Abstract

Wavelength dependencies of refractive indices of thin film materials differ for various deposition conditions, and it is practically impossible to attribute a single refractive index wavelength dependence to any typical thin film material. Besides objective reasons, differences in the optical parameters of thin films may also be connected with nonadequate choices of models and algorithms used for the processing of measurement data. The main goal of this paper is to present reliable wavelength dependencies of refractive indices of the most widely used slightly absorbing oxide thin film materials. These dependencies can be used by other researchers for comparison and verification of their own characterization results.

© 2011 Optical Society of America

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References

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  1. A. Duparré and D. Ristau, “2004 Topical Meeting on Optical Interference Coatings: Measurement Problem,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2004), paper WD1.
  2. A. Duparré and D. Ristau, “Optical Interference Coatings 2007 Measurement Problem,” Appl. Opt. 47, C179–C184(2008).
    [CrossRef] [PubMed]
  3. A. Duparré and D. Ristau, “2010 OSA Topical Meeting on Optical Interference Coatings: Measurement Problem,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2010), paper ThC1.
  4. M. Friz and F. Waibel, “Coating materials,” in N.Kaiser and H.K.Pulker, eds., Optical Interference Coatings (Springer-Verlag, 2003), pp. 105–130.
  5. B. T. Sullivan and J. A. Dobrowolski, “Deposition error compensation for optical multilayer coatings. I. theoretical description,” Appl. Opt. 31, 3821–3835 (1992).
    [CrossRef] [PubMed]
  6. D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Opt. 23, 3571–3596 (1984).
    [CrossRef] [PubMed]
  7. J. A. Dobrowolski, F. C. Ho, and A. Waldorf, “Determination of optical constants of thin film coating materials based on inverse synthesis,” Appl. Opt. 22, 3191–3200 (1983).
    [CrossRef] [PubMed]
  8. W. E. Case, “Algebraic method for extracting thin-film optical parameters from spectrophotometer measurements,” Appl. Opt. 22, 1832–1836 (1983).
    [CrossRef] [PubMed]
  9. L. Vriens and W. Rippens, “Optical constants of absorbing thin solid films on a substrate,” Appl. Opt. 22, 4105–4110 (1983).
    [CrossRef] [PubMed]
  10. R. C. McPhedran, L. C. Botten, D. R. McKenzie, and R. P. Netterfield, “Unambiguous determination of optical constants of absorbing films by reflectance and transmittance measurements,” Appl. Opt. 23, 1197–1205 (1984).
    [CrossRef] [PubMed]
  11. T. C. Paulick, “Inversion of normal-incidence (R,T) measurements to obtain n+ik for thin films,” Appl. Opt. 25, 562–564 (1986).
    [CrossRef] [PubMed]
  12. J. P. Borgogno, P. Bousquet, F. Flory, B. Lazarides, E. Pelletier, and P. Roche, “Inhomogeneity in films: limitation of the accuracy of optical monitoring of thin films,” Appl. Opt. 20, 90–94 (1981).
    [CrossRef] [PubMed]
  13. J. P. Borgogno, B. Lazarides, and E. Pelletier, “Automatic determination of optical constants of inhomogeneous thin films,” Appl. Opt. 21, 4020–4029 (1982).
    [CrossRef] [PubMed]
  14. J. P. Borgogno, F. Flory, P. Roche, B. Schmitt, G. Albrand, E. Pelletier, and H. A. Macleod, “Refractive index and inhomogeneity of thin films,” Appl. Opt. 23, 3567–3570 (1984).
    [CrossRef] [PubMed]
  15. A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, and J. A. Dobrowolski, “Influence of small inhomogeneities on the spectral characteristics of single thin films,” Appl. Opt. 36, 7188–7199 (1997).
    [CrossRef]
  16. T. Babeva, S. Kitova, and I. Konstantinov, “Photometric methods for determining the optical constants and the thicknesses of thin absorbing films: selection of a combination of photometric quantities on the basis of error analysis,” Appl. Opt. 40, 2675–2681 (2001).
    [CrossRef]
  17. A. Tikhonravov, M. Trubetskov, and G. DeBell, “On the accuracy of optical thin film parameter determination based on spectrophotometric data,” Proc. SPIE 5188, 190–199 (2003).
    [CrossRef]
  18. A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Gunster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE 5188, 331–342 (2003).
    [CrossRef]
  19. A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555–2560 (2002).
    [CrossRef] [PubMed]
  20. H. Schröder, “Bemerkung zur Theorie des Lichtdurchgangs durch Inhomogene durchsichtige Schichten,” Ann. Phys. 39, 55–58 (1941).
    [CrossRef]
  21. C. K. Carniglia, “Ellipsometric calculations for nonabsorbing thin films with linear refractive-index gradients,” J. Opt. Soc. Am. A 7, 848–856 (1990).
    [CrossRef]
  22. G. Koppelmann and K. Krebs, “Die Optischen Eigenschaften Dielektrischer Schichten mit Kleinen Homogenitatsstorungen,” Z. Phys. D 164, 539–556 (1961).
  23. A. V. Tikhonravov, M. K. Trubetskov, A. A. Tikhonravov, and A. Duparre, “Effects of interface roughness on the spectral properties of thin films and multilayers,” Appl. Opt. 42, 5140–5148 (2003).
    [CrossRef] [PubMed]
  24. J. Ferre-Borrull, A. Duparré, and E. Quesnel, “Procedure to characterize microroughness of optical thin films: application to ion-beam-sputtered vacuum-ultraviolet coatings,” Appl. Opt. 40, 2190–2199 (2001).
    [CrossRef]
  25. A. Duparré, J. Ferre-Borrull, S. Gliech, G. Notni, J. Steinert, and J. M. Bennett, “Surface characterization techniques for determining the root-mean-square roughness and power spectral densities of optical components,” Appl. Opt. 41, 154–171 (2002).
    [CrossRef] [PubMed]
  26. F. Lemarchand, C. Deumié, M. Zerrad, L. Abel-Tiberini, B. Bertussi, G. Georges, B. Lazaridès, M. Cathelinaud, M. Lequime, and C. Amra, “Optical characterization of an unknown single layer: Institut Fresnel contribution to the Optical Interference Coatings 2004 Topical Meeting Measurement Problem,” Appl. Opt. 45, 1312–1318 (2006).
    [CrossRef] [PubMed]
  27. A. V. Tikhonravov and M. K. Trubetskov, OptiChar software, http://www.optilayer.com.
  28. A. V. Tikhonravov, M. K. Trubetskov, G. Clark, B. T. Sullivan, and J. A. Dobrowolski, “Ellipsometric study of optical properties and small inhomogeneities of Nb2O5 films,” Proc. SPIE 3738, 183–187 (1999).
    [CrossRef]
  29. A. V. Tikhonravov, M. K. Trubetskov, and A. V. Krasilnikova, “Spectroscopic ellipsometry of slightly inhomogeneous non-absorbing thin films with arbitrary refractive index profiles: theoretical study,” Appl. Opt. 37, 5902–5911 (1998).
    [CrossRef]

