Abstract

The optical properties of ultrathin Au films on silicon have been studied in the infrared over a wide frequency range from 200 to 10,000cm1. Thick films show a Drude behavior; i.e., with increasing frequency the transmission increases; for films below the percolation threshold at about 5nm a negative slope for the frequency-dependent transmission is observed. When the thickness is further reduced, between 1 and 3nm an anomaly occurs: the relative transmission reaches maximum values above 100% compared with the bare substrate, indicating an antireflection coating of nanometer thickness for light of 5μm wavelength. This anomaly can be explained in the framework of effective-medium theories.

© 2007 Optical Society of America

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    [CrossRef]

2003 (1)

J. J. Tu, C. C. Homes, and M. Strongin, Phys. Rev. Lett. 90, 017402 (2003).
[CrossRef] [PubMed]

2002 (2)

G. Fahsold, M. Sinther, A. Priebe, S. Diez, and A. Pucci, Phys. Rev. B 65, 235408 (2002).
[CrossRef]

R. Lazzari and I. Simonsen, Thin Solid Films 419, 124 (2002).
[CrossRef]

2000 (1)

G. Fahsold, A. Bartel, O. Krauth, N. Magg, and A. Pucci, Phys. Rev. B 61, 14108 (2000).
[CrossRef]

1999 (1)

P. F. Henning, C. C. Homes, S. Maslov, G. L. Carr, D. N. Basov, B. Nikolic, and M. Stronggin, Phys. Rev. Lett. 83, 4880 (1999).
[CrossRef]

1998 (2)

A. M. Goldman and N. Markovic, Phys. Today 51(11), 39 (1998).
[CrossRef]

K. L. Ekinci and J. M. Valles, Phys. Rev. B 58, 7347 (1998).
[CrossRef]

1992 (1)

Y. Yagil, P. Gadenne, C. Julien, and G. Deutscher, Phys. Rev. B 46, 2503 (1992).
[CrossRef]

1991 (1)

T. W. Noh, P. H. Song, and A. J. Sievers, Phys. Rev. B 44, 5459 (1991).
[CrossRef]

1990 (2)

J. P. Clerk, G. Giraud, J. M. Laugier, and J. M. Luck, Adv. Phys. 39, 4883 (1990).

U. Teschner and K. Hübner, Phys. Status Solidi B 159, 917 (1990).
[CrossRef]

1985 (1)

1956 (1)

M. Tinkham, Phys. Rev. 104, 845 (1956).
[CrossRef]

1935 (1)

D. Bruggeman, Ann. Phys. 24, 6736 (1935).

1904 (1)

C. Maxwell-Garnett, Philos. Trans. R. Soc. London 203, 385 (1904).
[CrossRef]

Alexander, R. W.

Bartel, A.

G. Fahsold, A. Bartel, O. Krauth, N. Magg, and A. Pucci, Phys. Rev. B 61, 14108 (2000).
[CrossRef]

Basov, D. N.

P. F. Henning, C. C. Homes, S. Maslov, G. L. Carr, D. N. Basov, B. Nikolic, and M. Stronggin, Phys. Rev. Lett. 83, 4880 (1999).
[CrossRef]

Bedeaux, D.

D. Bedeaux and J. Vlieger, Optical Properties of Surfaces (Imperial College Press, 2001).

Bell, R. J.

Bruggeman, D.

D. Bruggeman, Ann. Phys. 24, 6736 (1935).

Carr, G. L.

P. F. Henning, C. C. Homes, S. Maslov, G. L. Carr, D. N. Basov, B. Nikolic, and M. Stronggin, Phys. Rev. Lett. 83, 4880 (1999).
[CrossRef]

Clerk, J. P.

J. P. Clerk, G. Giraud, J. M. Laugier, and J. M. Luck, Adv. Phys. 39, 4883 (1990).

Deutscher, G.

Y. Yagil, P. Gadenne, C. Julien, and G. Deutscher, Phys. Rev. B 46, 2503 (1992).
[CrossRef]

Diez, S.

G. Fahsold, M. Sinther, A. Priebe, S. Diez, and A. Pucci, Phys. Rev. B 65, 235408 (2002).
[CrossRef]

Ekinci, K. L.

K. L. Ekinci and J. M. Valles, Phys. Rev. B 58, 7347 (1998).
[CrossRef]

Fahsold, G.

G. Fahsold, M. Sinther, A. Priebe, S. Diez, and A. Pucci, Phys. Rev. B 65, 235408 (2002).
[CrossRef]

G. Fahsold, A. Bartel, O. Krauth, N. Magg, and A. Pucci, Phys. Rev. B 61, 14108 (2000).
[CrossRef]

Gadenne, P.

