Electrostatic forces acting on the tip in atomic force microscopy: Modelization and comparison with analytic expressions

With the model of equivalent charge distribution, we calculated the exact electrostatic force acting on the real (conical) tip of an atomic force microscope. This model applies to a conductive tip in front of a conductive plane. We compared the equivalent charge model with several analytic models used to date to approximate the electrostatic forces and discussed their degree of validity. We estimated the contribution of the cantilever to the total force and showed, on the basis of theoretical calculations and experimental results, that the contribution of cantilever may constitute the essential part of the electrostatic force in the range of distances used in electrostatic force microscopy in the air.