Scaling Relations for Implantation of Size-Selected Au, Ag, and Si Clusters into Graphite

The deposition of size-selected clusters represents a new route to the fabrication of truly nanometer-scale surface architectures, e.g., nanopores. We report a systematic experimental study, coupled with molecular dynamics simulations, of the implantation depths of size-selected Au7, Ag7, and Si7 clusters in the model graphite substrate. For impact energies between 1.0 and 5.5 keV, we find that the implantation depth scales linearly with the momentum of the clusters for all three types of cluster. This "universal" behavior is consistent with a (viscous) retarding force proportional to the velocity of the cluster, akin to Stokes's law.