Y. Yagil, P. Gadenne, C. Julien, and G. Deutscher, Phys. Rev. B 46, 2503 (1992).
[CrossRef]

Giraud, G.

J. P. Clerk, G. Giraud, J. M. Laugier, and J. M. Luck, Adv. Phys. 39, 4883 (1990).

Goldman, A. M.

A. M. Goldman and N. Markovic, Phys. Today 51(11), 39 (1998).
[CrossRef]

Henning, P. F.

P. F. Henning, C. C. Homes, S. Maslov, G. L. Carr, D. N. Basov, B. Nikolic, and M. Stronggin, Phys. Rev. Lett. 83, 4880 (1999).
[CrossRef]

Homes, C. C.

J. J. Tu, C. C. Homes, and M. Strongin, Phys. Rev. Lett. 90, 017402 (2003).
[CrossRef] [PubMed]

P. F. Henning, C. C. Homes, S. Maslov, G. L. Carr, D. N. Basov, B. Nikolic, and M. Stronggin, Phys. Rev. Lett. 83, 4880 (1999).
[CrossRef]

Hübner, K.

U. Teschner and K. Hübner, Phys. Status Solidi B 159, 917 (1990).
[CrossRef]

Julien, C.

Y. Yagil, P. Gadenne, C. Julien, and G. Deutscher, Phys. Rev. B 46, 2503 (1992).
[CrossRef]

Krauth, O.

G. Fahsold, A. Bartel, O. Krauth, N. Magg, and A. Pucci, Phys. Rev. B 61, 14108 (2000).
[CrossRef]

Laugier, J. M.

J. P. Clerk, G. Giraud, J. M. Laugier, and J. M. Luck, Adv. Phys. 39, 4883 (1990).

Lazzari, R.

R. Lazzari and I. Simonsen, Thin Solid Films 419, 124 (2002).
[CrossRef]

Long, L. L.

Luck, J. M.

J. P. Clerk, G. Giraud, J. M. Laugier, and J. M. Luck, Adv. Phys. 39, 4883 (1990).

Magg, N.

G. Fahsold, A. Bartel, O. Krauth, N. Magg, and A. Pucci, Phys. Rev. B 61, 14108 (2000).
[CrossRef]

Markovic, N.

A. M. Goldman and N. Markovic, Phys. Today 51(11), 39 (1998).
[CrossRef]

Maslov, S.

P. F. Henning, C. C. Homes, S. Maslov, G. L. Carr, D. N. Basov, B. Nikolic, and M. Stronggin, Phys. Rev. Lett. 83, 4880 (1999).
[CrossRef]

Maxwell-Garnett, C.

C. Maxwell-Garnett, Philos. Trans. R. Soc. London 203, 385 (1904).
[CrossRef]

Nikolic, B.

P. F. Henning, C. C. Homes, S. Maslov, G. L. Carr, D. N. Basov, B. Nikolic, and M. Stronggin, Phys. Rev. Lett. 83, 4880 (1999).
[CrossRef]

Noh, T. W.

T. W. Noh, P. H. Song, and A. J. Sievers, Phys. Rev. B 44, 5459 (1991).
[CrossRef]

Ordal, M. A.

Priebe, A.

G. Fahsold, M. Sinther, A. Priebe, S. Diez, and A. Pucci, Phys. Rev. B 65, 235408 (2002).
[CrossRef]

Pucci, A.

G. Fahsold, M. Sinther, A. Priebe, S. Diez, and A. Pucci, Phys. Rev. B 65, 235408 (2002).
[CrossRef]

G. Fahsold, A. Bartel, O. Krauth, N. Magg, and A. Pucci, Phys. Rev. B 61, 14108 (2000).
[CrossRef]

Querry, M. R.

Sievers, A. J.

T. W. Noh, P. H. Song, and A. J. Sievers, Phys. Rev. B 44, 5459 (1991).
[CrossRef]

Simonsen, I.

R. Lazzari and I. Simonsen, Thin Solid Films 419, 124 (2002).
[CrossRef]

Sinther, M.

G. Fahsold, M. Sinther, A. Priebe, S. Diez, and A. Pucci, Phys. Rev. B 65, 235408 (2002).
[CrossRef]

Song, P. H.

T. W. Noh, P. H. Song, and A. J. Sievers, Phys. Rev. B 44, 5459 (1991).
[CrossRef]

Stronggin, M.

P. F. Henning, C. C. Homes, S. Maslov, G. L. Carr, D. N. Basov, B. Nikolic, and M. Stronggin, Phys. Rev. Lett. 83, 4880 (1999).
[CrossRef]

Strongin, M.

J. J. Tu, C. C. Homes, and M. Strongin, Phys. Rev. Lett. 90, 017402 (2003).
[CrossRef] [PubMed]

Teschner, U.

