Abstract

The surface plasma wave technique for determining the dielectric constant (ω) and the thickness d of a metal film without a preset expression for (ω) is discussed. Two sets of solutions can be derived at a given frequency. By comparing d determined at another frequency, the correct (ω) and d solution can be determined.

© 1981 Optical Society of America

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References

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  1. F. Abeles, ed., Optical Properties and Electronic Structure of Metals and Alloys (North-Holland, Amsterdam, 1965).
  2. T. Lopez-Rios and G. Vuye, “Use of surface plasmon excitation for determination of the thickness and optical constants of very thin surface layers,” Surf. Sci. 81, 529–538 (1979).
    [Crossref]
  3. E. Kretschmann, “Die Bestimmung optischer konstanten von Metallen durch Anregung von Oberflachenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
    [Crossref]
  4. T. L. Haltorn and et al., Appl. Opt. 18, 1233–1236 (1979).
    [Crossref]
  5. E. Burstein and et al., “Surface polaritons-propagating electromagnetic modes at interfaces,” J. Vac. Sci. Technol. 11, 1004–1019 (1974).
    [Crossref]
  6. W. P. Chen and J. M. Chen, “Surface plasma wave study of submonolayer Cs and Cs–O covered Ag surfaces,” Surf. Sci. 91, 601–617 (1980).
    [Crossref]
  7. I. Pockrand, “Surface plasma oscillations at silver surfaces with thin transparent and absorbing coatings,” Surf. Sci. 72, 577–588 (1978).
    [Crossref]
  8. K. L. Nielsen, Methods in Numerical Analysis (Macmillan, New York, 1964), p. 308.
  9. L. G. Schulz, “The optical constants of silver, gold, copper, and aluminum. I. The absorption coefficient k,” J. Opt. Soc. Am. 44, 357–362 (1954).
    [Crossref]
  10. L. G. Schulz and F. R. Tangherlini, “Optical constants of silver, gold, copper, and aluminum. II. The index of refraction n,” J. Opt. Soc. Am. 44, 362–368 (1954).
    [Crossref]

1980 (1)

W. P. Chen and J. M. Chen, “Surface plasma wave study of submonolayer Cs and Cs–O covered Ag surfaces,” Surf. Sci. 91, 601–617 (1980).
[Crossref]

1979 (2)

T. Lopez-Rios and G. Vuye, “Use of surface plasmon excitation for determination of the thickness and optical constants of very thin surface layers,” Surf. Sci. 81, 529–538 (1979).
[Crossref]

T. L. Haltorn and et al., Appl. Opt. 18, 1233–1236 (1979).
[Crossref]

1978 (1)

I. Pockrand, “Surface plasma oscillations at silver surfaces with thin transparent and absorbing coatings,” Surf. Sci. 72, 577–588 (1978).
[Crossref]

1974 (1)

E. Burstein and et al., “Surface polaritons-propagating electromagnetic modes at interfaces,” J. Vac. Sci. Technol. 11, 1004–1019 (1974).
[Crossref]

1971 (1)

E. Kretschmann, “Die Bestimmung optischer konstanten von Metallen durch Anregung von Oberflachenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
[Crossref]

1954 (2)

Burstein, E.

E. Burstein and et al., “Surface polaritons-propagating electromagnetic modes at interfaces,” J. Vac. Sci. Technol. 11, 1004–1019 (1974).
[Crossref]

Chen, J. M.

W. P. Chen and J. M. Chen, “Surface plasma wave study of submonolayer Cs and Cs–O covered Ag surfaces,” Surf. Sci. 91, 601–617 (1980).
[Crossref]

Chen, W. P.

W. P. Chen and J. M. Chen, “Surface plasma wave study of submonolayer Cs and Cs–O covered Ag surfaces,” Surf. Sci. 91, 601–617 (1980).
[Crossref]

Haltorn, T. L.

Kretschmann, E.

E. Kretschmann, “Die Bestimmung optischer konstanten von Metallen durch Anregung von Oberflachenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
[Crossref]

Lopez-Rios, T.

