FRACTAL DIMENSION OF DISCONTINUOUS COPPER-FILMS

Fractal-like structures have been observed in discontinuous Cu films evaporated onto quartz substrates in vacuo (10(-8) torr). The microstructures of the films were examined with an electron microscope using a carbon replica. On the basis of the micrographs, the coverage coefficients and the distributions of the island sizes and gap sizes were determined for the Cu films with the coverage coefficient (p) ranging from 0.3 to 1. The discontinuous films were also simulated by computer for 0.1 < p < 1. The fractal dimensions of the evaporated and modelled films were determined using the box-counting method. It has been found that the fractal dimensions (D) depend on the film structure characterized by the coverage coefficient. In the coverage coefficient range considered the fractal dimension increases with increasing p from D = 1.74 to D = 2, approaching value D-c = 1.84 in a percolation threshold. The experimental values are in good agreement with the computer simulations.