Abstract

The characterization of optical multilayer coatings has been a challenging task for thin-film scientists and engineers because of the various complex, interdependent layer parameters that exist in the system. Spectroscopic phase-modulated ellipsometry has some advantages in the postanalysis of the layer parameters of such multilayer coatings because it suitably models the layer structure with respect to the ellipsometric measurements. An algorithm to characterize multilayer optical coatings with large numbers of layers has been described by spectroscopic ellipsometry by use of a discrete spectral zone fitting approach. A 23-layer multilayer highly reflecting mirror has been characterized by this technique in the wavelength range 280–1000 nm. The ellipsometric spectra (Ψ and Δ versus wavelength) have been fitted separately in three wavelength regimes. Fitting the ellipsometric spectra in the wavelength regime of 700–1000 nm permitted the sample structure to be determined. The data were then fitted in the wavelength range 280–340 nm, i.e., near the fundamental absorption edge of TiO2, to yield the dispersion relation for the optical constants of TiO2. Finally, the data were fitted in the wavelength range 340–700 nm, and the true dispersion of the refractive index of TiO2, along with the best-fitting sample structure, was obtained.

© 2001 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  8. P. M. Martin, D. C. Stewart, W. D. Bennett, J. D. Affinitto, M. E. Gross, “Multifunctional multilayer optical coatings,” J. Vac. Sci. Technol. A 15, 1098–1102 (1997).
    [CrossRef]
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    [CrossRef]
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  14. B. Drevellion, “Phase modulated ellipsometry from the ultra-violet to the infra-red: in-situ application to the growth of semiconductors,” Prog. Cryst. Growth Charact. 27, 1–87 (1993).
    [CrossRef]
  15. P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973).
    [CrossRef]
  16. G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313–314, 33–39 (1998).
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    [CrossRef]
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  22. P. Löbl, M. Huppertz, D. Mergel, “Nucleation and growth in TiO2 films prepared by sputtering and evaporation,” Thin Solid Films 251, 72–79 (1994).
    [CrossRef]
  23. G. P. de Larivière, J. M. Frigerio, J. Rivory, F. Ables, “Estimate of the degree of inhomogeneity of the refractive index of dielectric films from spectroscopic ellipsiometry,” Appl. Opt. 31, 6056–6061 (1992).
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    [CrossRef]
  26. A. R. Forouhi, I. Bloomer, “Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,” Phys. Rev. B 34, 7018–7026 (1986).
    [CrossRef]
  27. S. Adachi, “Model dielectric constants of GaP, GaAs, GaSb, InP, InAs and InSb,” Phys. Rev. B 35, 7454–7463 (1987).
    [CrossRef]
  28. M. Radecka, K. Zakrzewska, H. Czternastek, T. Stapinski, S. Debrus, “The influence of thermal annealing on the structural, electrical and optical properties of TiO2-x thin films,” Appl. Surf. Sci. 65–66, 227–234 (1993).
  29. N. Martin, C. Rousselot, C. Savall, F. Palmino, “Characterisations of titanium oxide films prepared by radio-frequency magnetron sputtering,” Thin Solid Films 287, 154–163 (1996).
    [CrossRef]
  30. J. D. DeLoach, G. Scarel, C. R. Aita, “Correlation between titania film structure and near ultra-violet optical absorption,” J. Appl. Phys. 85, 2377–2384 (1999).
    [CrossRef]
  31. H. Tang, K. Prasad, R. Sanjines, P. E. Schmid, F. Levy, “Electrical and optical properties of TiO2 anatase thin films,” J. Appl. Phys. 75, 2042–2047 (1994).
    [CrossRef]
  32. N. Daude, C. Gout, C. Jouanin, “Electronic band structure of titanium di-oxide,” Phys. Rev. B 15, 3229–3235 (1977).
    [CrossRef]
  33. P. Chindaudom, K. Vedam, Optical Characterisation ofInhomogeneous Transparent films on Transparent Substrates by Spectroscopic Ellipsometry, Vol. 19 of Physics of Thin Films, K. Vedam, ed. (Academic, San Diego, Calif., 1994), pp. 191–247.

2000 (1)

D. Bhattacharyya, N. K. Sahoo, S. Thakur, N. C. Das, “Spectroscopic ellipsometry of TiO2 layers prepared by ion-assisted electron-beam evaporation,” Thin Solid Films 360, 96–102 (2000).
[CrossRef]

1999 (2)

J. Back, W. S. Han, H. K. Cho, B. Lee, I. H. Choi, “Optically pumped continuous-wave operation of InAlGaAsInP based 155 µm vertical cavity surface emitting laser with SiO2/TiO2 di-electric mirror,” Electron. Lett. 35, 814–815 (1999).
[CrossRef]

J. D. DeLoach, G. Scarel, C. R. Aita, “Correlation between titania film structure and near ultra-violet optical absorption,” J. Appl. Phys. 85, 2377–2384 (1999).
[CrossRef]

1998 (3)

G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313–314, 33–39 (1998).

