Quantum size effects observed in high coverage Au layers on MoS$_{\mathrm{2}}$

Scanning tunneling microscopy has been used to study the surface of Au thin films grown on MoS$_{\mathrm{2}}$ at room temperature using thermal evaporation. Immediately after deposition, the surface consists of terraced triangular structures with lateral dimensions on the order of 3-10 nm. After annealing to 600 K these structures condense into isolated terraced islands with lateral dimensions that reach 100 nm in some cases. Height distribution analysis after annealing indicates a preference for certain island heights corresponding to~N $=$ 8, 15, 23, and 29~atomic layers of Au. This result suggests that the growth mechanism is driven by quantum confinement considerations rather than strain effects. The preferred or "magic" heights correspond to those islands with states furthest from the Fermi level. Unlike observations of Pd and Ag films, the spacing of these peaks is consistent with the surface fermi wave vector rather than the bulk.