Abstract

The optical constants of MgF2 (bulk) and BaF2, CaF2, LaF3, MgF2, Al2O3, HfO2, and SiO2 films deposited on MgF2 substrates are determined from photometric measurements through an iteration process of matching calculated and measured values of the reflectance and transmittance in the 120–230-nm vacuum ultraviolet wavelength region. The potential use of the listed fluorides and oxides as vacuum ultraviolet coating materials is discussed in part 2 of this paper.

© 1990 Optical Society of America

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References

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  1. E. T. Hutcheson, G. Hass, J. T. Cox, “Effect of Deposition Rate and Substrate Temperature on the Vacuum Ultraviolet Reflectance of MgF2- and LiF-Overcoated Aluminum Mirrors,” Appl. Opt. 11, 2245–2248 (1972).
    [CrossRef] [PubMed]
  2. T. T. Coleand, F. Oppenheimer, “Polarization by Reflection and Some Optical Constants in the Extreme Ultraviolet,” Appl. Opt. 1, 709–710 (1962).
    [CrossRef]
  3. G. Stephan, Y. Le Calvez, J. C. Lemonier, Mme S. Robin, “Properties optiques et spectre electronique du MgF2 et du CaF2 de 10 à 48 eV,” J. Phys. Chem. Solids 30, 601–608 (1969).
    [CrossRef]
  4. A. S. Barriere, A. Lachter, “Optical Transitions in Disordered Thin FIlms of the Ionic Compounds MgF2 and AlF3 as a Function of Their Conditions of Preparation,” Appl. Opt. 16, 2865–2871 (1977).
    [CrossRef] [PubMed]
  5. B. Vodar, “Absorption Spectra of Gases and Absorption and Reflection Spectra of Solids,” (A review of work at Bellevue), J. Quant. Spectrosc. Radiat. Transfer 2, 393–412 (1962).
    [CrossRef]
  6. M. W. Williams, R. A. MacRae, E. T. Arakawa, “Optical Properties of Magnesium Fluoride in the Vacuum Ultraviolet,” J. Appl. Phys. 38, 1701–1705 (1967).
    [CrossRef]
  7. O. R. Wood, H. G. Craighead, J. E. Sweeney, P. J. Maloney, “Vacuum Ultraviolet Loss in Magnesium Fluoride Films,” Appl. Opt. 23, 3644–3649 (1984).
    [CrossRef] [PubMed]
  8. A. Bideau-Mehu, Y. Guern, R. Abjean, “Influence of the Optical Constants on Fabry-Perot Coatings Characteristics in the Vacuum Ultraviolet Wavelength Range,” in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1984), pp. 265–267.
  9. E. Spiller, “Interference Filters for the Ultraviolet and the Surface Plasmon of Aluminum,” Appl. Opt. 13, 1209–1225(1974).
    [CrossRef] [PubMed]
  10. L. J. Lingg, J. D. Targove, J. P. Lehan, H. A. Macleod, “Ion-Assisted Deposition of Lanthanide Trifluorides for VUV Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 818, 86–92 (1987).
  11. O. S. Heavens, “Measurement of Optical Constants of Thin Films,” Phys. Thin Films 2, 193–238 (1964).
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 611.
  13. D. P. Arndt et al., “Multiple Determination of the Optical Constants of Thin-Film Coating Materials,” Appl. Opt. 23, 3571–3596 (1984).
    [CrossRef] [PubMed]
  14. J. M. Bennett, M. J. Booty, “Computational Method for Determining n and k for a Thin Film from the Measured Reflectance, Transmittance, and Film Thickness,” Appl. Opt. 5, 41–43 (1966).
    [CrossRef] [PubMed]
  15. J. M. Bennett, M. J. Booty, “Computer Program for Determining Optical Constants of a Film on an Opaque Substrate,” Appl. Opt. 8, 2366–2368 (1969).
    [CrossRef] [PubMed]
  16. W. N. Hansen, “Optical Characterization of Thin Films: Theory,” J. Opt. Soc. Am. 63, 793–801 (1973).
    [CrossRef]
  17. L. Ward, “A Survey of the Accuracies of Some Methods for the Determination of the Optical Constants of Thin Films,” Opt. Acta 32, 155–167 (1985).
    [CrossRef]
  18. M. C. Gupta, “Optical Constant Determination of Thin Films,” Appl. Opt. 27, 954–956 (1988).
    [CrossRef] [PubMed]
  19. F. Abeles, “Methods for Determining Optical Parameters of Thin Films,” Prog. Opt. 2, 249–288 (1963).
    [CrossRef]
  20. P. O. Nilsson, “Determination of Optical Constants from Intensity Measurements at Normal Incidence,” Appl. Opt. 7, 435–442 (1968).
    [CrossRef] [PubMed]
  21. M. Zukic, “Damped Least Squares Technique for the Design of Optical Multilayer Filters,” M.S. Thesis, Imperial College, London (1984).
  22. J. M. Bennett, “Scattering and Surface Evaluation Techniques for the Optics of the Future,” Opt. News 7, 17–27 (1985).
    [CrossRef]
  23. J. M. Zwiner, “Space Station Induced Environment Monitoring,” NASA Conference Publication 3021.
  24. H. R. Philipp, “Silicon Dioxide (SiO2) (Glass),” in Handbook of Optical Constants of Solids, E. D. Palik, Ed. (Academic, Orlando, FL, 1985), p. 749.

