Abstract

In this paper we present a fast method for the determination of dielectric permittivity = −r + i∊i and thickness d of metal layers from surface plasmon resonance reflection curves. The method is an iteration process using starting parameters derived directly from a reflection curve. The method is tested with simulations and is applied to experimental results. Accuracies reached for silver layers between 25–100 nm and gold layers between 40–75 nm are better than: r ±1%; i ±13% and d ±8%.

© 1990 Optical Society of America

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References

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  1. B. Liedberg, C. Nylander, I. Lundstrom, “Surface Plasmon Resonance for Gas Detection and Biosensing,” Sens. & Act. 4, 299–304 (1983).
    [CrossRef]
  2. M. T. Flanagan, R. H. Pantell, “Surface Plasmon Resonance and Immunosensors,” Electron. Lett. 20, 968–970 (1984).
    [CrossRef]
  3. R. P. H. Kooyman, H. Kolkman, J. van Gent, J. Greve, “Surface Plasmon Resonance Immunosensors: Sensitivity Considerations,” Ann. Chim. Acta 213, 35–45 (1988).
    [CrossRef]
  4. E. Kretschmann, “Die bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
    [CrossRef]
  5. W. P. Chen, J. M. Chen, “Use of Surface Plasma Waves for Determination of the Thickness and the Optical Constants of Thin Metallic Films,” J. Opt. Soc. Am. 71, 189–191 (1981).
    [CrossRef]
  6. J. M. Siqueiros, L. E. Regalado, R. Machorro, “Determination of (n,k) for Absorbing Thin Films Using Reflectance Measurements,” Appl. Opt. 27, 4260–4264 (1988).
    [CrossRef] [PubMed]
  7. W. L. Wolfe, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1963).
  8. J. R. Sambles, J. D. Pollard, G. W. Bradberry, “Liquid Layers Bound to a Gold Surface Supporting a Surface Plasmon Polariton,” Opt. Commun. 63, 288–292 (1987).
    [CrossRef]
  9. F. Yang, Z. Cao, J. Fang, “Use of Exchanging Media in ATR Configurations for Determination of Thickness and Optical Constants of Thin Metallic Films,” Appl. Opt. 27, 11–12 (1988).
    [CrossRef] [PubMed]

1988 (3)

1987 (1)

J. R. Sambles, J. D. Pollard, G. W. Bradberry, “Liquid Layers Bound to a Gold Surface Supporting a Surface Plasmon Polariton,” Opt. Commun. 63, 288–292 (1987).
[CrossRef]

1984 (1)

M. T. Flanagan, R. H. Pantell, “Surface Plasmon Resonance and Immunosensors,” Electron. Lett. 20, 968–970 (1984).
[CrossRef]

1983 (1)

B. Liedberg, C. Nylander, I. Lundstrom, “Surface Plasmon Resonance for Gas Detection and Biosensing,” Sens. & Act. 4, 299–304 (1983).
[CrossRef]

1981 (1)

1971 (1)

E. Kretschmann, “Die bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

Bradberry, G. W.

J. R. Sambles, J. D. Pollard, G. W. Bradberry, “Liquid Layers Bound to a Gold Surface Supporting a Surface Plasmon Polariton,” Opt. Commun. 63, 288–292 (1987).
[CrossRef]

Cao, Z.

Chen, J. M.

Chen, W. P.

Fang, J.

Flanagan, M. T.

M. T. Flanagan, R. H. Pantell, “Surface Plasmon Resonance and Immunosensors,” Electron. Lett. 20, 968–970 (1984).
[CrossRef]

Greve, J.

R. P. H. Kooyman, H. Kolkman, J. van Gent, J. Greve, “Surface Plasmon Resonance Immunosensors: Sensitivity Considerations,” Ann. Chim. Acta 213, 35–45 (1988).
[CrossRef]

Kolkman, H.

R. P. H. Kooyman, H. Kolkman, J. van Gent, J. Greve, “Surface Plasmon Resonance Immunosensors: Sensitivity Considerations,” Ann. Chim. Acta 213, 35–45 (1988).
[CrossRef]

Kooyman, R. P. H.