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterisation of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films313–314, 379–383 (1998).

S. Callard, A. Gagnaire, J. Joseph, “Characterisation of graded refractive index silicon oxynitride thin films by spectroscopic ellipsometry,” Thin Solid Films, 313–314, 384–388 (1998).

1997 (3)

I. Wakabayashi, K. Miyauchi, “Design of dielectric multilayer band-pass filters using arbitrary thickness of layers,” Electron. Commun. Jpn. Part 2 Electron. 80, 46–58 (1997).
[CrossRef]

P. M. Martin, D. C. Stewart, W. D. Bennett, J. D. Affinitto, M. E. Gross, “Multifunctional multilayer optical coatings,” J. Vac. Sci. Technol. A 15, 1098–1102 (1997).
[CrossRef]

H. Kumagai, K. Toyoda, K. Kobayashi, M. Obara, Y. Iimuna, “Titanium oxide/aluminum oxide multilayer reflectors for ‘water-window’ wavelengths,” Appl. Phys. Lett. 70, 2338–2340 (1997).
[CrossRef]

1996 (1)

N. Martin, C. Rousselot, C. Savall, F. Palmino, “Characterisations of titanium oxide films prepared by radio-frequency magnetron sputtering,” Thin Solid Films 287, 154–163 (1996).
[CrossRef]

1994 (2)

P. Löbl, M. Huppertz, D. Mergel, “Nucleation and growth in TiO2 films prepared by sputtering and evaporation,” Thin Solid Films 251, 72–79 (1994).
[CrossRef]

H. Tang, K. Prasad, R. Sanjines, P. E. Schmid, F. Levy, “Electrical and optical properties of TiO2 anatase thin films,” J. Appl. Phys. 75, 2042–2047 (1994).
[CrossRef]

1993 (5)

K. Sato, S. Adachi, “Optical properties of ZnTe,” J. Appl. Phys. 73, 926–931 (1993).
[CrossRef]

M. Radecka, K. Zakrzewska, H. Czternastek, T. Stapinski, S. Debrus, “The influence of thermal annealing on the structural, electrical and optical properties of TiO2-x thin films,” Appl. Surf. Sci. 65–66, 227–234 (1993).

K. Balasubranium, X. F. Han, H. Guenther, “Comparative study of titanium dioxide thin films produced by electron-beam evaporation and by reactive low-voltage ion plating,” Appl. Opt. 32, 5594–5600 (1993).
[CrossRef]

S. Russev, E. Valcheva, K. Germanova, “Investigation of the system InSb–SiO2 by spectroscopic multiangle ellipsometry,” Thin Solid Films 233, 231–235 (1993).
[CrossRef]

B. Drevellion, “Phase modulated ellipsometry from the ultra-violet to the infra-red: in-situ application to the growth of semiconductors,” Prog. Cryst. Growth Charact. 27, 1–87 (1993).
[CrossRef]

1992 (2)

1989 (3)

1987 (1)

S. Adachi, “Model dielectric constants of GaP, GaAs, GaSb, InP, InAs and InSb,” Phys. Rev. B 35, 7454–7463 (1987).
[CrossRef]

1986 (1)

A. R. Forouhi, I. Bloomer, “Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,” Phys. Rev. B 34, 7018–7026 (1986).
[CrossRef]

1982 (1)

B. Drevellion, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[CrossRef]

1977 (1)

N. Daude, C. Gout, C. Jouanin, “Electronic band structure of titanium di-oxide,” Phys. Rev. B 15, 3229–3235 (1977).
[CrossRef]

1976 (1)

1973 (1)

P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973).
[CrossRef]

1969 (1)

P. H. Smith, “A theoretical and experimental analysis of the ellipsometer,” Surf. Sci. 16, 34–66 (1969).
[CrossRef]

Ables, F.

Adachi, S.

K. Sato, S. Adachi, “Optical properties of ZnTe,” J. Appl. Phys. 73, 926–931 (1993).
[CrossRef]

S. Adachi, “Model dielectric constants of GaP, GaAs, GaSb, InP, InAs and InSb,” Phys. Rev. B 35, 7454–7463 (1987).
[CrossRef]

Affinitto, J. D.

