Study of the electrostatic force between a conducting tip in proximity with a metallic surface: Theory and experiment

A formula has been derived for the electrostatic force between the conducting tip and a planer metallic surface by exploiting the fact that the tip-sample geometry can be described by confocal hyperboloids of revolution. The prolate spheroidal coordinate system was found to be most convenient for this purpose. The general behavior of force curves obtained in the attractive regime using a conducting cantilever and an optical beam deflection system is in reasonably good agreement with the theory over a wide range of distances. The results are important in the context of design, development, and understanding of scanning probe microscopes involving voltage bias between the probe and sample. (C) 2000 American Institute of Physics. [S0021-8979(00)08022-1].