R. P. H. Kooyman, H. Kolkman, J. van Gent, J. Greve, “Surface Plasmon Resonance Immunosensors: Sensitivity Considerations,” Ann. Chim. Acta 213, 35–45 (1988).
[CrossRef]

Kretschmann, E.

E. Kretschmann, “Die bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

Liedberg, B.

B. Liedberg, C. Nylander, I. Lundstrom, “Surface Plasmon Resonance for Gas Detection and Biosensing,” Sens. & Act. 4, 299–304 (1983).
[CrossRef]

Lundstrom, I.

B. Liedberg, C. Nylander, I. Lundstrom, “Surface Plasmon Resonance for Gas Detection and Biosensing,” Sens. & Act. 4, 299–304 (1983).
[CrossRef]

Machorro, R.

Nylander, C.

B. Liedberg, C. Nylander, I. Lundstrom, “Surface Plasmon Resonance for Gas Detection and Biosensing,” Sens. & Act. 4, 299–304 (1983).
[CrossRef]

Pantell, R. H.

M. T. Flanagan, R. H. Pantell, “Surface Plasmon Resonance and Immunosensors,” Electron. Lett. 20, 968–970 (1984).
[CrossRef]

Pollard, J. D.

J. R. Sambles, J. D. Pollard, G. W. Bradberry, “Liquid Layers Bound to a Gold Surface Supporting a Surface Plasmon Polariton,” Opt. Commun. 63, 288–292 (1987).
[CrossRef]

Regalado, L. E.

Sambles, J. R.

J. R. Sambles, J. D. Pollard, G. W. Bradberry, “Liquid Layers Bound to a Gold Surface Supporting a Surface Plasmon Polariton,” Opt. Commun. 63, 288–292 (1987).
[CrossRef]

Siqueiros, J. M.

van Gent, J.

R. P. H. Kooyman, H. Kolkman, J. van Gent, J. Greve, “Surface Plasmon Resonance Immunosensors: Sensitivity Considerations,” Ann. Chim. Acta 213, 35–45 (1988).
[CrossRef]

Yang, F.

Ann. Chim. Acta (1)

R. P. H. Kooyman, H. Kolkman, J. van Gent, J. Greve, “Surface Plasmon Resonance Immunosensors: Sensitivity Considerations,” Ann. Chim. Acta 213, 35–45 (1988).
[CrossRef]

Appl. Opt. (2)

Electron. Lett. (1)

M. T. Flanagan, R. H. Pantell, “Surface Plasmon Resonance and Immunosensors,” Electron. Lett. 20, 968–970 (1984).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

J. R. Sambles, J. D. Pollard, G. W. Bradberry, “Liquid Layers Bound to a Gold Surface Supporting a Surface Plasmon Polariton,” Opt. Commun. 63, 288–292 (1987).
[CrossRef]

Sens. & Act. (1)

B. Liedberg, C. Nylander, I. Lundstrom, “Surface Plasmon Resonance for Gas Detection and Biosensing,” Sens. & Act. 4, 299–304 (1983).
[CrossRef]

Z. Phys. (1)

E. Kretschmann, “Die bestimmung optischer Konstanten von Metallen durch Anregung von Oberflächenplasmaschwingungen,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

Other (1)

W. L. Wolfe, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1963).

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Figures (3)

Fig. 1
Fig. 1

Definition of the characteristics of the SPR reflection curves; kx is the component of the wavevector parallel to the interfaces.

Fig. 2
Fig. 2

Definition of the layersystem, wavevectors (a) and the reflection coefficients (b,c). Layer 1 is the prism, layer 2 is the metal, and layer 3 is the bulk medium.

Fig. 3
Fig. 3

Experimental configuration for the measurement of the SPR reflection curve. The reflection R can be determined as a function of θ. The prism is rotated in steps of 0.01° and the reflection is measured with an accuracy of 10−3.

