Abstract

We consider the use of the ellipsometric constant Δ and the surface plasmon excitation angle θ of a metal substrate covered by a thin transparent isotropic film for the determination of the refractive index n and thickness d of the film. It is proved, using an expression for Δ(n,d) and θ(n,d) valid to first order in d, that it is in general not possible to find a unique n and d from measured values of Δ and θ. Exact calculation of Δ(n,d) and θ(n,d) for the case of a silver substrate covered by an organic thin film and 632.8-nm radiation confirms this result and establishes that the range of d where the proof applies is below ~35 nm. For a value of d of ~40 nm we find that the theoretical limit of uncertainty in n and d when both Δ and θ are known to ±0.01° is 0.01 and 0.05 nm, respectively.

© 1988 Optical Society of America

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References

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  1. I. R. Peterson, G. Veale, C. M. Montgomery, “The Preparation of Oleophilic Surfaces for Langmuir-Blodgett Deposition,” J. Colloid Interface Sci. 109, 527 (1986).
    [CrossRef]
  2. R. G. Nuzzo, F. A. Fusco, D. L. Allara, “Spontaneously Organized Molecular Assemblies. 3. Preparation and Properties of Solution Adsorbed Monolayers of Organic Disulfides on Gold Surfaces,” J. Am. Chem. Soc. 109, 2358 (1987).
    [CrossRef]
  3. A. Ulman, N. Tillman, J. Littman, “Self-assembling Monolayers of Thiols on Silver and Gold Surfaces: an FTIR Study of Molecular Orientation,” submitted to J. Phys. Chem.
  4. P. S. Vincett, G. G. Roberts, “Electrical and Photoelectrical Transport Properties of Langmuir-Blodgett Films and a Discussion of Possible Device Applications,” Thin Solid Films 68, 135 (1980).
    [CrossRef]
  5. J. F. Rabolt, M. Jurich, J. D. Swalen, “Infrared Reflection-Absorption Studies of Thin Films at Grazing Incidence,” Appl. Spectrosc. 39, 269 (1985).
    [CrossRef]
  6. F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the Thickness and Refractive Index of Very Thin Films and the Optical Properties of Surfaces by Ellipsometry,” J. Res. Natl. Bur. Stand. Sect. A 67, 363 (1963).
    [CrossRef]
  7. R. M. Corn, M. R. Philpott, “Surface Plasmon-Enhanced Raman Scattering at Thin Silver Films,” J. Chem. Phys. 80, 5245 (1984).
    [CrossRef]
  8. I. Pockrand, J. D. Swalin, J. G. Gordon, M. R. Philpott, “Surface Plasmon Spectroscopy of Organic Monolayer Assemblies,” Surf. Sci. 74, 237 (1977).
    [CrossRef]
  9. H. Arwin, D. E. Aspnes, “Determination of Optical Properties of Thin Organic Films by Spectroellipsometry,” Thin Solid Films 138, 195 (1986).
    [CrossRef]
  10. E. Kretschmann, H. Raether, “Radiative Decay of Nonradiative Surface Plasmons Excited by Light,” Z. Naturforsch. Teil A 23, 2135 (1968).
  11. E. Kretschmann, “The Determination of the Optical Constants of Metals by Excitation of Surface Plasmons,” Z. Phys. 241, 313 (1971).
    [CrossRef]
  12. I. Pockrand, J. D. Swalin, “Anomalous Dispersion of Surface Plasma Oscillations,” J. Opt. Soc. Am. 68, 1147 (1978).
    [CrossRef]
  13. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955), p. 62.
  14. I. Pockrand, “Surface Plasma Oscillations at Silver Surfaces with Thin Transparent and Absorbing Coatings,” Surf. Sci. 72, 577–588 (1978).
    [CrossRef]
  15. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 6.