1988 (1)

1987 (1)

L. J. Lingg, J. D. Targove, J. P. Lehan, H. A. Macleod, “Ion-Assisted Deposition of Lanthanide Trifluorides for VUV Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 818, 86–92 (1987).

1985 (2)

L. Ward, “A Survey of the Accuracies of Some Methods for the Determination of the Optical Constants of Thin Films,” Opt. Acta 32, 155–167 (1985).
[CrossRef]

J. M. Bennett, “Scattering and Surface Evaluation Techniques for the Optics of the Future,” Opt. News 7, 17–27 (1985).
[CrossRef]

1984 (2)

1977 (1)

1974 (1)

1973 (1)

1972 (1)

1969 (2)

G. Stephan, Y. Le Calvez, J. C. Lemonier, Mme S. Robin, “Properties optiques et spectre electronique du MgF2 et du CaF2 de 10 à 48 eV,” J. Phys. Chem. Solids 30, 601–608 (1969).
[CrossRef]

J. M. Bennett, M. J. Booty, “Computer Program for Determining Optical Constants of a Film on an Opaque Substrate,” Appl. Opt. 8, 2366–2368 (1969).
[CrossRef] [PubMed]

1968 (1)

1967 (1)

M. W. Williams, R. A. MacRae, E. T. Arakawa, “Optical Properties of Magnesium Fluoride in the Vacuum Ultraviolet,” J. Appl. Phys. 38, 1701–1705 (1967).
[CrossRef]

1966 (1)

1964 (1)

O. S. Heavens, “Measurement of Optical Constants of Thin Films,” Phys. Thin Films 2, 193–238 (1964).

1963 (1)

F. Abeles, “Methods for Determining Optical Parameters of Thin Films,” Prog. Opt. 2, 249–288 (1963).
[CrossRef]

1962 (2)

T. T. Coleand, F. Oppenheimer, “Polarization by Reflection and Some Optical Constants in the Extreme Ultraviolet,” Appl. Opt. 1, 709–710 (1962).
[CrossRef]

B. Vodar, “Absorption Spectra of Gases and Absorption and Reflection Spectra of Solids,” (A review of work at Bellevue), J. Quant. Spectrosc. Radiat. Transfer 2, 393–412 (1962).
[CrossRef]

Abeles, F.

F. Abeles, “Methods for Determining Optical Parameters of Thin Films,” Prog. Opt. 2, 249–288 (1963).
[CrossRef]

Abjean, R.

A. Bideau-Mehu, Y. Guern, R. Abjean, “Influence of the Optical Constants on Fabry-Perot Coatings Characteristics in the Vacuum Ultraviolet Wavelength Range,” in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1984), pp. 265–267.

Arakawa, E. T.

M. W. Williams, R. A. MacRae, E. T. Arakawa, “Optical Properties of Magnesium Fluoride in the Vacuum Ultraviolet,” J. Appl. Phys. 38, 1701–1705 (1967).
[CrossRef]

Arndt, D. P.

Barriere, A. S.

Bennett, J. M.

Bideau-Mehu, A.

A. Bideau-Mehu, Y. Guern, R. Abjean, “Influence of the Optical Constants on Fabry-Perot Coatings Characteristics in the Vacuum Ultraviolet Wavelength Range,” in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1984), pp. 265–267.

Booty, M. J.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 611.

Coleand, T. T.

Cox, J. T.

Craighead, H. G.

Guern, Y.

A. Bideau-Mehu, Y. Guern, R. Abjean, “Influence of the Optical Constants on Fabry-Perot Coatings Characteristics in the Vacuum Ultraviolet Wavelength Range,” in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1984), pp. 265–267.

Gupta, M. C.

Hansen, W. N.