P. M. Martin, D. C. Stewart, W. D. Bennett, J. D. Affinitto, M. E. Gross, “Multifunctional multilayer optical coatings,” J. Vac. Sci. Technol. A 15, 1098–1102 (1997).
[CrossRef]

Aita, C. R.

J. D. DeLoach, G. Scarel, C. R. Aita, “Correlation between titania film structure and near ultra-violet optical absorption,” J. Appl. Phys. 85, 2377–2384 (1999).
[CrossRef]

Albrand, G.

Allen, T. H.

Ankerhold, G.

F. Mitschke, G. Ankerhold, W. Lange, “Hard coatings for optically bi-stable interference filters,” Appl. Phys. B 48, 101–104 (1989).

Back, J.

J. Back, W. S. Han, H. K. Cho, B. Lee, I. H. Choi, “Optically pumped continuous-wave operation of InAlGaAsInP based 155 µm vertical cavity surface emitting laser with SiO2/TiO2 di-electric mirror,” Electron. Lett. 35, 814–815 (1999).
[CrossRef]

Balasubranium, K.

Bennett, J. M.

Bennett, W. D.

P. M. Martin, D. C. Stewart, W. D. Bennett, J. D. Affinitto, M. E. Gross, “Multifunctional multilayer optical coatings,” J. Vac. Sci. Technol. A 15, 1098–1102 (1997).
[CrossRef]

Bertran, E.

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterisation of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films313–314, 379–383 (1998).

Bhattacharyya, D.

D. Bhattacharyya, N. K. Sahoo, S. Thakur, N. C. Das, “Spectroscopic ellipsometry of TiO2 layers prepared by ion-assisted electron-beam evaporation,” Thin Solid Films 360, 96–102 (2000).
[CrossRef]

N. C. Das, D. Bhattacharyya, S. Thakur, “Characterisation of different single and multilayer films using phase modulated spectroscopic ellipsometry,” (Bhabha Atomic Research Centre, Mumbai, India, 1998).

Bloomer, I.

A. R. Forouhi, I. Bloomer, “Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,” Phys. Rev. B 34, 7018–7026 (1986).
[CrossRef]

Borgogno, J. P.

Bosch, S.

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterisation of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films313–314, 379–383 (1998).

Callard, S.

S. Callard, A. Gagnaire, J. Joseph, “Characterisation of graded refractive index silicon oxynitride thin films by spectroscopic ellipsometry,” Thin Solid Films, 313–314, 384–388 (1998).

Campmany, J.

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterisation of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films313–314, 379–383 (1998).

Canillas, A.

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterisation of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films313–314, 379–383 (1998).

Carnigila, C. K.

Chindaudom, P.

P. Chindaudom, K. Vedam, Optical Characterisation ofInhomogeneous Transparent films on Transparent Substrates by Spectroscopic Ellipsometry, Vol. 19 of Physics of Thin Films, K. Vedam, ed. (Academic, San Diego, Calif., 1994), pp. 191–247.

Cho, H. K.

J. Back, W. S. Han, H. K. Cho, B. Lee, I. H. Choi, “Optically pumped continuous-wave operation of InAlGaAsInP based 155 µm vertical cavity surface emitting laser with SiO2/TiO2 di-electric mirror,” Electron. Lett. 35, 814–815 (1999).
[CrossRef]

Choi, I. H.

J. Back, W. S. Han, H. K. Cho, B. Lee, I. H. Choi, “Optically pumped continuous-wave operation of InAlGaAsInP based 155 µm vertical cavity surface emitting laser with SiO2/TiO2 di-electric mirror,” Electron. Lett. 35, 814–815 (1999).
[CrossRef]

Czternastek, H.

M. Radecka, K. Zakrzewska, H. Czternastek, T. Stapinski, S. Debrus, “The influence of thermal annealing on the structural, electrical and optical properties of TiO2-x thin films,” Appl. Surf. Sci. 65–66, 227–234 (1993).

Dalby, J. L.

B. Drevellion, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[CrossRef]

Das, N. C.

D. Bhattacharyya, N. K. Sahoo, S. Thakur, N. C. Das, “Spectroscopic ellipsometry of TiO2 layers prepared by ion-assisted electron-beam evaporation,” Thin Solid Films 360, 96–102 (2000).
[CrossRef]

N. C. Das, D. Bhattacharyya, S. Thakur, “Characterisation of different single and multilayer films using phase modulated spectroscopic ellipsometry,” (Bhabha Atomic Research Centre, Mumbai, India, 1998).

Daude, N.

N. Daude, C. Gout, C. Jouanin, “Electronic band structure of titanium di-oxide,” Phys. Rev. B 15, 3229–3235 (1977).
[CrossRef]

de Larivière, G. P.