T. Lopez-Rios and G. Vuye, “Use of surface plasmon excitation for determination of the thickness and optical constants of very thin surface layers,” Surf. Sci. 81, 529–538 (1979).
[Crossref]

Nielsen, K. L.

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

Pockrand, I.

I. Pockrand, “Surface plasma oscillations at silver surfaces with thin transparent and absorbing coatings,” Surf. Sci. 72, 577–588 (1978).
[Crossref]

Schulz, L. G.

Tangherlini, F. R.

Vuye, G.

T. Lopez-Rios and G. Vuye, “Use of surface plasmon excitation for determination of the thickness and optical constants of very thin surface layers,” Surf. Sci. 81, 529–538 (1979).
[Crossref]

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

J. Vac. Sci. Technol. (1)

E. Burstein and et al., “Surface polaritons-propagating electromagnetic modes at interfaces,” J. Vac. Sci. Technol. 11, 1004–1019 (1974).
[Crossref]

Surf. Sci. (3)

W. P. Chen and J. M. Chen, “Surface plasma wave study of submonolayer Cs and Cs–O covered Ag surfaces,” Surf. Sci. 91, 601–617 (1980).
[Crossref]

I. Pockrand, “Surface plasma oscillations at silver surfaces with thin transparent and absorbing coatings,” Surf. Sci. 72, 577–588 (1978).
[Crossref]

T. Lopez-Rios and G. Vuye, “Use of surface plasmon excitation for determination of the thickness and optical constants of very thin surface layers,” Surf. Sci. 81, 529–538 (1979).
[Crossref]

Z. Phys. (1)

E. Kretschmann, “Die Bestimmung optischer konstanten von Metallen durch Anregung von Oberflachenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
[Crossref]

Other (2)

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

F. Abeles, ed., Optical Properties and Electronic Structure of Metals and Alloys (North-Holland, Amsterdam, 1965).

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Figures (2)

Fig. 1
Fig. 1

A prism–metal–vacuum Kretschmann configuration. The metal, vacuum, and prism are labeled as media 1, 2, and 3, respectively.

Fig. 2
Fig. 2

Numerical fitting of measured R versus Kx/(ω/c) curves at 6328 and 4358 Å. Solid curves are data. Calculated reflectances for each fitting are shown by the following symbols: For solid triangles, (d, 1) = (387 Å, −17.45 + i0.92); for solid circles, (d, 1) = (483 Å, −16.72 + i1.66); for open triangles, (d, 1) = (567 Å, −5.25 + i0.53); and for open circles, (d, 1) = (467 Å, −5.25 + i0.32).

Equations (11)

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Θ = Θ ATR = sin - 1 [ Re ( K ) c / n ] .
R = | γ 31 + γ 12 exp ( i 2 K Z 1 d ) 1 + γ 31 γ 12 exp ( i 2 K Z 1 d ) | 2 ,
γ 31 = 3 K Z 1 - 1 K Z 3 3 K Z 1 + 1 K Z 3 , γ 12 = 1 K Z 2 - 2 K Z 1 1 K Z 2 + 2 K Z 1 ,
K j z = ( j ω 2 c 2 - K x 2 ) 1 / 2             for j = 1 , 2 , 3 ,
K x = n ω c sin ( Θ ) ,
R ( Θ ) = 1 - 4 Im ( K 0 ) Im ( K R ) [ K x - Re ( K ) ] 2 + Im ( K ) 2 ,
K 0 = ( 1 2 1 + 2 ) 1 / 2 ω c = ( 1 2 1 + 2 ) 1 / 2 ω c + i ( 1 2 1 + 2 ) 1 / 2 1 2 2 1 ( 1 + 2 ) ω c ,
K R = ω c ( - γ 31 ) K = K 0 ( 2 1 + 2 ) ( 1 2 1 + 2 ) 3 / 2 × exp [ i 4 π d λ 1 ( 1 + 2 ) 1 / 2 ] .
W Θ = 2 Im ( K ) cos ( Θ ATR ) c / n ω ,
R min = 1 - 4 η / ( 1 + η ) 2 ,
η = Im ( K 0 ) / Im ( K R ) .