Abstract

The surface plasmon spectroscopy (SPS) technique is used in the characterization of dielectric-coated metal mirrors. Experiments performed on a MgF2-coated aluminum mirror indicate good agreement between SPS and ellipsometry techniques for the determination of coating thickness. In addition, the optical constants of aluminum obtained from the same experiment agree well with values presented in the literature. Advantages of SPS are that it is a simple procedure providing a high degree of accuracy, and only a single measurement is required to yield both the film thickness and the complex permittivity of the substrate.

© 1988 Optical Society of America

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References

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  1. E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-Consistency and Sum Rule Tests in the Kramers-Kronig Analysis of Optical Data: Applications to Aluminum,” Phys. Rev. B 22, 1612 (1980).
    [CrossRef]
  2. J. D. E. Mclntyre, “Optical Reflection Spectroscopy of Chemisorbed Monolayers,” in Optical Properties of Solids, New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1975), Chap. 11; D. E. Aspnes, “Spectroscopic Ellipsometry of Solids,” in Optical Properties of Solids, New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1975), Chap. 15.
  3. M. Malin, K. Vedam, “Generalized Ellipsometric Method for the Determination of all the Optical Constants of the System: Optically Absorbing Film on an Absorbing Substrate,” Surf. Sci. 56, 49 (1976).
    [CrossRef]
  4. A. Otto, “Spectroscopy of Surface Polaritons by Attenuated Total Reflection,” in Optical Properties of Solids, New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1975), Chap. 13.
  5. M. T. Flanagan, R. H. Pantell, “Surface Plasmon Resonance and Immunosensors,” Electron. Lett. 20, 968 (1984).
    [CrossRef]
  6. H. Raether, “The Dispersion Relation of Surface Plasmons on Rough Surfaces; A Comment on Roughness Data,” Surf. Sci. 125, 624 (1983); “Surface Plasmons and Roughness,” in Surface Polaritons, V. M. Agranovich, D. L. Mills, Eds. (North-Holland, Amsterdam, 1982), Chap. 9.
    [CrossRef]
  7. E. Fontana, R. H. Pantell, “Characterization of Multilayer Rough Surfaces Using Surface Plasmon Spectroscopy,” Phys. Rev. B 37, 3164 (1988).
    [CrossRef]
  8. E. Kretschmann, “Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflachenplasmaschwingungen,” Z. Phys. 241, 313 (1971).
    [CrossRef]
  9. W. P. Chen, J. M. Chen, “Use of Surface Plasma Waves for Determination of the Thickness and Optical Constants of Thin Metallic Films,” J. Opt. Soc. Am. 71, 189 (1981).
    [CrossRef]
  10. E. T. Hutcheson, G. Hass, J. K. Coulter, “A Direct Comparison of the Visible and Ultraviolet Reflectance of Aluminum Films Evaporated in Conventional and Ultra-High-Vacuum Systems,” Opt. Commun. 4, 213 (1971).
    [CrossRef]
  11. W. L. Wolfe, Properties of Optical Materials,” in Handbook of Optics, W. G. Discroll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978), p. 7.95.
  12. W. P. Chen, J. M. Chen, “Surface Plasma Wave study of Sub-monolayer Cs and Cs–O Covered Ag Surfaces,” Surf. Sci. 91, 601 (1980).
    [CrossRef]
  13. K. L. Nielsen, Methods in Numerical Analysis (Macmillan, New York, 1964), p. 308.
  14. A. G. Mathewson, H. P. Meyers, “Absolute Values of the Optical Constants of Some Pure Metals,” Phys. Scr. 4, 291 (1971).
    [CrossRef]
  15. G. Hass, J. E. Waylonis, “Optical Constants and Reflectance and Transmittance of Evaporated Aluminum in the Visible and Ultraviolet,” J. Opt. Soc. Am. 51, 719 (1961).
    [CrossRef]
  16. A. Otto, W. Sohler, “The Influence of the Substrate on the Optical Constants of Al Films,” Solid State Commun. 16, 1319 (1975).
    [CrossRef]
  17. W. D. Kimura, D. H. Ford, “Photoacoustic Calorimetry System for Glancing Incidence Mirror Absorptance Measurements,” Rev. Sci. Instrum. 57, 2754 (1986).
    [CrossRef]
  18. W. D. Kimura, F. J. Woodberry, L. F. DeSandre, “Model Comparisons with Glancing Incidence Measurements of Over-coated Metal Mirrors,” in Proceedings, 1986 Boulder Damage Symposium (to be published).