Debrus, S.

M. Radecka, K. Zakrzewska, H. Czternastek, T. Stapinski, S. Debrus, “The influence of thermal annealing on the structural, electrical and optical properties of TiO2-x thin films,” Appl. Surf. Sci. 65–66, 227–234 (1993).

DeLoach, J. D.

J. D. DeLoach, G. Scarel, C. R. Aita, “Correlation between titania film structure and near ultra-violet optical absorption,” J. Appl. Phys. 85, 2377–2384 (1999).
[CrossRef]

Dill, F. H.

P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973).
[CrossRef]

Drevellion, B.

B. Drevellion, “Phase modulated ellipsometry from the ultra-violet to the infra-red: in-situ application to the growth of semiconductors,” Prog. Cryst. Growth Charact. 27, 1–87 (1993).
[CrossRef]

B. Drevellion, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[CrossRef]

Forouhi, A. R.

A. R. Forouhi, I. Bloomer, “Optical dispersion relations for amorphous semiconductors and amorphous dielectrics,” Phys. Rev. B 34, 7018–7026 (1986).
[CrossRef]

Frigerio, J. M.

Gagnaire, A.

S. Callard, A. Gagnaire, J. Joseph, “Characterisation of graded refractive index silicon oxynitride thin films by spectroscopic ellipsometry,” Thin Solid Films, 313–314, 384–388 (1998).

Germanova, K.

S. Russev, E. Valcheva, K. Germanova, “Investigation of the system InSb–SiO2 by spectroscopic multiangle ellipsometry,” Thin Solid Films 233, 231–235 (1993).
[CrossRef]

Gout, C.

N. Daude, C. Gout, C. Jouanin, “Electronic band structure of titanium di-oxide,” Phys. Rev. B 15, 3229–3235 (1977).
[CrossRef]

Gross, M. E.

P. M. Martin, D. C. Stewart, W. D. Bennett, J. D. Affinitto, M. E. Gross, “Multifunctional multilayer optical coatings,” J. Vac. Sci. Technol. A 15, 1098–1102 (1997).
[CrossRef]

Guenther, H.

Guenther, K. H.

Han, W. S.

J. Back, W. S. Han, H. K. Cho, B. Lee, I. H. Choi, “Optically pumped continuous-wave operation of InAlGaAsInP based 155 µm vertical cavity surface emitting laser with SiO2/TiO2 di-electric mirror,” Electron. Lett. 35, 814–815 (1999).
[CrossRef]

Han, X. F.

Hauge, P. S.

P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973).
[CrossRef]

Huppertz, M.

P. Löbl, M. Huppertz, D. Mergel, “Nucleation and growth in TiO2 films prepared by sputtering and evaporation,” Thin Solid Films 251, 72–79 (1994).
[CrossRef]

Iimuna, Y.

H. Kumagai, K. Toyoda, K. Kobayashi, M. Obara, Y. Iimuna, “Titanium oxide/aluminum oxide multilayer reflectors for ‘water-window’ wavelengths,” Appl. Phys. Lett. 70, 2338–2340 (1997).
[CrossRef]

Itoh, T.

Jellison, G. E.

G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313–314, 33–39 (1998).

Joseph, J.

S. Callard, A. Gagnaire, J. Joseph, “Characterisation of graded refractive index silicon oxynitride thin films by spectroscopic ellipsometry,” Thin Solid Films, 313–314, 384–388 (1998).

Jouanin, C.

N. Daude, C. Gout, C. Jouanin, “Electronic band structure of titanium di-oxide,” Phys. Rev. B 15, 3229–3235 (1977).
[CrossRef]

Kilinova, E.

V. Kozhukharov, Ch. Trapalios, B. Samuneva, E. Kilinova, “Sol-gel processing of multilayer thin coatings,” J. Mater. Sci. Lett. 11, 1206–1208 (1992).
[CrossRef]

Kobayashi, K.

H. Kumagai, K. Toyoda, K. Kobayashi, M. Obara, Y. Iimuna, “Titanium oxide/aluminum oxide multilayer reflectors for ‘water-window’ wavelengths,” Appl. Phys. Lett. 70, 2338–2340 (1997).
[CrossRef]

Kozhukharov, V.

V. Kozhukharov, Ch. Trapalios, B. Samuneva, E. Kilinova, “Sol-gel processing of multilayer thin coatings,” J. Mater. Sci. Lett. 11, 1206–1208 (1992).
[CrossRef]

Kumagai, H.