Hass, G.

Heavens, O. S.

O. S. Heavens, “Measurement of Optical Constants of Thin Films,” Phys. Thin Films 2, 193–238 (1964).

Hutcheson, E. T.

Lachter, A.

Le Calvez, Y.

G. Stephan, Y. Le Calvez, J. C. Lemonier, Mme S. Robin, “Properties optiques et spectre electronique du MgF2 et du CaF2 de 10 à 48 eV,” J. Phys. Chem. Solids 30, 601–608 (1969).
[CrossRef]

Lehan, J. P.

L. J. Lingg, J. D. Targove, J. P. Lehan, H. A. Macleod, “Ion-Assisted Deposition of Lanthanide Trifluorides for VUV Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 818, 86–92 (1987).

Lemonier, J. C.

G. Stephan, Y. Le Calvez, J. C. Lemonier, Mme S. Robin, “Properties optiques et spectre electronique du MgF2 et du CaF2 de 10 à 48 eV,” J. Phys. Chem. Solids 30, 601–608 (1969).
[CrossRef]

Lingg, L. J.

L. J. Lingg, J. D. Targove, J. P. Lehan, H. A. Macleod, “Ion-Assisted Deposition of Lanthanide Trifluorides for VUV Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 818, 86–92 (1987).

Macleod, H. A.

L. J. Lingg, J. D. Targove, J. P. Lehan, H. A. Macleod, “Ion-Assisted Deposition of Lanthanide Trifluorides for VUV Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 818, 86–92 (1987).

MacRae, R. A.

M. W. Williams, R. A. MacRae, E. T. Arakawa, “Optical Properties of Magnesium Fluoride in the Vacuum Ultraviolet,” J. Appl. Phys. 38, 1701–1705 (1967).
[CrossRef]

Maloney, P. J.

Nilsson, P. O.

Oppenheimer, F.

Philipp, H. R.

H. R. Philipp, “Silicon Dioxide (SiO2) (Glass),” in Handbook of Optical Constants of Solids, E. D. Palik, Ed. (Academic, Orlando, FL, 1985), p. 749.

Robin, Mme S.

G. Stephan, Y. Le Calvez, J. C. Lemonier, Mme S. Robin, “Properties optiques et spectre electronique du MgF2 et du CaF2 de 10 à 48 eV,” J. Phys. Chem. Solids 30, 601–608 (1969).
[CrossRef]

Spiller, E.

Stephan, G.

G. Stephan, Y. Le Calvez, J. C. Lemonier, Mme S. Robin, “Properties optiques et spectre electronique du MgF2 et du CaF2 de 10 à 48 eV,” J. Phys. Chem. Solids 30, 601–608 (1969).
[CrossRef]

Sweeney, J. E.

Targove, J. D.

L. J. Lingg, J. D. Targove, J. P. Lehan, H. A. Macleod, “Ion-Assisted Deposition of Lanthanide Trifluorides for VUV Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 818, 86–92 (1987).

Vodar, B.

B. Vodar, “Absorption Spectra of Gases and Absorption and Reflection Spectra of Solids,” (A review of work at Bellevue), J. Quant. Spectrosc. Radiat. Transfer 2, 393–412 (1962).
[CrossRef]

Ward, L.

L. Ward, “A Survey of the Accuracies of Some Methods for the Determination of the Optical Constants of Thin Films,” Opt. Acta 32, 155–167 (1985).
[CrossRef]

Williams, M. W.

M. W. Williams, R. A. MacRae, E. T. Arakawa, “Optical Properties of Magnesium Fluoride in the Vacuum Ultraviolet,” J. Appl. Phys. 38, 1701–1705 (1967).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 611.

Wood, O. R.

Zukic, M.

M. Zukic, “Damped Least Squares Technique for the Design of Optical Multilayer Filters,” M.S. Thesis, Imperial College, London (1984).

Zwiner, J. M.

J. M. Zwiner, “Space Station Induced Environment Monitoring,” NASA Conference Publication 3021.

Appl. Opt. (10)

E. T. Hutcheson, G. Hass, J. T. Cox, “Effect of Deposition Rate and Substrate Temperature on the Vacuum Ultraviolet Reflectance of MgF2- and LiF-Overcoated Aluminum Mirrors,” Appl. Opt. 11, 2245–2248 (1972).
[CrossRef] [PubMed]

T. T. Coleand, F. Oppenheimer, “Polarization by Reflection and Some Optical Constants in the Extreme Ultraviolet,” Appl. Opt. 1, 709–710 (1962).
[CrossRef]

