Forces and Currents in Carbon Nanostructures: Are We Imaging Atoms?

First-principles calculations show that the rich variety of image patterns found in carbon nanostructures with the atomic force and scanning tunneling microscopes can be rationalized in terms of the chemical reactivity of the tip and the distance range explored in the experiments. For weakly reactive tips, the Pauli repulsion dominates the atomic contrast and force maxima are expected on low electronic density positions as the hollow site. With reactive tips, the interaction is strong enough to change locally the hybridization of the carbon atoms, making it possible to observe atomic resolution in both the attractive and the repulsive regime although with inverted contrast. Regarding STM images, we show that in the near-contact regime, due to current saturation, bright spots correspond to hollow positions instead of atomic sites, providing an explanation for the most common hexagonal pattern found in the experiments.

Figure 1

Total force (black) for a dimer-terminated Si tip and a $(17,0)$ SWCNT. Open (solid) symbols correspond to the tip on a carbon atom (hollow site). The vdW interaction (red, circles) gives a common attractive background that sets the absolute force values, but the short-range interaction (green, triangles) provides the atomic scale contrast in the near-contact regime, with force maxima on the hollow site (inset).

Figure 2

Forces on a SWCNT and on graphite(1000) with tips of different chemical reactivity. The color code and symbols are as in Fig. 1. Reactive tips [$W$ tip, H3-Si tip in (a)] change locally the hybridization and provide force maxima on the atoms.

Figure 3

Constant-height STM images on graphite(0001) ($\mathrm{bias}=-300\mathrm{mV}$), including multiple scattering effects, for a tip-surface distance of (a) 5 and (b) 3 Å. Both images display a hexagonal pattern but with maxima on either $C_{\beta }$ atoms or hollow sites. (c)–(e) Line profiles at three distances show that multiple scattering contributions, not included in the common perturbative approach (red line), are needed to capture the contrast inversion found in the exact solution (black line).