Quantitative Theory for Probe-Sample Interaction With Inhomogeneous Perturbation in Near-Field Scanning Microwave Microscopy

Abstract

A general approach for calculating tip–sample capacitance variation in near-field scanning microwave microscopy is presented. It can be applied to arbitrary tip shapes, thick and thin films, and variation due to inhomogeneous perturbation. The computation domain for the tip–sample interaction problem is reduced to a block perturbation area by applying Green’s theorem, and thus it can save substantial time and memory during calculating either electric field or contrast capacitance for three-dimensional models of near-field microwave microscopy. We show that this method can accurately calculate capacitance variation due to inhomogeneous perturbation in insulating or conductive samples, as verified by finite-element analysis results of commercial software and experimental data from microwave impedance microscopy. More importantly, the method in this paper also provides a rigorous framework to solve the inverse problem, which has great potential to improve resolution by deconvolution.