2008 (1)

2006 (1)

2003 (3)

A. V. Tikhonravov, M. K. Trubetskov, A. A. Tikhonravov, and A. Duparre, “Effects of interface roughness on the spectral properties of thin films and multilayers,” Appl. Opt. 42, 5140–5148 (2003).
[CrossRef] [PubMed]

A. Tikhonravov, M. Trubetskov, and G. DeBell, “On the accuracy of optical thin film parameter determination based on spectrophotometric data,” Proc. SPIE 5188, 190–199 (2003).
[CrossRef]

A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Gunster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE 5188, 331–342 (2003).
[CrossRef]

2002 (2)

2001 (2)

1999 (1)

A. V. Tikhonravov, M. K. Trubetskov, G. Clark, B. T. Sullivan, and J. A. Dobrowolski, “Ellipsometric study of optical properties and small inhomogeneities of Nb2O5 films,” Proc. SPIE 3738, 183–187 (1999).
[CrossRef]

1998 (1)

1997 (1)

1992 (1)

1990 (1)

1986 (1)

1984 (3)

1983 (3)

1982 (1)

1981 (1)

1961 (1)

G. Koppelmann and K. Krebs, “Die Optischen Eigenschaften Dielektrischer Schichten mit Kleinen Homogenitatsstorungen,” Z. Phys. D 164, 539–556 (1961).

