Current Research

One of the most potent achievments in AFM (atomic force microscopy) in the recent years was the use of a new type of cantilever called the qPlus sensor[1]. This much stiffer sensor allowed to image the surface in distances of a view tenth of a nanometer. With this amazing new technology Giessibl et. al. succeeded to obtain "subatomic resolution"[2]. This signifies that the images resolved substructures within an atomic dimension. The questions now to be raised are: how to understand these subatomic features? How is it possible that with a tip, extended on the scale of several nanometer, such small features can be resolved?

Figure 1

An important clue to understand the substructures is the observation that the sample-tip distance is of the order of some angstroems. This is the regime of atomic orbitals, so the structures may be ascribed to orbital overlap and the formation of covalent bonds between tip and sample. If, for simplicity, we assume the tip to have one front atom with two dangling sp3-bonds (we are talking about a silicon 100-tip) one can imagine that these two dangling bonds participate in creating such substructures in the atomic image. The images were taken on a silicon 111(7x7) surface. This surface is well investigated and it is considered to have one dangling sp3 bond perpendicular to the surface per surface atom. For our theoretical treatment we focus, in a first step, just on one atom of this complicated surface and correspondingly take the one perpendicular dangling bond into account. Our model tip also consists of only one atom namely the front atom with the two dangling bonds. So our problem is reduced to the overlap of two imaging tip orbitals and one imaged surface orbital. The actual geome try is shown in figure 1.

Figure 2

With this extremely simplified model we can easily perform a LCAO calculation to get the energy profile of this configuration. From the profile we deduce the forces between the tip and the sample atom which are due to covalent binding of the considered atoms. In a final step, the frequency shift is compared to experiments. Indeed it is possible to reproduce some aspects of the measured substructures. We find a doublepeak (figure 2) like in the experimental data and, moreover, this structures emerges within a reasonable distance and energy range.

This proves within a simple microscopic modelling that we have to deal with the orbital configuration of both tip and sample to understand subatomic structures in AFM and STM measurements. Actually, in the case considered the substructures are an image of the tip. One could think of imaging the tip with known surfaces.

Beyond this basic approach we started to investigate the tip-sample interactions with the LDA-method (Local Density Approximation). This state of the art technique shows very good results in predicting bulk properties of weakly correlated systems. It is also suitable for more complicated situations like our tip-sample problem. We expect to get more accurate results this way but we pay for it with considerable more complexity in the calculations.