Method to calculate electric fields at very small tip-sample distances in atomic force microscopy

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. (C) 2010 American Institute of Physics. [doi:10.1063/1.3467676]