Graphite

Graphite was the first substance to be imaged in air[99] and under liquids[98] at atomic resolution. Investigations under UHV conditions[117] as well as low temperature experiments[93,118] revealed the atomic scale structure of this surface. The relative ease of the imaging of the graphite surface under very different conditions has promoted its use as a calibration and test surface. Experiments going beyond the determination of the lateral scales revealed, however, that many unexpected effects play a role in the determination of the final appearance of the images.

Abbildung 4.283: Structure of the graphite crystal. The carbon atoms in the hexagonal rings at the surface occupy two inequivalent sites: At the A-site the carbon atom has a bond with the next lower layer, whereas at the B-site, there is no out-of-plane bond.

Figure 4.283 shows a schematic view of the structure of the graphite crystal. The carbon atoms are organized in layers of hexagons, with only weak bonding between the layers. This structure permits an easy cleavage of the surface, for instance by taping an adhesive tape to the surface and removing it carefully. The layered structure assures, too, that there are large, atomically flat terraces. As an example we show the topography of the graphite surface imaged at 6.8 K (figure 4.284). The image is similar to those obtained under other conditions. The hexagonal pattern of a graphite sheet is not resolved. Instead a mound-like pattern with the repeat distance of the unit cell of the graphite surface 0.54 nm is observed. At other times, hexagonal like structures or other structures are observed, but all with the periodicity of the graphite surface. Moreover, the height of the observed corrugation is often much larger than the height determined by He-scattering[119] or the calculated heights[114].

Abbildung 4.284: Low temperature image of graphite. The sample is held at 6.8 K. The size of the image is 3.3 nm. The height varies by 0.54 nm, from black to white.

This behavior can be understood by noting that the STM images of the graphite surface are determined by the density of states of the surface. The Fermi surface of graphite[90] is confined entirely to the edges of the hexagonal Brillouin zone[93] and the references therein). This means that, to a good approximation, the local density of states of the graphite surface at the Fermi energy can be represented by three standing waves[120]. Tersoff[72] showed, that the particular form of the Fermi surface leads to a point with vanishing tunneling current in the unit cell. Since the STM traces curves of constant density of states, this would lead to large corrugations, limited by the actual tip shape and by the timing of the scanning and the feedback loop. Another theory put forward to explain the giant corrugations by Soler[117] first noted that the forces between the tip and the sample can not be ignored. They argued, that because of the electronic structure of the graphite, the tip was so close to the surface that it would introduce a deformation of the surface. The different dependencies on the distance of the force and the tunneling current would explain the observed corrugations. Another explanation[121,122] involved contamination layers between the tip and the sample. These contamination layers in air consist partly of water and of other substances present in the air.

Mizes[120] also noted, that the different possible images of the graphite surface can be explained by multiple tip effects. If two or more tips coherently sample the amplitudes of the three standing waves describing the graphite surface a wide variety images can result. It is also possible to imagine entire leaflets of graphite are dragged across the graphite surface. Many tips in registry with the graphite surface sample the current. These images are, in principle, not distinguishable from single tip images of a large ordered area. This mode of imaging is more likely to occur at higher tunneling currents, where the tip is closer to the graphite surface. Steps, however, can only be imaged with a single or few atom tip and not with a leaflet of graphite. Normally, steps are only seen at low tunneling currents and high bias voltages, i.e., at larger separations between tip and graphite.

In summary, graphite is an excellent sample to check the operation of a microscope and to calibrate the $x$- and $y$-deflections. However, the details of the electronic structure and the intricacies of the surface condition of graphite make SXM-images of this surface all but easy to understand.