1988 (1)

E. Fontana, R. H. Pantell, “Characterization of Multilayer Rough Surfaces Using Surface Plasmon Spectroscopy,” Phys. Rev. B 37, 3164 (1988).
[CrossRef]

1986 (1)

W. D. Kimura, D. H. Ford, “Photoacoustic Calorimetry System for Glancing Incidence Mirror Absorptance Measurements,” Rev. Sci. Instrum. 57, 2754 (1986).
[CrossRef]

1984 (1)

M. T. Flanagan, R. H. Pantell, “Surface Plasmon Resonance and Immunosensors,” Electron. Lett. 20, 968 (1984).
[CrossRef]

1983 (1)

H. Raether, “The Dispersion Relation of Surface Plasmons on Rough Surfaces; A Comment on Roughness Data,” Surf. Sci. 125, 624 (1983); “Surface Plasmons and Roughness,” in Surface Polaritons, V. M. Agranovich, D. L. Mills, Eds. (North-Holland, Amsterdam, 1982), Chap. 9.
[CrossRef]

1981 (1)

1980 (2)

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-Consistency and Sum Rule Tests in the Kramers-Kronig Analysis of Optical Data: Applications to Aluminum,” Phys. Rev. B 22, 1612 (1980).
[CrossRef]

W. P. Chen, J. M. Chen, “Surface Plasma Wave study of Sub-monolayer Cs and Cs–O Covered Ag Surfaces,” Surf. Sci. 91, 601 (1980).
[CrossRef]

1976 (1)

M. Malin, K. Vedam, “Generalized Ellipsometric Method for the Determination of all the Optical Constants of the System: Optically Absorbing Film on an Absorbing Substrate,” Surf. Sci. 56, 49 (1976).
[CrossRef]

1975 (1)

A. Otto, W. Sohler, “The Influence of the Substrate on the Optical Constants of Al Films,” Solid State Commun. 16, 1319 (1975).
[CrossRef]

1971 (3)

A. G. Mathewson, H. P. Meyers, “Absolute Values of the Optical Constants of Some Pure Metals,” Phys. Scr. 4, 291 (1971).
[CrossRef]

E. Kretschmann, “Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflachenplasmaschwingungen,” Z. Phys. 241, 313 (1971).
[CrossRef]

E. T. Hutcheson, G. Hass, J. K. Coulter, “A Direct Comparison of the Visible and Ultraviolet Reflectance of Aluminum Films Evaporated in Conventional and Ultra-High-Vacuum Systems,” Opt. Commun. 4, 213 (1971).
[CrossRef]

1961 (1)

Chen, J. M.

W. P. Chen, J. M. Chen, “Use of Surface Plasma Waves for Determination of the Thickness and Optical Constants of Thin Metallic Films,” J. Opt. Soc. Am. 71, 189 (1981).
[CrossRef]

W. P. Chen, J. M. Chen, “Surface Plasma Wave study of Sub-monolayer Cs and Cs–O Covered Ag Surfaces,” Surf. Sci. 91, 601 (1980).
[CrossRef]

Chen, W. P.

W. P. Chen, J. M. Chen, “Use of Surface Plasma Waves for Determination of the Thickness and Optical Constants of Thin Metallic Films,” J. Opt. Soc. Am. 71, 189 (1981).
[CrossRef]

W. P. Chen, J. M. Chen, “Surface Plasma Wave study of Sub-monolayer Cs and Cs–O Covered Ag Surfaces,” Surf. Sci. 91, 601 (1980).
[CrossRef]

Coulter, J. K.

E. T. Hutcheson, G. Hass, J. K. Coulter, “A Direct Comparison of the Visible and Ultraviolet Reflectance of Aluminum Films Evaporated in Conventional and Ultra-High-Vacuum Systems,” Opt. Commun. 4, 213 (1971).
[CrossRef]

DeSandre, L. F.

W. D. Kimura, F. J. Woodberry, L. F. DeSandre, “Model Comparisons with Glancing Incidence Measurements of Over-coated Metal Mirrors,” in Proceedings, 1986 Boulder Damage Symposium (to be published).

Flanagan, M. T.

M. T. Flanagan, R. H. Pantell, “Surface Plasmon Resonance and Immunosensors,” Electron. Lett. 20, 968 (1984).
[CrossRef]

Fontana, E.