A. S. Barriere, A. Lachter, “Optical Transitions in Disordered Thin FIlms of the Ionic Compounds MgF2 and AlF3 as a Function of Their Conditions of Preparation,” Appl. Opt. 16, 2865–2871 (1977).
[CrossRef] [PubMed]

O. R. Wood, H. G. Craighead, J. E. Sweeney, P. J. Maloney, “Vacuum Ultraviolet Loss in Magnesium Fluoride Films,” Appl. Opt. 23, 3644–3649 (1984).
[CrossRef] [PubMed]

E. Spiller, “Interference Filters for the Ultraviolet and the Surface Plasmon of Aluminum,” Appl. Opt. 13, 1209–1225(1974).
[CrossRef] [PubMed]

D. P. Arndt et al., “Multiple Determination of the Optical Constants of Thin-Film Coating Materials,” Appl. Opt. 23, 3571–3596 (1984).
[CrossRef] [PubMed]

J. M. Bennett, M. J. Booty, “Computational Method for Determining n and k for a Thin Film from the Measured Reflectance, Transmittance, and Film Thickness,” Appl. Opt. 5, 41–43 (1966).
[CrossRef] [PubMed]

J. M. Bennett, M. J. Booty, “Computer Program for Determining Optical Constants of a Film on an Opaque Substrate,” Appl. Opt. 8, 2366–2368 (1969).
[CrossRef] [PubMed]

M. C. Gupta, “Optical Constant Determination of Thin Films,” Appl. Opt. 27, 954–956 (1988).
[CrossRef] [PubMed]

P. O. Nilsson, “Determination of Optical Constants from Intensity Measurements at Normal Incidence,” Appl. Opt. 7, 435–442 (1968).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

M. W. Williams, R. A. MacRae, E. T. Arakawa, “Optical Properties of Magnesium Fluoride in the Vacuum Ultraviolet,” J. Appl. Phys. 38, 1701–1705 (1967).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Chem. Solids (1)

G. Stephan, Y. Le Calvez, J. C. Lemonier, Mme S. Robin, “Properties optiques et spectre electronique du MgF2 et du CaF2 de 10 à 48 eV,” J. Phys. Chem. Solids 30, 601–608 (1969).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

B. Vodar, “Absorption Spectra of Gases and Absorption and Reflection Spectra of Solids,” (A review of work at Bellevue), J. Quant. Spectrosc. Radiat. Transfer 2, 393–412 (1962).
[CrossRef]

Opt. Acta (1)

L. Ward, “A Survey of the Accuracies of Some Methods for the Determination of the Optical Constants of Thin Films,” Opt. Acta 32, 155–167 (1985).
[CrossRef]

Opt. News (1)

J. M. Bennett, “Scattering and Surface Evaluation Techniques for the Optics of the Future,” Opt. News 7, 17–27 (1985).
[CrossRef]

Phys. Thin Films (1)

O. S. Heavens, “Measurement of Optical Constants of Thin Films,” Phys. Thin Films 2, 193–238 (1964).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

L. J. Lingg, J. D. Targove, J. P. Lehan, H. A. Macleod, “Ion-Assisted Deposition of Lanthanide Trifluorides for VUV Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 818, 86–92 (1987).

Prog. Opt. (1)

F. Abeles, “Methods for Determining Optical Parameters of Thin Films,” Prog. Opt. 2, 249–288 (1963).
[CrossRef]

Other (5)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 611.

A. Bideau-Mehu, Y. Guern, R. Abjean, “Influence of the Optical Constants on Fabry-Perot Coatings Characteristics in the Vacuum Ultraviolet Wavelength Range,” in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1984), pp. 265–267.

J. M. Zwiner, “Space Station Induced Environment Monitoring,” NASA Conference Publication 3021.

H. R. Philipp, “Silicon Dioxide (SiO2) (Glass),” in Handbook of Optical Constants of Solids, E. D. Palik, Ed. (Academic, Orlando, FL, 1985), p. 749.

M. Zukic, “Damped Least Squares Technique for the Design of Optical Multilayer Filters,” M.S. Thesis, Imperial College, London (1984).

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Figures (21)

Fig. 1
Fig. 1

Measurement of reflectance R1 from the wedged substrate to avoid contribution from the back side reflectance. Transmittance TM was measured on a 2-mm thick parallel substrate.

Fig. 2
Fig. 2

Beam diagram for theoretical derivation of the transmittance of the nonabsorbing thick slab.

Fig. 3
Fig. 3

Measurement of reflectance R 1 F of the single film deposited on the wedged substrate. R 2 F is the calculated reflectance of the single film with the substrate as an incident medium and air as an emerging medium. TF is the calculated transmittance of the single film sandwiched between two semi-infinite media—air and substrate.