1941 (1)

H. Schröder, “Bemerkung zur Theorie des Lichtdurchgangs durch Inhomogene durchsichtige Schichten,” Ann. Phys. 39, 55–58 (1941).
[CrossRef]

Abel-Tiberini, L.

Albrand, G.

Amotchkina, T.

A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Gunster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE 5188, 331–342 (2003).
[CrossRef]

Amotchkina, T. V.

Amra, C.

Arndt, D. P.

Azzam, R. M. A.

Babeva, T.

Bennett, J. M.

Bertussi, B.

Borgogno, J. P.

Botten, L. C.

Bousquet, P.

Carniglia, C. K.

Case, W. E.

Cathelinaud, M.

Clark, G.

A. V. Tikhonravov, M. K. Trubetskov, G. Clark, B. T. Sullivan, and J. A. Dobrowolski, “Ellipsometric study of optical properties and small inhomogeneities of Nb2O5 films,” Proc. SPIE 3738, 183–187 (1999).
[CrossRef]

DeBell, G.

A. Tikhonravov, M. Trubetskov, and G. DeBell, “On the accuracy of optical thin film parameter determination based on spectrophotometric data,” Proc. SPIE 5188, 190–199 (2003).
[CrossRef]

Deumié, C.

Dobrowolski, J. A.

Duparre, A.

Duparré, A.

Ferre-Borrull, J.

Flory, F.

Friz, M.

M. Friz and F. Waibel, “Coating materials,” in N.Kaiser and H.K.Pulker, eds., Optical Interference Coatings (Springer-Verlag, 2003), pp. 105–130.

Georges, G.

Gibson, U. J.

Gliech, S.

Gunster, S.

A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Gunster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE 5188, 331–342 (2003).
[CrossRef]

Günster, S.

Ho, F. C.

Hodgkin, V. A.

Kitova, S.

Klapp, W. P.

Kokarev, M. A.

Konstantinov, I.

Koppelmann, G.

G. Koppelmann and K. Krebs, “Die Optischen Eigenschaften Dielektrischer Schichten mit Kleinen Homogenitatsstorungen,” Z. Phys. D 164, 539–556 (1961).

Krasilnikova, A. V.

Krebs, K.

G. Koppelmann and K. Krebs, “Die Optischen Eigenschaften Dielektrischer Schichten mit Kleinen Homogenitatsstorungen,” Z. Phys. D 164, 539–556 (1961).

Lazarides, B.

Lazaridès, B.

Lemarchand, F.

Lequime, M.

Macleod, H. A.

McKenzie, D. R.

McPhedran, R. C.

Netterfield, R. P.

Notni, G.

Paulick, T. C.

Pelletier, E.

Purvis, M. K.

Quesnel, E.

Quinn, D. M.

Rippens, W.

Ristau, D.

A. Duparré and D. Ristau, “Optical Interference Coatings 2007 Measurement Problem,” Appl. Opt. 47, C179–C184(2008).
[CrossRef] [PubMed]

A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Gunster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE 5188, 331–342 (2003).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555–2560 (2002).
[CrossRef] [PubMed]

A. Duparré and D. Ristau, “2010 OSA Topical Meeting on Optical Interference Coatings: Measurement Problem,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2010), paper ThC1.

A. Duparré and D. Ristau, “2004 Topical Meeting on Optical Interference Coatings: Measurement Problem,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2004), paper WD1.

Roche, P.

Schmitt, B.

Schröder, H.

H. Schröder, “Bemerkung zur Theorie des Lichtdurchgangs durch Inhomogene durchsichtige Schichten,” Ann. Phys. 39, 55–58 (1941).
[CrossRef]

Steinert, J.

Strome, D. H.

Sullivan, B. T.

Swenson, R.

Temple, P. A.

Thonn, T. F.

Tikhonravov, A.

