeq-ur-Rahman, G. Yu, K. M. Krishna, T. Soga, J. Watanabe, T. Jimbo, M. Umeno, “Determination of optical constants of solgel-derived inhomogeneous TiO2 films by spectroscopic ellipsometry and transmission spectroscopy,” Appl. Opt. 37, 691–697 (1998).
[CrossRef]

I. Hodgkinson, Q. H. Wu, J. Hazel, “Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide,” Appl. Opt. 37, 2653–2659 (1998).
[CrossRef]

1997 (2)

J. S. Chen, S. Chao, J. S. Kao, G. R. Lai, W. H. Wang, “Substrate-dependent optical absorption characteristics of titanium dioxide thin films,” Appl. Opt. 36, 4403–4408 (1997).
[CrossRef] [PubMed]

B. P. Pal, G. R. Chakravarty, “All-fiber wavelength selective components for optical communication,” Commun. Instr. 5, 181–208 (1997).

1996 (1)

1993 (2)

G. Parjadis de Lariviére, J. M. Frigerio, F. Bridou, J. Rivory, “Modelling of ellipsometric data of inhomogeneous TiO2 films,” Thin Solid Films 233–234, 458–462 (1993).
[CrossRef]

F. Flory, D. Endelema, E. Pelletier, I. Hodgkinson, “Anisotropy in thin films: modeling and measurement of guided and nonguided optical properties: application to TiO2 films,” Appl. Opt. 32, 5649–5659 (1993).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

1985 (1)

P. Ramanlal, L. M. Sander, “Theory of ballistic aggregation,” Phys. Rev. Lett. 54, 1828–1831 (1985).
[CrossRef] [PubMed]

1984 (1)

R. Messier, A. P. Giri, R. A. Roy, “Revised structure zone model for thin film physical structure,” J. Vac. Sci. Technol. A 2, 500–503 (1984).
[CrossRef]

1977 (2)

A. G. Dirks, H. J. Leamy, “Columnar nanostructure in vapor deposited thin films,” Thin Solid Films 45, 219–323 (1977).
[CrossRef]

J. A. Thornton, “High rate thick film growth,” Annu. Rev. Mater. Sci. 7, 239–260 (1977).
[CrossRef]

1975 (1)

1971 (1)

1969 (1)

B. A. Movchan, A. V. Demchishin, “Study of the structure and properties of thick vacuum condensates of nickel, titanium, tungsten, aluminium oxide and zirconium dioxide,” Phys. Met. Metallogr. (USSR) 28, 83–90 (1969).

Albrand, G.

Allen, T. H.

Alvarez-Herrero, A.

A. Alvarez-Herrero, A. J. Fort, H. Guerrero, E. Bernabeu, “Ellipsometric characterization and influence of relative humidity on TiO2 layers optical properties,” Thin Solid Films 349, 212–219 (1999).
[CrossRef]

Álvarez-Herrero, A.

Aspnes, D. E.

R. W. Collins, D. E. Aspnes, E. A. Irene, “Proceedings of the Second International Conference on Spectroscopic Ellipsometry,” Thin Solid Films 313–314 (1998).

D. E. Aspnes, A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975).
[CrossRef]

Azzam, R. M. A.

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

Bashara, N. N.

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

Bennett, J. M.

Bernabeu, E.

A. Álvarez-Herrero, R. L. Heredero, E. Bernabeu, D. Levy, “Adsorption of water on porous Vycor glass studied by ellipsometry,” Appl. Opt. 40, 527–532 (2001).
[CrossRef]

A. Alvarez-Herrero, A. J. Fort, H. Guerrero, E. Bernabeu, “Ellipsometric characterization and influence of relative humidity on TiO2 layers optical properties,” Thin Solid Films 349, 212–219 (1999).
[CrossRef]

Borgogno, J. P.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993).

Bridou, F.

G. Parjadis de Lariviére, J. M. Frigerio, F. Bridou, J. Rivory, “Modelling of ellipsometric data of inhomogeneous TiO2 films,” Thin Solid Films 233–234, 458–462 (1993).
[CrossRef]

Carniglia, C. K.

Chakravarty, G. R.

B. P. Pal, G. R. Chakravarty, “All-fiber wavelength selective components for optical communication,” Commun. Instr. 5, 181–208 (1997).

Chao, S.

Chen, J. S.

Collins, R. W.

R. W. Collins, D. E. Aspnes, E. A. Irene, “Proceedings of the Second International Conference on Spectroscopic Ellipsometry,” Thin Solid Films 313–314 (1998).

Demchishin, A. V.

