Integral Equation Modeling of Electrostatic Interactions in Atomic Force Microscopy

Since its invention in 1986 [BQG86], the atomic force microscope (AFM) has evolved as a major tool for characterizing materials. Of the several operational modes of the AFM, the noncontact mode is normally used to determine the sample surface charge distribution. In this range of tip - sample separation, the Coulombic interaction between the tip and the sample dominates over magnetic and van der Waal forces. Despite the simple and explicit expression of Coulomb's law, mapping AFM images to sample charge distributions cannot be done in a straightforward way because of the finite size of the AFM tip and the roughness of the sample. Thus, researchers have been approaching this inverse problem from the opposite direction by making efforts to predict AFM measurements based on assumed sample properties. Numerous models have been proposed to tackle this electrostatic problem. Binnig, G., Quate, C.F., Gerber, Ch.: Atomic force microscope. Phys. Rev. Lett., 56, 930-933 (1986).