devote Sec. \[sectionsurface\] to develop a model of the carbon film that is consistent with the experimental observations. To this end holographic images of the substrate film are analyzed (Sec. \[SubstrateHolography\]). First principle DFT calculations allow for the determination of the substrate-Au interaction (Sec. \[SubstrateDFT\]).

In Sec. \[sectiondynamics\] the observed islands are analyzed in detail. Their thickness is determined holographically (Sec.\[sectionFilmChar\]) and their stability tested in a heating experiment (Sec. \[sectionTemp\]).

In Sec. \[sectionMCfilm\] the formation of the islands and the shape of the Au clusters on their surface is modeled with MC simulations followed by the conclusion Sec. \[sectionConclusions\].

Methods {#sectionmethods}
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Experimental: substrate and sample preparation {#sectionsamples}
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The commercial a-C substrate films were produced by evaporation in a carbon arc by Arizona Carbon Foils and distributed by Plano GmbH as type S160. The films are mounted on a 200 nm mesh Cu grid for support. The film thickness is given by the manufacturer as $d_{\rm
  subs} = 10 - 12.5$ nm with a density of $\rho_{\rm subs} \approx
2.0$ g/cm$^3$ corresponding to a mass of $2 - 2.5 \mu {\rm g}/{\rm
  cm}^2$. The density of the substrate is closer to that of graphite ($\rho_{\rm graph} = 2.267$ 