Rigorous approach to calculation of capacitance images of metallic samples for use in capacitance microscopy

A high-efficiency rigorous approach for the solution of the two-dimensional Laplace equation with Dirichlet’s boundary conditions is developed to tackle electrostatic problems involving metallic cylinders of arbitrarily cross-sections. In this paper, we demonstrate how this novel algorithm can be used to address the problems arising in the capacitance microscopy to provide a higher resolution in studies of micro-cavities and whiskers on the surface of metallic samples. The precise capacitance images of the probe/sample systems are presented.