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The Optical Properties of Semi-Continuous Metal Films: A Scaling Based Model

Published online by Cambridge University Press:  28 February 2011

Y. Yagil ,
M. Yosefin ,
D. J. Bergman  and
G. Deutscher
Y. Yagil
Affiliation:
Department of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978 Tel - Aviv, Israel
M. Yosefin
Affiliation:
Department of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978 Tel - Aviv, Israel
D. J. Bergman
Affiliation:
Department of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978 Tel - Aviv, Israel
G. Deutscher
Affiliation:
Department of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978 Tel - Aviv, Israel
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Abstract

We present a calculation of the optical properties of thin semi-continuous metal films near the percolative metal-insulator transition. The model is based on scaling assumptions, reflecting the fractal nature of these films. The film is divided into small squares of linear size L and the local complex conductivity of each square is calculated, using finite size scaling arguments and taking into account both ohmic resistance within the metallic clusters and intercluster capacitance. The size L, over which the finite size scaling is done, is related to the optical frequency by the anomalous diffusion relation, i.e. L(ω) α ωl/(2+θ). In this calculation two types of conductivities are found : good ones for the ‘metallic’ squares, showing that large clusters are present within these squares, and poor conductivities for ‘dielectric’ squares, where only small clusters are present. Moreover, the ‘metallic’ and ‘dielectric’ squares are not identical, thus a certain distribution of each type has to be considered. The width of the distribution is quite large close to the percolation threshold and decreases to zero when the film becomes homogeneous. The optical properties of the whole sample are obtained by summing the contribution from all squares, using a wide bimodal distribution function. Comparison with recent experimental results shows good agreement between this model and the experimental data.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 195: Symposium S – Physical Phenomena in Granular Materials , 1990 , 65
Copyright
Copyright © Materials Research Society 1990

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References

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