H. Kumagai, K. Toyoda, K. Kobayashi, M. Obara, Y. Iimuna, “Titanium oxide/aluminum oxide multilayer reflectors for ‘water-window’ wavelengths,” Appl. Phys. Lett. 70, 2338–2340 (1997).
[CrossRef]

Lange, W.

F. Mitschke, G. Ankerhold, W. Lange, “Hard coatings for optically bi-stable interference filters,” Appl. Phys. B 48, 101–104 (1989).

Lazarides, B.

Lee, B.

J. Back, W. S. Han, H. K. Cho, B. Lee, I. H. Choi, “Optically pumped continuous-wave operation of InAlGaAsInP based 155 µm vertical cavity surface emitting laser with SiO2/TiO2 di-electric mirror,” Electron. Lett. 35, 814–815 (1999).
[CrossRef]

Levy, F.

H. Tang, K. Prasad, R. Sanjines, P. E. Schmid, F. Levy, “Electrical and optical properties of TiO2 anatase thin films,” J. Appl. Phys. 75, 2042–2047 (1994).
[CrossRef]

Löbl, P.

P. Löbl, M. Huppertz, D. Mergel, “Nucleation and growth in TiO2 films prepared by sputtering and evaporation,” Thin Solid Films 251, 72–79 (1994).
[CrossRef]

Macleod, H. A.

H. A. Macleod, “Thin film optical coating design,” in Thin Films for Optical Systems, F. R. Flory, ed. (Marcel Dekker, New York, (1995), pp. 1–39.

Marbot, R.

B. Drevellion, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[CrossRef]

Martin, N.

N. Martin, C. Rousselot, C. Savall, F. Palmino, “Characterisations of titanium oxide films prepared by radio-frequency magnetron sputtering,” Thin Solid Films 287, 154–163 (1996).
[CrossRef]

Martin, P. M.

P. M. Martin, D. C. Stewart, W. D. Bennett, J. D. Affinitto, M. E. Gross, “Multifunctional multilayer optical coatings,” J. Vac. Sci. Technol. A 15, 1098–1102 (1997).
[CrossRef]

Mergel, D.

P. Löbl, M. Huppertz, D. Mergel, “Nucleation and growth in TiO2 films prepared by sputtering and evaporation,” Thin Solid Films 251, 72–79 (1994).
[CrossRef]

Mitschke, F.

F. Mitschke, G. Ankerhold, W. Lange, “Hard coatings for optically bi-stable interference filters,” Appl. Phys. B 48, 101–104 (1989).

Miyauchi, K.

I. Wakabayashi, K. Miyauchi, “Design of dielectric multilayer band-pass filters using arbitrary thickness of layers,” Electron. Commun. Jpn. Part 2 Electron. 80, 46–58 (1997).
[CrossRef]

Obara, M.

H. Kumagai, K. Toyoda, K. Kobayashi, M. Obara, Y. Iimuna, “Titanium oxide/aluminum oxide multilayer reflectors for ‘water-window’ wavelengths,” Appl. Phys. Lett. 70, 2338–2340 (1997).
[CrossRef]

Paesold, G.

Palmino, F.

N. Martin, C. Rousselot, C. Savall, F. Palmino, “Characterisations of titanium oxide films prepared by radio-frequency magnetron sputtering,” Thin Solid Films 287, 154–163 (1996).
[CrossRef]

Pelletier, E.

Perrin, J.

B. Drevellion, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[CrossRef]

Phillip, H. R.

H. R. Phillip, “Silicon dioxide (SiO2) (glass),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), Chap. 5, pp. 749–763.
[CrossRef]

Popov, K. V.

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterisation of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films313–314, 379–383 (1998).

Prasad, K.

H. Tang, K. Prasad, R. Sanjines, P. E. Schmid, F. Levy, “Electrical and optical properties of TiO2 anatase thin films,” J. Appl. Phys. 75, 2042–2047 (1994).
[CrossRef]

Pulker, K. K.

Radecka, M.

M. Radecka, K. Zakrzewska, H. Czternastek, T. Stapinski, S. Debrus, “The influence of thermal annealing on the structural, electrical and optical properties of TiO2-x thin films,” Appl. Surf. Sci. 65–66, 227–234 (1993).

Ritter, E.

Rivory, J.

Rousselot, C.

N. Martin, C. Rousselot, C. Savall, F. Palmino, “Characterisations of titanium oxide films prepared by radio-frequency magnetron sputtering,” Thin Solid Films 287, 154–163 (1996).
[CrossRef]

Russev, S.

S. Russev, E. Valcheva, K. Germanova, “Investigation of the system InSb–SiO2 by spectroscopic multiangle ellipsometry,” Thin Solid Films 233, 231–235 (1993).
[CrossRef]

Sahoo, N. K.