A. Tikhonravov, M. Trubetskov, and G. DeBell, “On the accuracy of optical thin film parameter determination based on spectrophotometric data,” Proc. SPIE 5188, 190–199 (2003).
[CrossRef]

A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Gunster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE 5188, 331–342 (2003).
[CrossRef]

A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Gunster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE 5188, 331–342 (2003).
[CrossRef]

Tikhonravov, A. A.

Tikhonravov, A. V.

Trubetskov, M.

A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Gunster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE 5188, 331–342 (2003).
[CrossRef]

A. Tikhonravov, M. Trubetskov, and G. DeBell, “On the accuracy of optical thin film parameter determination based on spectrophotometric data,” Proc. SPIE 5188, 190–199 (2003).
[CrossRef]

Trubetskov, M. K.

Tuttle Hart, T.

Vriens, L.

Waibel, F.

M. Friz and F. Waibel, “Coating materials,” in N.Kaiser and H.K.Pulker, eds., Optical Interference Coatings (Springer-Verlag, 2003), pp. 105–130.

Waldorf, A.

Zerrad, M.

Ann. Phys. (1)

H. Schröder, “Bemerkung zur Theorie des Lichtdurchgangs durch Inhomogene durchsichtige Schichten,” Ann. Phys. 39, 55–58 (1941).
[CrossRef]

Appl. Opt. (19)

J. P. Borgogno, P. Bousquet, F. Flory, B. Lazarides, E. Pelletier, and P. Roche, “Inhomogeneity in films: limitation of the accuracy of optical monitoring of thin films,” Appl. Opt. 20, 90–94 (1981).
[CrossRef] [PubMed]

J. P. Borgogno, B. Lazarides, and E. Pelletier, “Automatic determination of optical constants of inhomogeneous thin films,” Appl. Opt. 21, 4020–4029 (1982).
[CrossRef] [PubMed]

W. E. Case, “Algebraic method for extracting thin-film optical parameters from spectrophotometer measurements,” Appl. Opt. 22, 1832–1836 (1983).
[CrossRef] [PubMed]

J. A. Dobrowolski, F. C. Ho, and A. Waldorf, “Determination of optical constants of thin film coating materials based on inverse synthesis,” Appl. Opt. 22, 3191–3200 (1983).
[CrossRef] [PubMed]

L. Vriens and W. Rippens, “Optical constants of absorbing thin solid films on a substrate,” Appl. Opt. 22, 4105–4110 (1983).
[CrossRef] [PubMed]

R. C. McPhedran, L. C. Botten, D. R. McKenzie, and R. P. Netterfield, “Unambiguous determination of optical constants of absorbing films by reflectance and transmittance measurements,” Appl. Opt. 23, 1197–1205 (1984).
[CrossRef] [PubMed]

J. P. Borgogno, F. Flory, P. Roche, B. Schmitt, G. Albrand, E. Pelletier, and H. A. Macleod, “Refractive index and inhomogeneity of thin films,” Appl. Opt. 23, 3567–3570 (1984).
[CrossRef] [PubMed]

D. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, “Multiple determination of the optical constants of thin-film coating materials,” Appl. Opt. 23, 3571–3596 (1984).
[CrossRef] [PubMed]

T. C. Paulick, “Inversion of normal-incidence (R,T) measurements to obtain n+ik for thin films,” Appl. Opt. 25, 562–564 (1986).
[CrossRef] [PubMed]

B. T. Sullivan and J. A. Dobrowolski, “Deposition error compensation for optical multilayer coatings. I. theoretical description,” Appl. Opt. 31, 3821–3835 (1992).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, and J. A. Dobrowolski, “Influence of small inhomogeneities on the spectral characteristics of single thin films,” Appl. Opt. 36, 7188–7199 (1997).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, and A. V. Krasilnikova, “Spectroscopic ellipsometry of slightly inhomogeneous non-absorbing thin films with arbitrary refractive index profiles: theoretical study,” Appl. Opt. 37, 5902–5911 (1998).
[CrossRef]

J. Ferre-Borrull, A. Duparré, and E. Quesnel, “Procedure to characterize microroughness of optical thin films: application to ion-beam-sputtered vacuum-ultraviolet coatings,” Appl. Opt. 40, 2190–2199 (2001).
[CrossRef]