U. Teschner and K. Hübner, Phys. Status Solidi B 159, 917 (1990).
[CrossRef]

Tinkham, M.

M. Tinkham, Phys. Rev. 104, 845 (1956).
[CrossRef]

Tu, J. J.

J. J. Tu, C. C. Homes, and M. Strongin, Phys. Rev. Lett. 90, 017402 (2003).
[CrossRef] [PubMed]

Valles, J. M.

K. L. Ekinci and J. M. Valles, Phys. Rev. B 58, 7347 (1998).
[CrossRef]

Vlieger, J.

D. Bedeaux and J. Vlieger, Optical Properties of Surfaces (Imperial College Press, 2001).

Yagil, Y.

Y. Yagil, P. Gadenne, C. Julien, and G. Deutscher, Phys. Rev. B 46, 2503 (1992).
[CrossRef]

Adv. Phys. (1)

J. P. Clerk, G. Giraud, J. M. Laugier, and J. M. Luck, Adv. Phys. 39, 4883 (1990).

Ann. Phys. (1)

D. Bruggeman, Ann. Phys. 24, 6736 (1935).

Appl. Opt. (1)

Philos. Trans. R. Soc. London (1)

C. Maxwell-Garnett, Philos. Trans. R. Soc. London 203, 385 (1904).
[CrossRef]

Phys. Rev. (1)

M. Tinkham, Phys. Rev. 104, 845 (1956).
[CrossRef]

Phys. Rev. B (5)

G. Fahsold, M. Sinther, A. Priebe, S. Diez, and A. Pucci, Phys. Rev. B 65, 235408 (2002).
[CrossRef]

T. W. Noh, P. H. Song, and A. J. Sievers, Phys. Rev. B 44, 5459 (1991).
[CrossRef]

G. Fahsold, A. Bartel, O. Krauth, N. Magg, and A. Pucci, Phys. Rev. B 61, 14108 (2000).
[CrossRef]

Y. Yagil, P. Gadenne, C. Julien, and G. Deutscher, Phys. Rev. B 46, 2503 (1992).
[CrossRef]

K. L. Ekinci and J. M. Valles, Phys. Rev. B 58, 7347 (1998).
[CrossRef]

Phys. Rev. Lett. (2)

P. F. Henning, C. C. Homes, S. Maslov, G. L. Carr, D. N. Basov, B. Nikolic, and M. Stronggin, Phys. Rev. Lett. 83, 4880 (1999).
[CrossRef]

J. J. Tu, C. C. Homes, and M. Strongin, Phys. Rev. Lett. 90, 017402 (2003).
[CrossRef] [PubMed]

Phys. Status Solidi B (1)

U. Teschner and K. Hübner, Phys. Status Solidi B 159, 917 (1990).
[CrossRef]

Phys. Today (1)

A. M. Goldman and N. Markovic, Phys. Today 51(11), 39 (1998).
[CrossRef]

Thin Solid Films (1)

R. Lazzari and I. Simonsen, Thin Solid Films 419, 124 (2002).
[CrossRef]

Other (1)

D. Bedeaux and J. Vlieger, Optical Properties of Surfaces (Imperial College Press, 2001).

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Figures (3)

Fig. 1
Fig. 1

AFM images of (a) 3 nm and (b) 7 nm thick gold films thermally evaporated on silicon at room temperature in ultra high vacuum.

Fig. 2
Fig. 2

Frequency-dependent transmission of gold films with different thicknesses normalized to the transmission of the bare Si substrate. Thicker films exhibit a metallic Drude behavior, which develops to an almost frequency-independent transmission at the percolation threshold at around 5 nm . Below 3 nm an anomaly occurs with a maximum of nearly 110% relative transmission at about 2000 cm 1 . For the very thin film the transmission is again lower.

Fig. 3
Fig. 3

Comparison between the measured 2 nm spectrum and a simulation based on Eqs. (1, 2, 3, 4). Inset: the relative transmission at 2000 cm 1 behaves nonmonotonically with film thickness and shows a clear maximum with values well above 100% at about 2 nm .

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

T f T s = n s + 1 n s + 1 + 2 δ ϵ 2 + δ 2 g ,
g = ϵ s + ( ϵ 1 2 + ϵ 2 2 ) ϵ 1 ( 1 + ϵ s ) .
ϵ ̂ m ( ω ) = ϵ 1 + i ϵ 2 = 1 ω p 2 ω 2 + i ω τ ,
f ϵ ̂ m ( ω ) ϵ ̂ e f f ( ω ) ϵ ̂ m ( ω ) + ϵ ̂ e f f ( ω ) + ( 1 f ) ϵ ̂ i ( ω ) + ϵ ̂ e f f ( ω ) ϵ ̂ i ( ω ) ϵ ̂ e f f ( ω ) = 0 .

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