Copyright 2010 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.A method to calculate electric magnitudes at very small tip-sample distances in atomic force
microscopy is presented. We show that the method accurately calculates the electrostatic potential and vertical force for electrostatic force microscopy geometries that cannot be correctly simulated by the standard techniques. This technique can accurately calculate tip-sample distances four orders of magnitude smaller than the tip radius. We also demonstrate that, at this range, traditional techniques underestimate the electrostatic force in almost 30%. Finally, we calculate the jump-to-contact distance for geometries obtained from experiments that combine atomic force microscopy and scanning tunneling microscopy.J. J. Sáenz, P. Varona, E. Serrano, and F. Rodríguez for insightful discussions. This work was supported by Ministerio de Educación y Ciencia Grant Nos. TIN 2007-65989 and Comunidad Autonoma de Madrid S-SEM-0255-200
