Contribution of the numerical approach to kelvin probe force microscopy on the atomic-scale

The goal of this chapter is to gather and detail recent numerical developments addressing the issue of atomic-scale measurements in Kelvin Probe Force Microscopy (KPFM). It is argued why the problem requires the combination between the atomistic description of the distance- and bias voltage-dependent force field occurring between the tip and the surface, as well as an accurate numerical implementation of the complex noncontact atomic force microscopy and KPFM setup. When combining these tools, it is possible to draw conclusions regarding the origin of the atomic-scale KPFM contrast and its connections with usual physical observables such as the surface potential and the local work function. These aspects are discussed with respect to the surface of a bulk ionic crystal.