  Control of nucleation sites is an important goal in materials growth: nuclei
in regular arrays may show emergent photonic or electronic behavior, and once
the nuclei coalesce into thin films, the nucleation density influences
parameters such as surface roughness, stress, and grain boundary structure.
Tailoring substrate properties to control nucleation is therefore a powerful
tool for designing functional thin films and nanomaterials. Here, we examine
nucleation control for metals deposited on two-dimensional (2D) materials in a
situation where substrate effects are absent and heterogeneous nucleation sites
are minimized. Through quantification of faceted, epitaxial Au island
nucleation on graphene, we show that ultra-low nucleation densities with nuclei
several micrometers apart can be achieved on suspended graphene under
conditions where we measure the nucleation density to be 2-3 orders of
magnitude higher on the adjacent supported substrate. We estimate diffusion
distances using nucleation theory and find a strong sensitivity of nucleation
and diffusion to suspended graphene thickness. We suggest that nucleation site
density control via substrate tuning may act as a platform for applications
where non-lithographic patterning of metals on graphene is beneficial.