1987

R. G. Nuzzo, F. A. Fusco, D. L. Allara, “Spontaneously Organized Molecular Assemblies. 3. Preparation and Properties of Solution Adsorbed Monolayers of Organic Disulfides on Gold Surfaces,” J. Am. Chem. Soc. 109, 2358 (1987).
[CrossRef]

1986

H. Arwin, D. E. Aspnes, “Determination of Optical Properties of Thin Organic Films by Spectroellipsometry,” Thin Solid Films 138, 195 (1986).
[CrossRef]

I. R. Peterson, G. Veale, C. M. Montgomery, “The Preparation of Oleophilic Surfaces for Langmuir-Blodgett Deposition,” J. Colloid Interface Sci. 109, 527 (1986).
[CrossRef]

1985

1984

R. M. Corn, M. R. Philpott, “Surface Plasmon-Enhanced Raman Scattering at Thin Silver Films,” J. Chem. Phys. 80, 5245 (1984).
[CrossRef]

1980

P. S. Vincett, G. G. Roberts, “Electrical and Photoelectrical Transport Properties of Langmuir-Blodgett Films and a Discussion of Possible Device Applications,” Thin Solid Films 68, 135 (1980).
[CrossRef]

1978

I. Pockrand, J. D. Swalin, “Anomalous Dispersion of Surface Plasma Oscillations,” J. Opt. Soc. Am. 68, 1147 (1978).
[CrossRef]

I. Pockrand, “Surface Plasma Oscillations at Silver Surfaces with Thin Transparent and Absorbing Coatings,” Surf. Sci. 72, 577–588 (1978).
[CrossRef]

1977

I. Pockrand, J. D. Swalin, J. G. Gordon, M. R. Philpott, “Surface Plasmon Spectroscopy of Organic Monolayer Assemblies,” Surf. Sci. 74, 237 (1977).
[CrossRef]

1971

E. Kretschmann, “The Determination of the Optical Constants of Metals by Excitation of Surface Plasmons,” Z. Phys. 241, 313 (1971).
[CrossRef]

1968

E. Kretschmann, H. Raether, “Radiative Decay of Nonradiative Surface Plasmons Excited by Light,” Z. Naturforsch. Teil A 23, 2135 (1968).

1963

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the Thickness and Refractive Index of Very Thin Films and the Optical Properties of Surfaces by Ellipsometry,” J. Res. Natl. Bur. Stand. Sect. A 67, 363 (1963).
[CrossRef]

Allara, D. L.

R. G. Nuzzo, F. A. Fusco, D. L. Allara, “Spontaneously Organized Molecular Assemblies. 3. Preparation and Properties of Solution Adsorbed Monolayers of Organic Disulfides on Gold Surfaces,” J. Am. Chem. Soc. 109, 2358 (1987).
[CrossRef]

Arwin, H.

H. Arwin, D. E. Aspnes, “Determination of Optical Properties of Thin Organic Films by Spectroellipsometry,” Thin Solid Films 138, 195 (1986).
[CrossRef]

Aspnes, D. E.

H. Arwin, D. E. Aspnes, “Determination of Optical Properties of Thin Organic Films by Spectroellipsometry,” Thin Solid Films 138, 195 (1986).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 6.

Corn, R. M.

R. M. Corn, M. R. Philpott, “Surface Plasmon-Enhanced Raman Scattering at Thin Silver Films,” J. Chem. Phys. 80, 5245 (1984).
[CrossRef]

Fusco, F. A.

R. G. Nuzzo, F. A. Fusco, D. L. Allara, “Spontaneously Organized Molecular Assemblies. 3. Preparation and Properties of Solution Adsorbed Monolayers of Organic Disulfides on Gold Surfaces,” J. Am. Chem. Soc. 109, 2358 (1987).
[CrossRef]

Gordon, J. G.

I. Pockrand, J. D. Swalin, J. G. Gordon, M. R. Philpott, “Surface Plasmon Spectroscopy of Organic Monolayer Assemblies,” Surf. Sci. 74, 237 (1977).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955), p. 62.

Jurich, M.

Kretschmann, E.

E. Kretschmann, “The Determination of the Optical Constants of Metals by Excitation of Surface Plasmons,” Z. Phys. 241, 313 (1971).
[CrossRef]

E. Kretschmann, H. Raether, “Radiative Decay of Nonradiative Surface Plasmons Excited by Light,” Z. Naturforsch. Teil A 23, 2135 (1968).

Littman, J.

A. Ulman, N. Tillman, J. Littman, “Self-assembling Monolayers of Thiols on Silver and Gold Surfaces: an FTIR Study of Molecular Orientation,” submitted to J. Phys. Chem.