T. Babeva, S. Kitova, and I. Konstantinov, “Photometric methods for determining the optical constants and the thicknesses of thin absorbing films: selection of a combination of photometric quantities on the basis of error analysis,” Appl. Opt. 40, 2675–2681 (2001).
[CrossRef]

A. Duparré, J. Ferre-Borrull, S. Gliech, G. Notni, J. Steinert, and J. M. Bennett, “Surface characterization techniques for determining the root-mean-square roughness and power spectral densities of optical components,” Appl. Opt. 41, 154–171 (2002).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555–2560 (2002).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, A. A. Tikhonravov, and A. Duparre, “Effects of interface roughness on the spectral properties of thin films and multilayers,” Appl. Opt. 42, 5140–5148 (2003).
[CrossRef] [PubMed]

F. Lemarchand, C. Deumié, M. Zerrad, L. Abel-Tiberini, B. Bertussi, G. Georges, B. Lazaridès, M. Cathelinaud, M. Lequime, and C. Amra, “Optical characterization of an unknown single layer: Institut Fresnel contribution to the Optical Interference Coatings 2004 Topical Meeting Measurement Problem,” Appl. Opt. 45, 1312–1318 (2006).
[CrossRef] [PubMed]

A. Duparré and D. Ristau, “Optical Interference Coatings 2007 Measurement Problem,” Appl. Opt. 47, C179–C184(2008).
[CrossRef] [PubMed]

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

Proc. SPIE (3)

A. V. Tikhonravov, M. K. Trubetskov, G. Clark, B. T. Sullivan, and J. A. Dobrowolski, “Ellipsometric study of optical properties and small inhomogeneities of Nb2O5 films,” Proc. SPIE 3738, 183–187 (1999).
[CrossRef]

A. Tikhonravov, M. Trubetskov, and G. DeBell, “On the accuracy of optical thin film parameter determination based on spectrophotometric data,” Proc. SPIE 5188, 190–199 (2003).
[CrossRef]

A. Tikhonravov, M. Trubetskov, T. Amotchkina, A. Tikhonravov, D. Ristau, and S. Gunster, “Reliable determination of wavelength dependence of thin film refractive index,” Proc. SPIE 5188, 331–342 (2003).
[CrossRef]

Z. Phys. D (1)

G. Koppelmann and K. Krebs, “Die Optischen Eigenschaften Dielektrischer Schichten mit Kleinen Homogenitatsstorungen,” Z. Phys. D 164, 539–556 (1961).

Other (4)

A. V. Tikhonravov and M. K. Trubetskov, OptiChar software, http://www.optilayer.com.

A. Duparré and D. Ristau, “2004 Topical Meeting on Optical Interference Coatings: Measurement Problem,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2004), paper WD1.

A. Duparré and D. Ristau, “2010 OSA Topical Meeting on Optical Interference Coatings: Measurement Problem,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2010), paper ThC1.

M. Friz and F. Waibel, “Coating materials,” in N.Kaiser and H.K.Pulker, eds., Optical Interference Coatings (Springer-Verlag, 2003), pp. 105–130.

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Figures (20)

Fig. 1
Fig. 1

Schematic of a slightly inhomogeneous dielectric thin film.

Fig. 2
Fig. 2

Shifts of transmittance maxima from the transmittance of the uncoated substrate in the case of n > n s and positive film inhomogeneity (a model niobium pentoxide film with physical thickness of 400 nm on quartz substrate is used as an example): solid curve, transmittance of a homogeneous film; dashed curve, transmittance in the case of δ = 3 % ; and dotted curve, transmittance of the uncoated substrate.

Fig. 3
Fig. 3

Shifts of transmittance minima from the transmittance of the uncoated substrate in the case of n < n s and positive film inhomogeneity (a model silicon dioxide film with physical thickness of 400 nm on BK7 substrate is used as an example): solid curve, transmittance of a homogeneous film; dashed curve, transmittance in the case of δ = 3 % ; and dotted curve, transmittance of the uncoated substrate.

Fig. 4
Fig. 4

Reflectance and transmittance of the HfO 2 sample on a fused silica substrate at 8 ° in the 200 to 1600 nm spectral region.

