Vertical and lateral electrostatic forces in a tip-plane system studied with a Green function plus surface charge method

An effective method to calculate the electrostatic force between a microscopic tip and an infinite metallic plane is proposed and tested. The Green function method is used to integrate out exactly the potential distribution in the plane. The plane plus tip problem is thus reduced to a boundary value problem for the tip surface only, enabling solution by a standard numerical method. The main advantage of this approach is that systems with an arbitrary plane potential distribution may be solved with the same method and comparable numerical efficiency to problems with a constant plane potential. The method is used to calculate the electrostatic force on a tip due to a plane with a step potential and a local quadratic potential island. The calculated perpendicular force components agree with previously published theoretical results. In addition, lateral components of the tip-surface force are computed and shown to be comparable to the vertical component close to a potential step, in agreement with the published experimental data. This suggests the possibility of using lateral, as well as vertical force data in atomic force microscopy for the detection and imaging of potential steps. (c) 2007 American Institute of Physics.