Fig. 4
Fig. 4

Beam diagram for theoretical derivation of transmittance T 0 F of the single film deposited on the nonabsorbing substrate.

Fig. 5
Fig. 5

Schematic diagram of the single beam VUV spectrophotometer.

Fig. 6
Fig. 6

Reflectance R1 and transmittance TM measurements on the MgF2 wedged and a 2-mm thick parallel substrate, respectively.

Fig. 7
Fig. 7

Optical constants of the MgF2 substrate determined using Eqs. (8) and (12).

Fig. 8
Fig. 8

Reflectance R 1 F and transmittance T M F of a 53-nm thick BaF2 film deposited on the MgF2 substrate.

Fig. 9
Fig. 9

Optical constants of BaF2 determined from R and T measurements of 53-, 45-, and 94.5-nm thick films deposited on the MgF2 substrate.

Fig. 10
Fig. 10

Reflectance R 1 F and transmittance T M F of a 99-nm thick CaF2 film deposited on the MgF2 substrate.

Fig. 11
Fig. 11

Optical constants of CaF2 determined from R and T measurements of 99- and 54.5-nm thick films deposited on the MgF2 substrate.

Fig. 12
Fig. 12

Reflectance R 1 F and transmittance T M F of a 51-nm thick LaF3 film deposited on the MgF2 substrate.

Fig. 13
Fig. 13

Optical constants of LaF3 determined from R and T measurements of 51-, 68-, and 83-nm thick films deposited on the MgF2 substrate.

Fig. 14
Fig. 14

Reflectance R 1 F and transmittance T M F of a 68-nm thick MgF2 film deposited on the MgF2 substrate.

Fig. 15
Fig. 15

Optical constants of MgF2 determined from R and T measurements of 68- and 109-nm thick films deposited on the MgF2 substrate.

Fig. 16
Fig. 16

Reflectance R 1 F and transmittance T M F of a 112-nm thick Al2O3 film deposited on the MgF2 substrate.

Fig. 17
Fig. 17

Optical constants of Al2O3 determined from R and T measurements of 112-, 152-, and 99-nm thick films deposited on the MgF2 substrate.

Fig. 18
Fig. 18

Reflectance R 1 F and transmittance T M F of a 30-nm thick HfO2 film deposited on the MgF2 substrate.

Fig. 19
Fig. 19

Optical constants of HfO2 determined from R and T measurements of 30- and 48.5-nm thick films deposited on the MgF2 substrate.

Fig. 20
Fig. 20

Reflectance R 1 F and transmittance T M F of a 51-nm thick SiO2 film deposited on the MgF2 substrate.

Fig. 21
Fig. 21

Optical constants of SiO2 determined from R and T measurements of 131-, 121-, and 51-nm thick films deposited on the MgF2 substrate.

Tables (1)

Tables Icon

Table I Deposition Conditions

Equations (17)

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T 0 = T 1 ( 1 - R 1 ) + T 1 R 1 2 ( 1 - R 1 ) + T 1 R 1 4 ( 1 - R 1 ) + T 1 R 1 6 ( 1 - R 1 ) + ,
T 0 = T 1 ( 1 - R 1 + R 1 2 - R 1 3 + R 1 4 - R 1 5 + R 1 6 + ) .
T 0 = T 1 1 + R 1 = 1 - R 1 1 + R 1 ,
A = 1 - T M T 0 ,
C = T M T 0 .
R 1 = ( n - 1 ) 2 ( n + 1 ) 2 ,
n = 1 + R 1 1 - R 1 .
I ( z ) = I ( 0 ) exp ( - α z ) ,
α = 4 π λ k ,
k = - λ 4 π z ln [ I ( z ) I ( 0 ) ] .
k = - λ 4 π D ln ( T M T 0 ) ,
T 0 F = T F T 1 [ 1 + R 1 R 2 F + ( R 1 R 2 F ) 2 + ( R 1 R 2 F ) 3 + ( R 1 R 2 F ) 4 ] ,
T 0 F = T F T 1 1 - R 1 R 2 F = T F ( 1 - R 1 ) 1 - R 1 R 2 F ,
T C F = C T F ( 1 - R 1 ) 1 - R 1 R 2 F .
F = W 1 ( R 1 F - R C F ) 2 + W 2 ( T M F - T C F ) 2 ,
F = F [ R 1 F , R C F , T M F , T C F ( R 2 F ) ]
F T = n = 1 L F n ,

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