Mapping van der Waals forces with frequency modulation dynamic force microscopy

Nanometre-size gold clusters supported on MoS2( 0001) are investigated by means of ultrahigh-vacuum frequency modulation dynamic force microscopy. Topography and frequency shift images are simultaneously obtained using the average tunnelling current to regulate the tip-substrate distance. Two families of clusters are observed, giving different frequency shift images. While the topographic and frequency shift profiles have similar shapes on small clusters ( size less than or similar to 1 nm), they are quite different near the top of large clusters ( size greater than or similar to 4 nm): the topographic profile is rounded, but the frequency shift profile exhibits rather steep edges and a depression near the centre of the island. It is demonstrated that these differences result from the finite range of van der Waals forces. On small islands, the frequency shift is dominated by the interaction of the tip with the substrate. On large islands, it is dominated by the interaction with the island. The particular observed shape results from the geometry of the island. These interpretations are comforted by analytical and numerical calculations. In particular, the characteristic shape of the frequency shift profiles on large islands can be reproduced by introducing realistic parameters and considering only the contribution of van der Waals forces.