McCrackin, F. L.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the Thickness and Refractive Index of Very Thin Films and the Optical Properties of Surfaces by Ellipsometry,” J. Res. Natl. Bur. Stand. Sect. A 67, 363 (1963).
[CrossRef]

Montgomery, C. M.

I. R. Peterson, G. Veale, C. M. Montgomery, “The Preparation of Oleophilic Surfaces for Langmuir-Blodgett Deposition,” J. Colloid Interface Sci. 109, 527 (1986).
[CrossRef]

Nuzzo, R. G.

R. G. Nuzzo, F. A. Fusco, D. L. Allara, “Spontaneously Organized Molecular Assemblies. 3. Preparation and Properties of Solution Adsorbed Monolayers of Organic Disulfides on Gold Surfaces,” J. Am. Chem. Soc. 109, 2358 (1987).
[CrossRef]

Passaglia, E.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the Thickness and Refractive Index of Very Thin Films and the Optical Properties of Surfaces by Ellipsometry,” J. Res. Natl. Bur. Stand. Sect. A 67, 363 (1963).
[CrossRef]

Peterson, I. R.

I. R. Peterson, G. Veale, C. M. Montgomery, “The Preparation of Oleophilic Surfaces for Langmuir-Blodgett Deposition,” J. Colloid Interface Sci. 109, 527 (1986).
[CrossRef]

Philpott, M. R.

R. M. Corn, M. R. Philpott, “Surface Plasmon-Enhanced Raman Scattering at Thin Silver Films,” J. Chem. Phys. 80, 5245 (1984).
[CrossRef]

I. Pockrand, J. D. Swalin, J. G. Gordon, M. R. Philpott, “Surface Plasmon Spectroscopy of Organic Monolayer Assemblies,” Surf. Sci. 74, 237 (1977).
[CrossRef]

Pockrand, I.

I. Pockrand, J. D. Swalin, “Anomalous Dispersion of Surface Plasma Oscillations,” J. Opt. Soc. Am. 68, 1147 (1978).
[CrossRef]

I. Pockrand, “Surface Plasma Oscillations at Silver Surfaces with Thin Transparent and Absorbing Coatings,” Surf. Sci. 72, 577–588 (1978).
[CrossRef]

I. Pockrand, J. D. Swalin, J. G. Gordon, M. R. Philpott, “Surface Plasmon Spectroscopy of Organic Monolayer Assemblies,” Surf. Sci. 74, 237 (1977).
[CrossRef]

Rabolt, J. F.

Raether, H.

E. Kretschmann, H. Raether, “Radiative Decay of Nonradiative Surface Plasmons Excited by Light,” Z. Naturforsch. Teil A 23, 2135 (1968).

Roberts, G. G.

P. S. Vincett, G. G. Roberts, “Electrical and Photoelectrical Transport Properties of Langmuir-Blodgett Films and a Discussion of Possible Device Applications,” Thin Solid Films 68, 135 (1980).
[CrossRef]

Steinberg, H. L.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the Thickness and Refractive Index of Very Thin Films and the Optical Properties of Surfaces by Ellipsometry,” J. Res. Natl. Bur. Stand. Sect. A 67, 363 (1963).
[CrossRef]

Stromberg, R. R.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the Thickness and Refractive Index of Very Thin Films and the Optical Properties of Surfaces by Ellipsometry,” J. Res. Natl. Bur. Stand. Sect. A 67, 363 (1963).
[CrossRef]

Swalen, J. D.

Swalin, J. D.

I. Pockrand, J. D. Swalin, “Anomalous Dispersion of Surface Plasma Oscillations,” J. Opt. Soc. Am. 68, 1147 (1978).
[CrossRef]

I. Pockrand, J. D. Swalin, J. G. Gordon, M. R. Philpott, “Surface Plasmon Spectroscopy of Organic Monolayer Assemblies,” Surf. Sci. 74, 237 (1977).
[CrossRef]

Tillman, N.

A. Ulman, N. Tillman, J. Littman, “Self-assembling Monolayers of Thiols on Silver and Gold Surfaces: an FTIR Study of Molecular Orientation,” submitted to J. Phys. Chem.