D. Bhattacharyya, N. K. Sahoo, S. Thakur, N. C. Das, “Spectroscopic ellipsometry of TiO2 layers prepared by ion-assisted electron-beam evaporation,” Thin Solid Films 360, 96–102 (2000).
[CrossRef]

Samuneva, B.

V. Kozhukharov, Ch. Trapalios, B. Samuneva, E. Kilinova, “Sol-gel processing of multilayer thin coatings,” J. Mater. Sci. Lett. 11, 1206–1208 (1992).
[CrossRef]

Sanjines, R.

H. Tang, K. Prasad, R. Sanjines, P. E. Schmid, F. Levy, “Electrical and optical properties of TiO2 anatase thin films,” J. Appl. Phys. 75, 2042–2047 (1994).
[CrossRef]

Sato, K.

K. Sato, S. Adachi, “Optical properties of ZnTe,” J. Appl. Phys. 73, 926–931 (1993).
[CrossRef]

Savall, C.

N. Martin, C. Rousselot, C. Savall, F. Palmino, “Characterisations of titanium oxide films prepared by radio-frequency magnetron sputtering,” Thin Solid Films 287, 154–163 (1996).
[CrossRef]

Saxer, A.

Scarel, G.

J. D. DeLoach, G. Scarel, C. R. Aita, “Correlation between titania film structure and near ultra-violet optical absorption,” J. Appl. Phys. 85, 2377–2384 (1999).
[CrossRef]

Schmell, R. A.

Schmid, P. E.

H. Tang, K. Prasad, R. Sanjines, P. E. Schmid, F. Levy, “Electrical and optical properties of TiO2 anatase thin films,” J. Appl. Phys. 75, 2042–2047 (1994).
[CrossRef]

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P. H. Smith, “A theoretical and experimental analysis of the ellipsometer,” Surf. Sci. 16, 34–66 (1969).
[CrossRef]

Stapinski, T.

M. Radecka, K. Zakrzewska, H. Czternastek, T. Stapinski, S. Debrus, “The influence of thermal annealing on the structural, electrical and optical properties of TiO2-x thin films,” Appl. Surf. Sci. 65–66, 227–234 (1993).

Stewart, D. C.

P. M. Martin, D. C. Stewart, W. D. Bennett, J. D. Affinitto, M. E. Gross, “Multifunctional multilayer optical coatings,” J. Vac. Sci. Technol. A 15, 1098–1102 (1997).
[CrossRef]

Taga, Y.

Tang, H.

H. Tang, K. Prasad, R. Sanjines, P. E. Schmid, F. Levy, “Electrical and optical properties of TiO2 anatase thin films,” J. Appl. Phys. 75, 2042–2047 (1994).
[CrossRef]

Thakur, S.

D. Bhattacharyya, N. K. Sahoo, S. Thakur, N. C. Das, “Spectroscopic ellipsometry of TiO2 layers prepared by ion-assisted electron-beam evaporation,” Thin Solid Films 360, 96–102 (2000).
[CrossRef]

N. C. Das, D. Bhattacharyya, S. Thakur, “Characterisation of different single and multilayer films using phase modulated spectroscopic ellipsometry,” (Bhabha Atomic Research Centre, Mumbai, India, 1998).

Tikhonravov, A. V.

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterisation of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films313–314, 379–383 (1998).

Toyoda, K.

H. Kumagai, K. Toyoda, K. Kobayashi, M. Obara, Y. Iimuna, “Titanium oxide/aluminum oxide multilayer reflectors for ‘water-window’ wavelengths,” Appl. Phys. Lett. 70, 2338–2340 (1997).
[CrossRef]

Trapalios, Ch.

V. Kozhukharov, Ch. Trapalios, B. Samuneva, E. Kilinova, “Sol-gel processing of multilayer thin coatings,” J. Mater. Sci. Lett. 11, 1206–1208 (1992).
[CrossRef]

Tuttle-Hart, T.

Valcheva, E.

S. Russev, E. Valcheva, K. Germanova, “Investigation of the system InSb–SiO2 by spectroscopic multiangle ellipsometry,” Thin Solid Films 233, 231–235 (1993).
[CrossRef]

Vedam, K.

P. Chindaudom, K. Vedam, Optical Characterisation ofInhomogeneous Transparent films on Transparent Substrates by Spectroscopic Ellipsometry, Vol. 19 of Physics of Thin Films, K. Vedam, ed. (Academic, San Diego, Calif., 1994), pp. 191–247.