B. A. Movchan, A. V. Demchishin, “Study of the structure and properties of thick vacuum condensates of nickel, titanium, tungsten, aluminium oxide and zirconium dioxide,” Phys. Met. Metallogr. (USSR) 28, 83–90 (1969).

Dirks, A. G.

A. G. Dirks, H. J. Leamy, “Columnar nanostructure in vapor deposited thin films,” Thin Solid Films 45, 219–323 (1977).
[CrossRef]

Endelema, D.

Flory, F.

Fort, A. J.

A. Alvarez-Herrero, A. J. Fort, H. Guerrero, E. Bernabeu, “Ellipsometric characterization and influence of relative humidity on TiO2 layers optical properties,” Thin Solid Films 349, 212–219 (1999).
[CrossRef]

Frigerio, J. M.

G. Parjadis de Lariviére, J. M. Frigerio, F. Bridou, J. Rivory, “Modelling of ellipsometric data of inhomogeneous TiO2 films,” Thin Solid Films 233–234, 458–462 (1993).
[CrossRef]

Giri, A. P.

R. Messier, A. P. Giri, R. A. Roy, “Revised structure zone model for thin film physical structure,” J. Vac. Sci. Technol. A 2, 500–503 (1984).
[CrossRef]

Gregg, S. J.

S. J. Gregg, K. S. W. Sing, Adsorption, Surface Area and Porosity (Academic, New York, 1997).

Guenther, K. H.

Guerrero, H.

A. Alvarez-Herrero, A. J. Fort, H. Guerrero, E. Bernabeu, “Ellipsometric characterization and influence of relative humidity on TiO2 layers optical properties,” Thin Solid Films 349, 212–219 (1999).
[CrossRef]

Hazel, J.

I. Hodgkinson, J. Hazel, Q. H. Wu, “In situ measurement of principal refractive indices of thin films by two-angle ellipsometry,” Thin Solid Films 313–314, 368–372 (1998).
[CrossRef]

I. Hodgkinson, Q. H. Wu, J. Hazel, “Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide,” Appl. Opt. 37, 2653–2659 (1998).
[CrossRef]

Heredero, R. L.

Hodgkinson, I.

Irene, E. A.

R. W. Collins, D. E. Aspnes, E. A. Irene, “Proceedings of the Second International Conference on Spectroscopic Ellipsometry,” Thin Solid Films 313–314 (1998).

Jimbo, T.

Kao, J. S.

Kim, S. Y.

Krishna, K. M.

Lai, G. R.

Lazarides, B.

Leamy, H. J.

A. G. Dirks, H. J. Leamy, “Columnar nanostructure in vapor deposited thin films,” Thin Solid Films 45, 219–323 (1977).
[CrossRef]

Levy, D.

Messier, R.

R. Messier, A. P. Giri, R. A. Roy, “Revised structure zone model for thin film physical structure,” J. Vac. Sci. Technol. A 2, 500–503 (1984).
[CrossRef]

Mosaddeq-ur-Rahman, Md.

Movchan, B. A.

B. A. Movchan, A. V. Demchishin, “Study of the structure and properties of thick vacuum condensates of nickel, titanium, tungsten, aluminium oxide and zirconium dioxide,” Phys. Met. Metallogr. (USSR) 28, 83–90 (1969).

Pal, B. P.

B. P. Pal, G. R. Chakravarty, “All-fiber wavelength selective components for optical communication,” Commun. Instr. 5, 181–208 (1997).

Parjadis de Lariviére, G.

G. Parjadis de Lariviére, J. M. Frigerio, F. Bridou, J. Rivory, “Modelling of ellipsometric data of inhomogeneous TiO2 films,” Thin Solid Films 233–234, 458–462 (1993).
[CrossRef]

Pelletier, E.

Pulker, H. K.

H. K. Pulker, Coatings on Glass (Elsevier, Amsterdam, 1999).

Ramanlal, P.

P. Ramanlal, L. M. Sander, “Theory of ballistic aggregation,” Phys. Rev. Lett. 54, 1828–1831 (1985).
[CrossRef] [PubMed]

Rivory, J.

G. Parjadis de Lariviére, J. M. Frigerio, F. Bridou, J. Rivory, “Modelling of ellipsometric data of inhomogeneous TiO2 films,” Thin Solid Films 233–234, 458–462 (1993).
[CrossRef]

Roy, R. A.

R. Messier, A. P. Giri, R. A. Roy, “Revised structure zone model for thin film physical structure,” J. Vac. Sci. Technol. A 2, 500–503 (1984).
[CrossRef]

Sander, L. M.