E. Fontana, R. H. Pantell, “Characterization of Multilayer Rough Surfaces Using Surface Plasmon Spectroscopy,” Phys. Rev. B 37, 3164 (1988).
[CrossRef]

Ford, D. H.

W. D. Kimura, D. H. Ford, “Photoacoustic Calorimetry System for Glancing Incidence Mirror Absorptance Measurements,” Rev. Sci. Instrum. 57, 2754 (1986).
[CrossRef]

Hass, G.

E. T. Hutcheson, G. Hass, J. K. Coulter, “A Direct Comparison of the Visible and Ultraviolet Reflectance of Aluminum Films Evaporated in Conventional and Ultra-High-Vacuum Systems,” Opt. Commun. 4, 213 (1971).
[CrossRef]

G. Hass, J. E. Waylonis, “Optical Constants and Reflectance and Transmittance of Evaporated Aluminum in the Visible and Ultraviolet,” J. Opt. Soc. Am. 51, 719 (1961).
[CrossRef]

Hutcheson, E. T.

E. T. Hutcheson, G. Hass, J. K. Coulter, “A Direct Comparison of the Visible and Ultraviolet Reflectance of Aluminum Films Evaporated in Conventional and Ultra-High-Vacuum Systems,” Opt. Commun. 4, 213 (1971).
[CrossRef]

Inokuti, M.

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-Consistency and Sum Rule Tests in the Kramers-Kronig Analysis of Optical Data: Applications to Aluminum,” Phys. Rev. B 22, 1612 (1980).
[CrossRef]

Kimura, W. D.

W. D. Kimura, D. H. Ford, “Photoacoustic Calorimetry System for Glancing Incidence Mirror Absorptance Measurements,” Rev. Sci. Instrum. 57, 2754 (1986).
[CrossRef]

W. D. Kimura, F. J. Woodberry, L. F. DeSandre, “Model Comparisons with Glancing Incidence Measurements of Over-coated Metal Mirrors,” in Proceedings, 1986 Boulder Damage Symposium (to be published).

Kretschmann, E.

E. Kretschmann, “Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflachenplasmaschwingungen,” Z. Phys. 241, 313 (1971).
[CrossRef]

Malin, M.

M. Malin, K. Vedam, “Generalized Ellipsometric Method for the Determination of all the Optical Constants of the System: Optically Absorbing Film on an Absorbing Substrate,” Surf. Sci. 56, 49 (1976).
[CrossRef]

Mathewson, A. G.

A. G. Mathewson, H. P. Meyers, “Absolute Values of the Optical Constants of Some Pure Metals,” Phys. Scr. 4, 291 (1971).
[CrossRef]

Mclntyre, J. D. E.

J. D. E. Mclntyre, “Optical Reflection Spectroscopy of Chemisorbed Monolayers,” in Optical Properties of Solids, New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1975), Chap. 11; D. E. Aspnes, “Spectroscopic Ellipsometry of Solids,” in Optical Properties of Solids, New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1975), Chap. 15.

Meyers, H. P.

A. G. Mathewson, H. P. Meyers, “Absolute Values of the Optical Constants of Some Pure Metals,” Phys. Scr. 4, 291 (1971).
[CrossRef]

Nielsen, K. L.

K. L. Nielsen, Methods in Numerical Analysis (Macmillan, New York, 1964), p. 308.

Otto, A.

A. Otto, W. Sohler, “The Influence of the Substrate on the Optical Constants of Al Films,” Solid State Commun. 16, 1319 (1975).
[CrossRef]

A. Otto, “Spectroscopy of Surface Polaritons by Attenuated Total Reflection,” in Optical Properties of Solids, New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1975), Chap. 13.

Pantell, R. H.

E. Fontana, R. H. Pantell, “Characterization of Multilayer Rough Surfaces Using Surface Plasmon Spectroscopy,” Phys. Rev. B 37, 3164 (1988).
[CrossRef]

M. T. Flanagan, R. H. Pantell, “Surface Plasmon Resonance and Immunosensors,” Electron. Lett. 20, 968 (1984).
[CrossRef]

Raether, H.

H. Raether, “The Dispersion Relation of Surface Plasmons on Rough Surfaces; A Comment on Roughness Data,” Surf. Sci. 125, 624 (1983); “Surface Plasmons and Roughness,” in Surface Polaritons, V. M. Agranovich, D. L. Mills, Eds. (North-Holland, Amsterdam, 1982), Chap. 9.
[CrossRef]

Sasaki, T.