Ulman, A.

A. Ulman, N. Tillman, J. Littman, “Self-assembling Monolayers of Thiols on Silver and Gold Surfaces: an FTIR Study of Molecular Orientation,” submitted to J. Phys. Chem.

Veale, G.

I. R. Peterson, G. Veale, C. M. Montgomery, “The Preparation of Oleophilic Surfaces for Langmuir-Blodgett Deposition,” J. Colloid Interface Sci. 109, 527 (1986).
[CrossRef]

Vincett, P. S.

P. S. Vincett, G. G. Roberts, “Electrical and Photoelectrical Transport Properties of Langmuir-Blodgett Films and a Discussion of Possible Device Applications,” Thin Solid Films 68, 135 (1980).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 6.

Appl. Spectrosc.

J. Am. Chem. Soc.

R. G. Nuzzo, F. A. Fusco, D. L. Allara, “Spontaneously Organized Molecular Assemblies. 3. Preparation and Properties of Solution Adsorbed Monolayers of Organic Disulfides on Gold Surfaces,” J. Am. Chem. Soc. 109, 2358 (1987).
[CrossRef]

J. Chem. Phys.

R. M. Corn, M. R. Philpott, “Surface Plasmon-Enhanced Raman Scattering at Thin Silver Films,” J. Chem. Phys. 80, 5245 (1984).
[CrossRef]

J. Colloid Interface Sci.

I. R. Peterson, G. Veale, C. M. Montgomery, “The Preparation of Oleophilic Surfaces for Langmuir-Blodgett Deposition,” J. Colloid Interface Sci. 109, 527 (1986).
[CrossRef]

J. Opt. Soc. Am.

J. Res. Natl. Bur. Stand. Sect. A

F. L. McCrackin, E. Passaglia, R. R. Stromberg, H. L. Steinberg, “Measurement of the Thickness and Refractive Index of Very Thin Films and the Optical Properties of Surfaces by Ellipsometry,” J. Res. Natl. Bur. Stand. Sect. A 67, 363 (1963).
[CrossRef]

Surf. Sci.

I. Pockrand, “Surface Plasma Oscillations at Silver Surfaces with Thin Transparent and Absorbing Coatings,” Surf. Sci. 72, 577–588 (1978).
[CrossRef]

I. Pockrand, J. D. Swalin, J. G. Gordon, M. R. Philpott, “Surface Plasmon Spectroscopy of Organic Monolayer Assemblies,” Surf. Sci. 74, 237 (1977).
[CrossRef]

Thin Solid Films

H. Arwin, D. E. Aspnes, “Determination of Optical Properties of Thin Organic Films by Spectroellipsometry,” Thin Solid Films 138, 195 (1986).
[CrossRef]

P. S. Vincett, G. G. Roberts, “Electrical and Photoelectrical Transport Properties of Langmuir-Blodgett Films and a Discussion of Possible Device Applications,” Thin Solid Films 68, 135 (1980).
[CrossRef]

Z. Naturforsch. Teil A

E. Kretschmann, H. Raether, “Radiative Decay of Nonradiative Surface Plasmons Excited by Light,” Z. Naturforsch. Teil A 23, 2135 (1968).

Z. Phys.

E. Kretschmann, “The Determination of the Optical Constants of Metals by Excitation of Surface Plasmons,” Z. Phys. 241, 313 (1971).
[CrossRef]

Other

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955), p. 62.

A. Ulman, N. Tillman, J. Littman, “Self-assembling Monolayers of Thiols on Silver and Gold Surfaces: an FTIR Study of Molecular Orientation,” submitted to J. Phys. Chem.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p. 6.

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Figures (4)

Fig. 1
Fig. 1

Configuration in which both reflection ellipsometry and SP spectroscopy can be performed. A metal film with refractive index n1 and thickness d1 is in contact with the base of a prism with refractive index n0. The metal film is covered by a thin film of refractive index n2 and thickness d2. The refractive index of the ambient is n3. A light beam from an ellipsometer is incident at an angle ϕ. A light beam from a SP spectrometer is incident on the base of the prism at the SP excitation angle θ.

