Fractal Geometry of Percolation in Thin Gold Films

  • Richard F. Voss
  • Robert B. Laibowitz
  • Eileen I. Alessandrini


Transmission electron micrographs of thin evaporated gold films with thickness varying from 6 to 10 nm were analyzed by computer. The films cover the range from electrically insulating to conducting and thus span the 2D percolation threshold. The film geometry is interpreted in terms of both the scaling theory of percolation and Mandelbrot’s fractal geometry. We find that Au-Au and Au-substrate interactions set a small scale correlation length of order 20nm. Small clusters are dominated by these effects and have simple almost-circular shapes. At larger scales, however, the irregular connected clusters are ramified with a perimeter linearly proportional to area. Near the percolation threshold the large scale power-law correlations and area distributions are consistent with the scaling theory of 2nd order phase transitions. The collection of all clusters forms a fractal distribution with D=2 while the largest cluster has D = 2−β/v ≃ 1.9. Many of the usual analytic scaling relations between universal exponents are shown to have fractal geometric basis.


Fractal Dimension Large Cluster Pair Correlation Function Percolation Cluster Thin Gold Film 
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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Richard F. Voss
    • 1
  • Robert B. Laibowitz
    • 1
  • Eileen I. Alessandrini
    • 1
  1. 1.IBM Thomas J. Watson Research CenterYorktown HeightsUSA

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