Localization of the phantom force induced by the tunneling current

The phantom force is an apparently repulsive force, which can dominate the atomic contrast of an AFM image when a tunneling current is present. We described this effect with a simple resistive model, in which the tunneling current causes a voltage drop at the sample area underneath the probe tip. Because tunneling is a highly local process, the areal current density is quite high, which leads to an appreciable local voltage drop that in turn changes the electrostatic attraction between tip and sample. However, Si(111)-7x7 has a metallic surface state and it might be proposed that electrons should instead propagate along the surface state, as through a thin metal film on a semiconducting surface, before propagating into the bulk. In this paper, we first measure the phantom force on a sample that displays a metallic surface state [here, Si(111)-7x7] using tips with various radii. If the metallic surface state would lead to a constant electrostatic potential on the surface, we would expect a direct dependence of the phantom force with tip radius. In a second set of experiments, we study H/Si(100), a surface that does not have a metallic surface state. We conclude that a metallic surface state does not suppress the phantom force, but that the local resistance R-s has a strong effect on the magnitude of the phantom force.