Fig. 2
Fig. 2

Curves of Δ and θ calculated using exact equations. n2 = 1.5, □; 1.6, ○. Next to each symbol is written the value of d2 in nanometers.

Fig. 3
Fig. 3

Curves of Δ and Ψ calculated using exact equations. n2 = 1.5, □; 1.6, ○. Next to each symbol is written the value of d2 in nanometers.

Fig. 4
Fig. 4

Curves of Δ and θ calculated using exact equations. n2 = 1.53, d2 = 40.68–41.68 nm, ○; n2 1.54, d2 = 40.00–41.00 nm, ■; n2 = 1.55, d2 = 39.35–40.35 nm, Δ; □ indicates an uncertainty in Δ and θ of 0.01°.

Equations (23)

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Δ = A ( n 2 ) d 2 + Δ ° ,
θ = B ( n 2 ) d 2 + θ ° ,
A ( n 2 b ) A ( n 2 a ) = B ( n 2 b ) B ( n 2 a ) .
A ( n 2 b ) = A ( n 2 a ) + A ( n 2 a ) ( n 2 b - n 2 a ) ,
B ( n 2 b ) = B ( n 2 a ) + B ( n 2 a ) ( n 2 b - n 2 a ) ,
A ( n 2 a ) A ( n 2 a ) = B ( n 2 a ) B ( n 2 a ) .
δ ( tan Ψ ) tan Ψ + i δ Δ = 4 π i n 3 d 2 cos ϕ λ × 1 ( 2 - 3 ) ( 1 - 2 ) 2 ( 1 - 3 ) ( 1 cot 2 ϕ - 3 ) ,
A ( n 2 ) = 4 π n 3 cos ϕ λ 1 ( 2 - 3 ) ( 1 - 2 ) 2 ( 1 - 3 ) ( 1 cot 2 ϕ - 3 ) .
A ( n 2 ) = 8 π n 2 n 3 cos ϕ λ 1 ( 1 3 - 2 2 ) 2 2 ( 1 - 3 ) ( 1 cot 2 ϕ - 3 ) .
δ k = ω c 2 π d 2 λ ( 2 - 3 ) ( 1 3 ) 2 ( 2 - 1 ) 2 ( 1 + 3 ) 2 ( 3 - 1 ) ( - 1 3 ) 1 / 2 .
B ( n 2 ) = c ω δ k n 0 cos θ ° .
B ( n 2 ) = 4 π n 2 λ n 0 cos θ ° ( 1 3 ) 2 ( 2 - 1 ) 2 ( 1 + 3 ) 2 ( 3 - 1 ) ( - 1 3 ) 1 / 2 × { 1 - ( 2 - 3 ) [ 1 / 2 - 1 / ( 2 - 1 ) ] } .
A ( n 2 ) A ( n 2 ) = B ( n 2 ) B ( n 2 ) = 2 n 2 ( 3 1 - 2 2 ) ( 2 - 3 ) ( 1 - 2 ) .
ρ p ρ s = ( tan Ψ ) exp [ ( i Δ ) ,
E 0 = ( E 0 x x ^ + E 0 z z ^ ) exp [ i ( k x x + k 0 z z - ω t ) ] ,
E 1 ± = ( E 1 x ± x ^ + E 1 z ± z ^ ) exp [ i ( k x x ± k 1 z z - ω t ) ] .
E 3 = ( E 3 x x ^ + E 3 z z ^ ) exp [ i ( k x x - k 3 z z - ω t ) ] .
[ 1 1 Γ 1 0 0 0 0 1 1 1 1 0 0 0 0 Γ 2 1 1 Ω 0 Ω 1 - Ω 1 Γ 1 0 0 0 0 Ω 1 - Ω 1 Ω 2 - Ω 2 0 0 0 0 Ω 2 Γ 2 - Ω 2 - Ω 3 ] [ E 0 x E 1 x + E 1 x - E 2 x + E 2 x - E 3 x ] = [ 0 0 0 0 0 0 ] ,
Γ i = exp ( i 2 k i z d i ) ,
Ω i = i / k i z ,
k i z = [ ( ω / c ) 2 i - k x 2 ] 1 / 2 ,
DetA = 0.
θ = sin - 1 k x r ( ω / c ) n 0 .

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