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 ${\mathrm{A}\mathrm{u}}_7$, ${\mathrm{A}\mathrm{g}}_7$, and ${\mathrm{S}\mathrm{i}}_7$ 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.

Figure 1

(a) STM image ($5\times 5\mu {\mathrm{m}}^2$) of the graphite surface showing etch pits created by oxidative etching after $\mathrm{S}\mathrm{i}_7{}^{+}$ cluster implantation at 4.5 keV. (b) Height profile corresponding to the white line in (a).

Figure 2

The distribution of the etch pit depths obtained after implantation of $\mathrm{S}\mathrm{i}_7{}^{+}$ clusters into graphite at 1.0, 2.5, and 4.5 keV. The data are fitted to Gaussian distributions.

Figure 3

The implantation depths for ${\mathrm{A}\mathrm{u}}_7$, ${\mathrm{A}\mathrm{g}}_7$, and ${\mathrm{S}\mathrm{i}}_7$ clusters in graphite as a function of (a) kinetic energy, (b) velocity, and (c) momentum. The depths are given with respect to the topmost graphite layer. The data for $\mathrm{A}\mathrm{g}_7{}^{-}$ are obtained from Ref. 13. In (c), the dashed lines are the best fit straight lines for ${\mathrm{A}\mathrm{u}}_7$ and ${\mathrm{A}\mathrm{u}}_7$ (see text). The filled circles are the depths of the damage tracks from MD simulations for ${\mathrm{S}\mathrm{i}}_7$. The crosses are the calculated center-of-mass cluster implantation depths.

Figure 4

Snapshot from MD simulations of cluster implantation into graphite, after completion of the collisional phase, for normally incident, seven-atom clusters at 4 keV. (a) ${\mathrm{A}\mathrm{g}}_7$ cluster; (b) ${\mathrm{S}\mathrm{i}}_7$ cluster. In (b) there is more damage underneath the implanted cluster, caused by recoil C atoms. Note also the sputtered C atom above the surface in this case. The cluster atoms are shown in green.