P. Chindaudom, K. Vedam, Optical Characterisation ofInhomogeneous Transparent films on Transparent Substrates by Spectroscopic Ellipsometry, Vol. 19 of Physics of Thin Films, K. Vedam, ed. (Academic, San Diego, Calif., 1994), pp. 191–247.

Violet, A.

B. Drevellion, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
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I. Wakabayashi, K. Miyauchi, “Design of dielectric multilayer band-pass filters using arbitrary thickness of layers,” Electron. Commun. Jpn. Part 2 Electron. 80, 46–58 (1997).
[CrossRef]

Zakrzewska, K.

M. Radecka, K. Zakrzewska, H. Czternastek, T. Stapinski, S. Debrus, “The influence of thermal annealing on the structural, electrical and optical properties of TiO2-x thin films,” Appl. Surf. Sci. 65–66, 227–234 (1993).

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Appl. Phys. B (1)

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Appl. Phys. Lett. (1)

H. Kumagai, K. Toyoda, K. Kobayashi, M. Obara, Y. Iimuna, “Titanium oxide/aluminum oxide multilayer reflectors for ‘water-window’ wavelengths,” Appl. Phys. Lett. 70, 2338–2340 (1997).
[CrossRef]

Appl. Surf. Sci. (1)

M. Radecka, K. Zakrzewska, H. Czternastek, T. Stapinski, S. Debrus, “The influence of thermal annealing on the structural, electrical and optical properties of TiO2-x thin films,” Appl. Surf. Sci. 65–66, 227–234 (1993).

Electron. Commun. Jpn. Part 2 Electron. (1)

I. Wakabayashi, K. Miyauchi, “Design of dielectric multilayer band-pass filters using arbitrary thickness of layers,” Electron. Commun. Jpn. Part 2 Electron. 80, 46–58 (1997).
[CrossRef]

Electron. Lett. (1)

J. Back, W. S. Han, H. K. Cho, B. Lee, I. H. Choi, “Optically pumped continuous-wave operation of InAlGaAsInP based 155 µm vertical cavity surface emitting laser with SiO2/TiO2 di-electric mirror,” Electron. Lett. 35, 814–815 (1999).
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[CrossRef]

J. Appl. Phys. (3)

K. Sato, S. Adachi, “Optical properties of ZnTe,” J. Appl. Phys. 73, 926–931 (1993).
[CrossRef]

J. D. DeLoach, G. Scarel, C. R. Aita, “Correlation between titania film structure and near ultra-violet optical absorption,” J. Appl. Phys. 85, 2377–2384 (1999).
[CrossRef]

H. Tang, K. Prasad, R. Sanjines, P. E. Schmid, F. Levy, “Electrical and optical properties of TiO2 anatase thin films,” J. Appl. Phys. 75, 2042–2047 (1994).
[CrossRef]

J. Mater. Sci. Lett. (1)

V. Kozhukharov, Ch. Trapalios, B. Samuneva, E. Kilinova, “Sol-gel processing of multilayer thin coatings,” J. Mater. Sci. Lett. 11, 1206–1208 (1992).
[CrossRef]

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

P. M. Martin, D. C. Stewart, W. D. Bennett, J. D. Affinitto, M. E. Gross, “Multifunctional multilayer optical coatings,” J. Vac. Sci. Technol. A 15, 1098–1102 (1997).
[CrossRef]

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S. Adachi, “Model dielectric constants of GaP, GaAs, GaSb, InP, InAs and InSb,” Phys. Rev. B 35, 7454–7463 (1987).
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B. Drevellion, “Phase modulated ellipsometry from the ultra-violet to the infra-red: in-situ application to the growth of semiconductors,” Prog. Cryst. Growth Charact. 27, 1–87 (1993).
[CrossRef]

Rev. Sci. Instrum. (1)

B. Drevellion, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[CrossRef]

Surf. Sci. (1)

P. H. Smith, “A theoretical and experimental analysis of the ellipsometer,” Surf. Sci. 16, 34–66 (1969).
[CrossRef]

Thin Solid Films (7)

D. Bhattacharyya, N. K. Sahoo, S. Thakur, N. C. Das, “Spectroscopic ellipsometry of TiO2 layers prepared by ion-assisted electron-beam evaporation,” Thin Solid Films 360, 96–102 (2000).
[CrossRef]

G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313–314, 33–39 (1998).

S. Russev, E. Valcheva, K. Germanova, “Investigation of the system InSb–SiO2 by spectroscopic multiangle ellipsometry,” Thin Solid Films 233, 231–235 (1993).
[CrossRef]

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterisation of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films313–314, 379–383 (1998).