Fig. 5
Fig. 5

Total losses in the film and substrate in the spectral region from 225 to 1600 nm .

Fig. 6
Fig. 6

Comparison of measured reflectance and transmittance data in the 225 to 800 nm spectral region with reflectance and transmittance of the uncoated fused silica substrate.

Fig. 7
Fig. 7

Fitting of measured reflectance and transmittance data in the 225 to 800 nm spectral region (gray crosses) by model reflectance and transmittance (solid curves) at the end of the discrepancy function minimization: absorbing model of HfO 2 film.

Fig. 8
Fig. 8

Wavelength dependencies of the refractive index (solid curve) and extinction coefficient (dashed curve) of the HfO 2 film found in the frame of the absorbing thin film model based on R and T data.

Fig. 9
Fig. 9

Fitting of measured reflectance data (gray crosses) by model reflectance (solid curve) at the end of discrepancy function minimization: nonabsorbing model of HfO 2 film.

Fig. 10
Fig. 10

Wavelength dependencies of the refractive index of HfO 2 film found in the frame of nonabsorbing thin film model based on R data (solid curve). Dashed curve shows the wavelength dependence found in the frame of the absorbing model based on R and T data.

Fig. 11
Fig. 11

Transmittance of the niobium pentoxide film on the fused silica substrate (gray crosses) and transmittance of the uncoated substrate (solid curve).

Fig. 12
Fig. 12

Fitting of measured transmittance data (gray crosses) by model transmittance (solid curve) obtained in the frame of the inhomogeneous model of Nb 2 O 5 film.

Fig. 13
Fig. 13

Wavelength dependence of the refractive index of the Nb 2 O 5 film found in the frame of the inhomogeneous thin film model (solid curve). The dashed curve shows the wavelength dependence of the refractive index of Nb 2 O 5 from Ref. [28].

Fig. 14
Fig. 14

Refractive indices of HfO 2 films produced by ion beam sputtering (solid curve), RF sputtering (dotted curve), and APS technology (gray curve).

Fig. 15
Fig. 15

Refractive indices of Nb 2 O 5 films produced by ion beam sputtering (solid curve), ac magnetron sputtering (dotted curve), and magnetron sputtering in the Helios coater (gray curve): note that the second and third dependencies are almost undistinguished.

Fig. 16
Fig. 16

Refractive indices of Ta 2 O 5 films produced by ion beam sputtering (solid curve), magnetron sputtering in the Helios coater (dotted curve), and RF magnetron sputtering (gray curve).

Fig. 17
Fig. 17

Refractive indices of SiO 2 films produced by ion beam sputtering (solid curve) and magnetron sputtering in the Helios coater (dotted curve).

Fig. 18
Fig. 18

Refractive indices of Al 2 O 3 films produced by ion beam sputtering (solid curve) and RF sputtering (dotted curve).

Fig. 19
Fig. 19

Refractive indices of TiO 2 films produced by ion beam sputtering (solid curve) and electron beam evaporation (dotted curve).

Fig. 20
Fig. 20

Extinction coefficients of HfO 2 films produced by APS technology, RF sputtering, and ion beam sputtering of Al 2 O 3 film produced by RF sputtering and of TiO 2 film produced by ion beam sputtering.

Tables (1)

Tables Icon

Table 1 Summary of Information Related to the Thin Film Samples Whose Refractive Index Wavelength Dependencies Are Presented in Figs. 14, 15, 16, 17, 18, 19

Equations (6)

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

δ = n o n i n ,
r = [ ( n a n s ) δ 2 ( n a + n s ) ] cos φ + i ( n a n s n n ) sin φ [ ( n a + n s ) δ 2 ( n a n s ) ] cos φ + i ( n a n s n + n ) sin φ .
δ T = 4 n a n s ( n a n s ) ( n a + n s ) 3 δ .
n ( λ ) = n + A λ 2 + B λ 4 , k ( λ ) = B 0 exp ( B 1 / λ B 2 λ ) .
n ( z , λ ) = q ( z ) n ( λ ) ,
q ( z ) = 1 + δ ( z / h 1 / 2 ) ,

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