P. Ramanlal, L. M. Sander, “Theory of ballistic aggregation,” Phys. Rev. Lett. 54, 1828–1831 (1985).
[CrossRef] [PubMed]

Saxer, A.

Schmell, R. A.

Sing, K. S. W.

S. J. Gregg, K. S. W. Sing, Adsorption, Surface Area and Porosity (Academic, New York, 1997).

Soga, T.

Studna, A. A.

Thornton, J. A.

J. A. Thornton, “High rate thick film growth,” Annu. Rev. Mater. Sci. 7, 239–260 (1977).
[CrossRef]

Tien, P. K.

Tolmachev, V. A.

V. A. Tolmachev, “Adsorption-ellipsometry method of studying the optical profile, thickness, and porosity of thin films,” J. Opt. Technol. 66, 596–607 (1999).
[CrossRef]

V. A. Tolmachev, “Determination of the porosity of uniform films by adsorption-ellipsometric method,” Opt. Spectrosc. 84, 584–588 (1998).

Tuttle-Hart, T.

Umeno, M.

Wang, W. H.

Watanabe, J.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993).

Wu, Q. H.

I. Hodgkinson, J. Hazel, Q. H. Wu, “In situ measurement of principal refractive indices of thin films by two-angle ellipsometry,” Thin Solid Films 313–314, 368–372 (1998).
[CrossRef]

I. Hodgkinson, Q. H. Wu, J. Hazel, “Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide,” Appl. Opt. 37, 2653–2659 (1998).
[CrossRef]

Yu, G.

Annu. Rev. Mater. Sci. (1)

J. A. Thornton, “High rate thick film growth,” Annu. Rev. Mater. Sci. 7, 239–260 (1977).
[CrossRef]

Appl. Opt. (9)

D. E. Aspnes, A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975).
[CrossRef]

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]

J. S. Chen, S. Chao, J. S. Kao, G. R. Lai, W. H. Wang, “Substrate-dependent optical absorption characteristics of titanium dioxide thin films,” Appl. Opt. 36, 4403–4408 (1997).
[CrossRef] [PubMed]

I. Hodgkinson, Q. H. Wu, J. Hazel, “Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide,” Appl. Opt. 37, 2653–2659 (1998).
[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]

F. Flory, D. Endelema, E. Pelletier, I. Hodgkinson, “Anisotropy in thin films: modeling and measurement of guided and nonguided optical properties: application to TiO2 films,” Appl. Opt. 32, 5649–5659 (1993).
[CrossRef] [PubMed]

Md. Mosaddeq-ur-Rahman, G. Yu, K. M. Krishna, T. Soga, J. Watanabe, T. Jimbo, M. Umeno, “Determination of optical constants of solgel-derived inhomogeneous TiO2 films by spectroscopic ellipsometry and transmission spectroscopy,” Appl. Opt. 37, 691–697 (1998).
[CrossRef]

A. Álvarez-Herrero, R. L. Heredero, E. Bernabeu, D. Levy, “Adsorption of water on porous Vycor glass studied by ellipsometry,” Appl. Opt. 40, 527–532 (2001).
[CrossRef]

P. K. Tien, “Light waves in thin films and integrated optics,” Appl. Opt. 10, 2395–2413 (1971).
[CrossRef] [PubMed]

Commun. Instr. (1)

B. P. Pal, G. R. Chakravarty, “All-fiber wavelength selective components for optical communication,” Commun. Instr. 5, 181–208 (1997).

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

J. Opt. Technol. (1)

J. Vac. Sci. Technol. A (1)

R. Messier, A. P. Giri, R. A. Roy, “Revised structure zone model for thin film physical structure,” J. Vac. Sci. Technol. A 2, 500–503 (1984).
[CrossRef]

Opt. Spectrosc. (1)

V. A. Tolmachev, “Determination of the porosity of uniform films by adsorption-ellipsometric method,” Opt. Spectrosc. 84, 584–588 (1998).

Phys. Met. Metallogr. (USSR) (1)

B. A. Movchan, A. V. Demchishin, “Study of the structure and properties of thick vacuum condensates of nickel, titanium, tungsten, aluminium oxide and zirconium dioxide,” Phys. Met. Metallogr. (USSR) 28, 83–90 (1969).

