The unique mechanical and electronic properties of fullerenes, nanotubes, graphene and carbon nano-ribbons make them very promising materials for nanotechnological applications. First-principles calculations of forces and currents between a tip and carbon nanostructures show that the rich variety of image patterns found in atomic-scale AFM and STM measurements can be rationalized in terms of the chemical reactivity of the tip and the distance range explored in the experiments.

The Experimental Puzzle: Honeycomb versus Hexagonal Images

The simple honeycomb structure shared by these materials represents both a perfect testing ground and a fundamental challenge for STM and AFM with true atomic resolution (FM-AFM). Graphite can be imaged with atomic resolution even in ambient conditions but, after 25 years of research, there is no consensus yet whether the maxima in the atomic-scale images correspond to atoms or to the hollow sites. The first STM images of the graphite(0001) surface did not display the expected honeycomb pattern but a hexagonal arrangement of bright spots (fig. 1) [1].

The accepted interpretation relies on a subtle electronic effect [2]. The Bernal stacking makes the two surface atoms inequivalent. Cα atoms, with a nearest neighbor right below in the second layer, do not contribute significantly to the density of states (DOS) close to the Fermi level and only the Cβ atoms are imaged as bright spots at low bias voltages. Although a honeycomb pattern should be recovered for larger biases, the experimental evidence accumulated [3], shows that STM images with a hexagonal pattern are overwhelmingly recorded over a broad range of bias voltages and distance operation conditions. The situation gets even more confusing when one realizes that images with hexagonal symmetry can be also linked with maxima at the hollow sites in the center of the hexagons.

The situation is also puzzling in FM-AFM, as we have experimental results from world-class groups showing either a hexagonal or a honeycomb array of bright spots [4-7]. STM and AFM experiments on graphite are difficult to interpret as carbon planes can be easily pulled out by the interaction with the tip, resulting in local contact for relatively far distances.

Single wall carbon nanotubes (SWCNT), much stiffer in the normal direction, offer an excellent alternative to determine the variation of forces and currents with distance. FM-AFM images on SWCNT using semiconductor tips [6] only reach clear atomic contrast at small tip-sample distances. Force spectroscopy data on different sites show maximum attractive forces that are a factor of 10 smaller than those typical for semiconductor surfaces. Therefore, a van der Waals (vdW) tip-CNT interaction has been assumed and the bright spots in the images have been interpreted as hollow sites.

Force Contrast: The Role of Tip Reactivity

Understanding this puzzling situation requires a theoretical analysis that identifies unambiguously the interaction responsible for the atomic contrast in low-dimensional carbon materials and that can reconcile the apparently contradictory experimental results. To that end, we have carried out an extensive set of first principles calculations to map out the tip-sample interaction and the electronic currents between several tip apexes with different chemical reactivity and both a (17,0) SWCNT (with a radius close to the one used in the experiments) and a graphite(0001) surface [8]. For an accurate representation of the interaction, we combine density functional theory (DFT) calculations using the PBE exchange-correlation functional for the short-range (SR) chemical force with a semi-empirical atomistic approach for the vdW interaction [8].

The pattern that emerges from these calculations is that the tip reactivity plays a crucial role in the determination of the nature of the atomic contrast but this is always controlled by the SR chemical interaction and not by the vdW. These conclusions are illustrated by the force versus distance curves calculated on top of a carbon atom and on the hollow site for two representative cases: a Si tip with a dimer at the apex (fig. 1d) and a W tip (fig. 1e).

With rather inert tips, the total force is attractive mainly due to the vdW contribution, but this interaction does not yield itself atomic contrast. SR interactions are basically repulsive (essentially the Pauli repulsion between electronic clouds) and force maxima correspond to the positions with lower electronic density like the hollow sites, resulting in a hexagonal pattern. For very reactive tips, particularly metallic ones, the SR attractive interaction dominates the total force and gives a honeycomb contrast with maximal forces on the atoms (fig. 1e). This enhanced tip-sample interaction is due to the high reactivity of the dangling bond in the outermost apex atom, that makes a change in the hybridization of the carbon atom on the nanotube (from sp2 to sp3) energetically favorable, resulting in the formation of a chemical bond. Beyond the force maximum, the interaction on the top site decreases due to the strong Pauli repulsion and there is a crossing of the force curves that results in force maxima on the hollow sites. Thus, our results predict a reversal of the FM-AFM image contrast for very close distances when metallic tips are used.