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-Consistency and Sum Rule Tests in the Kramers-Kronig Analysis of Optical Data: Applications to Aluminum,” Phys. Rev. B 22, 1612 (1980).
[CrossRef]

Shiles, E.

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-Consistency and Sum Rule Tests in the Kramers-Kronig Analysis of Optical Data: Applications to Aluminum,” Phys. Rev. B 22, 1612 (1980).
[CrossRef]

Smith, D. Y.

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-Consistency and Sum Rule Tests in the Kramers-Kronig Analysis of Optical Data: Applications to Aluminum,” Phys. Rev. B 22, 1612 (1980).
[CrossRef]

Sohler, W.

A. Otto, W. Sohler, “The Influence of the Substrate on the Optical Constants of Al Films,” Solid State Commun. 16, 1319 (1975).
[CrossRef]

Vedam, K.

M. Malin, K. Vedam, “Generalized Ellipsometric Method for the Determination of all the Optical Constants of the System: Optically Absorbing Film on an Absorbing Substrate,” Surf. Sci. 56, 49 (1976).
[CrossRef]

Waylonis, J. E.

Wolfe, W. L.

W. L. Wolfe, Properties of Optical Materials,” in Handbook of Optics, W. G. Discroll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978), p. 7.95.

Woodberry, F. J.

W. D. Kimura, F. J. Woodberry, L. F. DeSandre, “Model Comparisons with Glancing Incidence Measurements of Over-coated Metal Mirrors,” in Proceedings, 1986 Boulder Damage Symposium (to be published).

Electron. Lett. (1)

M. T. Flanagan, R. H. Pantell, “Surface Plasmon Resonance and Immunosensors,” Electron. Lett. 20, 968 (1984).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Commun. (1)

E. T. Hutcheson, G. Hass, J. K. Coulter, “A Direct Comparison of the Visible and Ultraviolet Reflectance of Aluminum Films Evaporated in Conventional and Ultra-High-Vacuum Systems,” Opt. Commun. 4, 213 (1971).
[CrossRef]

Phys. Rev. B (2)

E. Fontana, R. H. Pantell, “Characterization of Multilayer Rough Surfaces Using Surface Plasmon Spectroscopy,” Phys. Rev. B 37, 3164 (1988).
[CrossRef]

E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-Consistency and Sum Rule Tests in the Kramers-Kronig Analysis of Optical Data: Applications to Aluminum,” Phys. Rev. B 22, 1612 (1980).
[CrossRef]

Phys. Scr. (1)

A. G. Mathewson, H. P. Meyers, “Absolute Values of the Optical Constants of Some Pure Metals,” Phys. Scr. 4, 291 (1971).
[CrossRef]

Rev. Sci. Instrum. (1)

W. D. Kimura, D. H. Ford, “Photoacoustic Calorimetry System for Glancing Incidence Mirror Absorptance Measurements,” Rev. Sci. Instrum. 57, 2754 (1986).
[CrossRef]

Solid State Commun. (1)

A. Otto, W. Sohler, “The Influence of the Substrate on the Optical Constants of Al Films,” Solid State Commun. 16, 1319 (1975).
[CrossRef]

Surf. Sci. (3)

W. P. Chen, J. M. Chen, “Surface Plasma Wave study of Sub-monolayer Cs and Cs–O Covered Ag Surfaces,” Surf. Sci. 91, 601 (1980).
[CrossRef]

M. Malin, K. Vedam, “Generalized Ellipsometric Method for the Determination of all the Optical Constants of the System: Optically Absorbing Film on an Absorbing Substrate,” Surf. Sci. 56, 49 (1976).
[CrossRef]

H. Raether, “The Dispersion Relation of Surface Plasmons on Rough Surfaces; A Comment on Roughness Data,” Surf. Sci. 125, 624 (1983); “Surface Plasmons and Roughness,” in Surface Polaritons, V. M. Agranovich, D. L. Mills, Eds. (North-Holland, Amsterdam, 1982), Chap. 9.
[CrossRef]

Z. Phys. (1)

E. Kretschmann, “Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflachenplasmaschwingungen,” Z. Phys. 241, 313 (1971).
[CrossRef]

Other (5)

A. Otto, “Spectroscopy of Surface Polaritons by Attenuated Total Reflection,” in Optical Properties of Solids, New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1975), Chap. 13.