Phys. Rev. Lett. (1)

P. Ramanlal, L. M. Sander, “Theory of ballistic aggregation,” Phys. Rev. Lett. 54, 1828–1831 (1985).
[CrossRef] [PubMed]

Thin Solid Films (5)

I. Hodgkinson, J. Hazel, Q. H. Wu, “In situ measurement of principal refractive indices of thin films by two-angle ellipsometry,” Thin Solid Films 313–314, 368–372 (1998).
[CrossRef]

G. Parjadis de Lariviére, J. M. Frigerio, F. Bridou, J. Rivory, “Modelling of ellipsometric data of inhomogeneous TiO2 films,” Thin Solid Films 233–234, 458–462 (1993).
[CrossRef]

A. Alvarez-Herrero, A. J. Fort, H. Guerrero, E. Bernabeu, “Ellipsometric characterization and influence of relative humidity on TiO2 layers optical properties,” Thin Solid Films 349, 212–219 (1999).
[CrossRef]

A. G. Dirks, H. J. Leamy, “Columnar nanostructure in vapor deposited thin films,” Thin Solid Films 45, 219–323 (1977).
[CrossRef]

R. W. Collins, D. E. Aspnes, E. A. Irene, “Proceedings of the Second International Conference on Spectroscopic Ellipsometry,” Thin Solid Films 313–314 (1998).

Other (4)

H. K. Pulker, Coatings on Glass (Elsevier, Amsterdam, 1999).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993).

S. J. Gregg, K. S. W. Sing, Adsorption, Surface Area and Porosity (Academic, New York, 1997).

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

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Figures (9)

Fig. 1
Fig. 1

Simulation of the TiO2-SPF system. Resonance shift of the sixth TE mode versus the overlayer’s refractive index by use of Eq. (7) and consideration of n ef = 1.46 and d = 1212 nm. The linear relation of the refractive index of the layer and the resonance shift for changes of the refractive index as high as 0.1 can be observed.

Fig. 2
Fig. 2

Experimental setup for measuring the resonance shift of the coupling modes between the SPF and the dielectric film.

Fig. 3
Fig. 3

Ellipsometric model of the film. The TiO2 layer was considered inhomogeneous, with superficial roughness. The inhomogeneity was simulated by use of a variable concentration of voids (100-C%) along the thickness of the layer.

Fig. 4
Fig. 4

Refractive indices of sublayer 1 (the closest one to the ambient) and sublayer 20 (the closest one to the substrate). The difference between both sublayers (inhomogeneity of the film) is more than 0.2. The ellipsometric measurements were carried out at 30% ± 2% RH and 23 °C ± 1 °C.

Fig. 5
Fig. 5

Experimental spectral response of the SPF device with the TiO2 overlayer (36% ± 1% RH, 21.5 °C ± 0.5 °C). The coupling resonances with the TE and TM guided modes of the film are evidenced.

Fig. 6
Fig. 6

Experimental and theoretical data of the resonances of the (a) TM and (b) TE modes of the SPF-TiO2 system. Experimental data measured at 36% ± 1% RH and 21.5 °C ± 0.5 °C.

Fig. 7
Fig. 7

Water adsorption isotherm for sample 1 by ellipsometric measurements (T = 25.5 °C ± 0.5 °C).

Fig. 8
Fig. 8

Water adsorption isotherm for sample 2 by resonance shift of SPF measurements (T = 26.1 °C ± 0.6 °C).

Fig. 9
Fig. 9

Pore size distribution calculated with the Pierce method from the ellipsometric and the resonance shift data (Figs. 7 and 8, respectively).

Tables (2)

Tables Icon

Table 1 Regression Results for the Inhomogeneous Model

Tables Icon

Table 2 Results of Size Pore Distribution Obtained from the Ellipsometric Data and the Resonance Shift of the SPF Device

Equations (12)

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

2πdλno2-neo21/2=mπ+ϕ1+ϕ2,
ϕi=tan-1 ς neo2-ni21/2no2-neo21/2, i=1, 2,
λTM=2πd noTM2-nef2mπ+ϕ1TM+ϕ2TM,
λTE=2πd noTE2-nef2mπ+ϕ1TE+ϕ2TE,
It=I01+α cos 2ωpt+β sin 2ωpt,
tan Ψ=1+α1-α1/2tan A, cos Δ=β1-α21/2,
tan Ψ expiΔ=rr,
ln RH=-2γVLRT1rm,
r=1+A2-1λ2λ2-B+Cλ2λ2-λ02λ2-λ02+γ2λ2, i=Cλ3γλ2-λ02+γ2λ2,
nλ=1+A2-1λ2λ2-B1/2.
Aeffective=1.451, Acladding=1.448, Beffective=Bcladding=0.009.
raverage=0 rpdVdrpdrp0dVdrpdrp.

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