S. Callard, A. Gagnaire, J. Joseph, “Characterisation of graded refractive index silicon oxynitride thin films by spectroscopic ellipsometry,” Thin Solid Films, 313–314, 384–388 (1998).

N. Martin, C. Rousselot, C. Savall, F. Palmino, “Characterisations of titanium oxide films prepared by radio-frequency magnetron sputtering,” Thin Solid Films 287, 154–163 (1996).
[CrossRef]

P. Löbl, M. Huppertz, D. Mergel, “Nucleation and growth in TiO2 films prepared by sputtering and evaporation,” Thin Solid Films 251, 72–79 (1994).
[CrossRef]

Other (4)

H. R. Phillip, “Silicon dioxide (SiO2) (glass),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), Chap. 5, pp. 749–763.
[CrossRef]

P. Chindaudom, K. Vedam, Optical Characterisation ofInhomogeneous Transparent films on Transparent Substrates by Spectroscopic Ellipsometry, Vol. 19 of Physics of Thin Films, K. Vedam, ed. (Academic, San Diego, Calif., 1994), pp. 191–247.

H. A. Macleod, “Thin film optical coating design,” in Thin Films for Optical Systems, F. R. Flory, ed. (Marcel Dekker, New York, (1995), pp. 1–39.

N. C. Das, D. Bhattacharyya, S. Thakur, “Characterisation of different single and multilayer films using phase modulated spectroscopic ellipsometry,” (Bhabha Atomic Research Centre, Mumbai, India, 1998).

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Figures (5)

Fig. 1
Fig. 1

Ψ and Δ versus wavelength spectra in the wavelength regime 700–1000 nm. Circles, experimental data (Ψ); dashed curve, theoretical spectrum (Ψ); triangles, experimental data (Δ); solid curve, theoretical spectrum (Δ). Inset, best-fit sample structure for the multilayer sample. In this figure and in Fig. 4, A means angstroms.

Fig. 2
Fig. 2

Ψ and Δ versus wavelength spectra in the wavelength regime 280–340 nm. Circles, experimental data (Ψ); dotted–dashed curve, theoretical spectrum (Ψ) with the Sato–Adachi dispersion relation; long-dashed curve, theoretical spectrum (Ψ) with the Forouhi–Bloomer dispersion relation; triangles, experimental data (Δ); short-dashed curve, theoretical spectrum (Δ) with the Sato–Adachi dispersion relation; solid curve, theoretical spectrum (Δ) with the Forouhi–Bloomer dispersion relation.

Fig. 3
Fig. 3

Dispersion of refractive index with wavelength for TiO2 layers obtained from the best-fit parameters of the Forouhi–Bloomer dispersion relation. Inset, variation of absorption coefficient versus photon energy for TiO2 films above the fundamental absorption edge (3.2–4.2 eV) as obtained from the best-fit parameters of the Forouhi–Bloomer dispersion relation.

Fig. 4
Fig. 4

Ψ and Δ versus wavelength spectra in the wavelength regime 400–700 nm: circles, experimental data (Ψ); dashed curve, theoretical spectrum (Ψ); triangles, experimental data (Δ); solid curve, theoretical spectrum (Δ). Inset, best-fit sample as obtained from fitting the ellipsometric data in the wavelength range 400–700 nm.

Fig. 5
Fig. 5

Ψ and Δ versus wavelength spectra in the wavelength regime 280–1000 nm: circles, experimental data (Ψ); dashed curve, theoretical spectrum (Ψ); triangles, experimental data (Δ); solid curve, theoretical spectrum (Δ).

Equations (16)

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

ρ=rp/rs=tan ψ expiΔ,
χ2=1/2N-PiNIsiexp-Isical2+Iciexp-Icical2,
εE=ε+A0Eg-1.5fχ0,
χ0=E+ιΓ/Eg, fχ0=χ0-22-1+χ00.5-1-χ00.5.
εE=n=1Aox/n3Eg-Gox/n2-E-Γ,
αhν  Eg-hν1/2,
nE=ε+b0E+c0/E2-bE+c,
kE=aE-Eg2/E2-bE+c,
bo=a/q-b2/2+Egb-Eg2+c,
co=a/qEg2+cb/2-2Egc,
q=1/24c-b21/2,
ε=5.2, a=0.586, b=7.307 eV, c=13.626 eV2, Eg=3.194 eV.
αhν  Eg-hν2,
ε=5.3, a=0.586, b=7.26 eV, c=13.63 eV2, Eg=3.186 eV.
n2λ=As+Bsλ2/λ2-λ02,
As=5.00, Bs=0.326, λ0=373.366.

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