J. D. E. Mclntyre, “Optical Reflection Spectroscopy of Chemisorbed Monolayers,” in Optical Properties of Solids, New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1975), Chap. 11; D. E. Aspnes, “Spectroscopic Ellipsometry of Solids,” in Optical Properties of Solids, New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1975), Chap. 15.

K. L. Nielsen, Methods in Numerical Analysis (Macmillan, New York, 1964), p. 308.

W. L. Wolfe, Properties of Optical Materials,” in Handbook of Optics, W. G. Discroll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978), p. 7.95.

W. D. Kimura, F. J. Woodberry, L. F. DeSandre, “Model Comparisons with Glancing Incidence Measurements of Over-coated Metal Mirrors,” in Proceedings, 1986 Boulder Damage Symposium (to be published).

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Figures (5)

Fig. 1
Fig. 1

Multilayer configuration of the MgF2-coated aluminum mirror. The parameters to be determined are the coating thickness d and the complex permittivity of the Al.

Fig. 2
Fig. 2

Experimental configuration for exciting a surface plasmon at the Al–MgF2 interface.

Fig. 3
Fig. 3

ATR curves for the mirror illustrated in Fig. 1. Curves (a), (b), and (c) are for laser wavelengths λ = 6328, 5145, and 4880 Å, respectively. The angle indicated in the horizontal axes of these plots represents the internal angle θ shown in Fig. 2. The solid lines in these plots are best-fit curves using Eq. (3) with the parameters listed in Table II.

Fig. 4
Fig. 4

Diagram illustrating the ellipsometer operation. A laser beam, either linearly or circularly polarized, is incident on the mirror surface at an angle θ = 70°. The ellipsometric parameters characterizing the state of polarization of the reflected beam, Δ and ψ in Eq. (15), are obtained from the time dependence imposed by the rotating analyzer on the transmitted flux.

Fig. 5
Fig. 5

Wavelength dependence of the (a) real and (b) imaginary parts of the complex permittivity of aluminum obtained by Hass and Waylonis15 (continuous lines) and the ones reported in this work, (●).

Tables (4)

Tables Icon

Table I MgF2 and Prism Refractive Indices at Three Wavelengths (see Figs. 1 and 2)

Tables Icon

Table II Aluminum Complex Permittivity = ′ + i∊″ and MgF2 Coating Thickness d Obtained Using the SPS Technique Assuming the Coating Refractive Index Values Given in Table I

Tables Icon

Table III Comparison Between Measured and Calculated Normal Incidence Reflectivity for an Aluminum-Vacuum Interface.

Tables Icon

Table IV MgF2 Thickness Obtained for the Al Mirror Using Different Methods

Equations (16)

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n Al = 2 + 2 + 2 , κ Al = 2 + 2 - 2 ,
θ c = sin - 1 ( n / n p ) ,
k sp = 2 π λ - 1 n p sin ( θ min ) ,
R ( θ ) = | r 12 + r 23 exp ( - i 2 k 2 d ) 1 + r 12 r 23 exp ( - i 2 k 2 d ) | 2 ,
r 12 = 1 k 2 - 2 k 1 1 k 2 + 2 k 1 ,
r 23 = 2 k 3 - 3 k 2 2 k 3 + 3 k 2 ,
k i = 2 π λ - 1 ( i - 1 sin 2 θ ) 1 / 2 , i = 1 , 2 , 3 ,
1.0 - R ( θ ) 4 k 0 k R ( k x - k 0 - k R ) 2 + ( k 0 + k R ) 2 ,
k 0 k 0 + i k 0 = 2 π λ ( n 2 n 2 + ) 1 / 2 ,
k R k R + i k R = 4 π λ exp ( i ϕ 0 ) + n 2 ( n 2 - n 2 ) 3 / 2 × exp [ - ( 4 π λ n 2 d n 2 + 1 / 2 ) ] ,
ϕ 0 = 2 tan - 1 { ( n 2 + ) n p 2 - n 2 1 / 2 n p 2 } ,
k x = 2 π λ n p sin θ .
θ min = sin - 1 { λ ( k 0 + k R ) 2 π n p } ,
R min = 1 - 4 η ( 1 + η ) 2 ,
η = k 0 k R ,             θ 1 / 2 = λ π n p k SP ( cos θ min ) - 1 .
r p r s = tan Ψ exp ( i Δ ) ,

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