Modelling of 'sub-atomic' contrast resulting from back-bonding on Si(111)-7×7

It has recently been shown that 'sub-atomic' contrast can be observed during NC-AFM imaging of the Si(111)-7×7 substrate with a passivated tip, resulting in triangular shaped atoms [Sweetman et al. Nano Lett. 2014, 14, 2265]. The symmetry of the features, and the well-established nature of the dangling bond structure of the silicon adatom means that in this instance the contrast cannot arise from the orbital structure of the atoms, and it was suggested by simple symmetry arguments that the contrast could only arise from the backbonding symmetry of the surface adatoms. However, no modelling of the system has been performed in order to understand the precise origin of the contrast. In this paper we provide a detailed explanation for 'sub-atomic' contrast observed on Si(111)-7×7 using a simple model based on Lennard-Jones potentials, coupled with a flexible tip, as proposed by Hapala et al. [Phys. Rev. B 2014, 90, 085421] in the context of interpreting sub-molecular contrast. Our results show a striking similarity to experimental results, and demonstrate how 'sub-atomic' contrast can arise from a flexible tip exploring an asymmetric potential created due to the positioning of the surrounding surface atoms.