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An analytical model of the electrostatic force between the tip of anon-contact Atomic Force Microscope (nc-AFM) and the (001) surface of an ioniccrystal is reported. The model is able to account for the atomic contrast ofthe local contact potential difference (CPD) observed while nc-AFM-based KelvinProbe Force Microscopy (KPFM) experiments. With the goal in mind to put inevidence this short-range electrostatic force, the Madelung potential arisingat the surface of the ionic crystal is primarily derived. The expression of theforce which is deduced can be split into two major contributions: the firststands for the coupling between the microscopic structure of the tip apex andthe capacitor formed between the tip, the ionic crystal and thecounter-electrode; the second term depicts the influence of the Madelungsurface potential on the mesoscopic part of the tip, independently from itsmicroscopic structure. These short-range electrostatic forces are in the rangeof ten pico-Newtons. When explicitly considering the crystal polarization, ananalytical expression of the bias voltage to be applied on the tip tocompensate for the local CPD, i.e. to cancel the short-range electrostaticforce, is derived. The compensated CPD has the lateral periodicity of theMadelung surface potential. However, the strong dependence on the tip geometry,the applied modulation voltage as well as the tip-sample distance, which caneven lead to an overestimation of the real surface potential, makesquantitative KPFM measurements of the local CPD extremely difficult.

Analytical Approach to the Local Contact Potential Difference on (001) Ionic Surfaces: Implications for Kelvin Probe Force Microscopy