Rigorous Approach to Calculation of Capacitance Images of Metallic Samples for Use in Capacitance Microscopy

Abstract

Abstract-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.

Rigorous Approach to Analysis of Two-Dimensional Potential Problems, Wave Propagation and Scattering for Multi-conductor Systems

“…Here the power of the method is illustrated by the analysis of multi-conductor transmission lines. Other possible applications of our method for the problems modelled by the Laplace equation include impedance calculations for the transmission lines with adjustable inner conductor, published in [39] and capacitance calculations for the capacitance microscope [40].…”