Tables (2)

Tables Icon

Table I Results from Simulated Reflection Curves (A) and with Fit Procedure (B)

Tables Icon

Table II Dielectric Permittivity and Thickness of Silver Films*

Equations (11)

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r 123 = r 12 b 23 + a 23 ( Re r 12 - i Im r 12 ) exp ( 2 i d k z 2 ) b 23 + a 23 ( Re r 12 + i Im r 12 ) exp ( 2 i d k z 2 ) .
k x 0 = ω c r 3 r - 3 .
k min = k x 0 + Γ + , R min = 1 - 4 A i B exp ( - ϕ d ) [ A i + B exp ( - ϕ d ) ] 2 , Δ k = 2 [ A i + B exp ( - ϕ d ) ] ,
d = - 1 ϕ ln [ Δ k 4 B ( 1 R min ) ] , i = Δ k 4 A ( 1 ± R min ) , r = 3 k min 2 k min 2 - 3 ( ω c ) 2 .
A = ω c 1 2 r 2 ( 3 r r - 3 ) 3 / 2 . B = ω c 2 r + 3 ( 3 r r - 3 ) 3 / 2 Im r 12 . ϕ = 2 ω c r r - 3 . Γ + = ω c 2 r + 3 ( 3 r r - 3 ) 3 / 2 Re r 12 exp ( - ϕ d ) . Re r 12 = a 2 - 1 2 a 2 + 1 2 ,
Im r 12 = 2 a 1 a 2 + 1 2 .
k min = k x 0 + Γ + + B 2 exp ( - 2 ϕ d ) Γ new 2 A i , R min = 1 - 4 B exp ( - ϕ d ) ( A i + Γ + Γ new ) ( B exp ( - i ϕ d ) Γ new + B 2 exp ( - 2 ϕ d ) Γ new 2 A i + A i Γ new 2 ) 2 + ( A i + B exp ( - ϕ d ) + Γ + Γ new ) 2 , Δ k = 2 ( A i + B exp ( - ϕ d ) + Γ + Γ new ) + 2 ( B exp ( - ϕ d ) Γ new + B 2 exp ( - 2 ϕ d ) Γ new 2 A i + A i 2 ) 2 A i + B exp ( - ϕ d ) + Γ + Γ new ,
Γ new = d ω c i r r - 3 - i 4 r 2 ( 3 r - 3 ) ω c .
k x 0 = k min - Γ + - B 2 exp ( - 2 ϕ d ) Γ new 2 A i = k min * 2 ( A i + B exp ( - ϕ d ) ) = Δ k - 2 ( B exp ( - ϕ d ) Γ new + B 2 exp ( - 2 ϕ d ) Γ new 2 A i + A i Γ new 2 ) 2 A i + B exp ( - ϕ d ) + Γ + Γ new = Δ k * 1 - 4 A i B exp ( - ϕ d ) [ A i + B exp ( - ϕ d ) ] 2 = R min - ( 1 - R min ) ( B exp ( - ϕ d ) Γ new + B 2 exp ( - 2 ϕ d ) Γ new 2 A i + A i Γ new 2 ) [ A i + B exp ( - ϕ d ) + Γ + Γ new ] [ A i + B exp ( - ϕ d ) ] = R min *
d = - 1 ϕ ln ( Δ k * 4 B [ 1 R min * ) ] i = Δ k * 4 A ( 1 ± R min * ) r = 3 k min * 2 k min * 2 - 3 ( ω c ) 2
r 12 2 = ( - r k z 1 - 1 Re k z 2 ) 2 + ( i k z 1 - 1 Im k z 2 ) 2 ( - r k z 1 + 1 Re k z 2 ) 2 + ( i k z 1 + 1 Im k z 2 ) 2 , k z 1 = ω c 1 r - 1 3 - 3 r r - 3 , k z 2 = ( 1 2 r - 3 ) 2 + i 2 4 ( cos α 2 - i sin α 2 ) = Re k z 2 + i Im k z 2 , α = arctan [ r 2 i ( r - 3 ) ] + π 2 .

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