Theory of electrostatic probe microscopy: A simple perturbative approach

Abstract

A theoretical approach to electrostatic scanning probe microscopy is presented. We show that a simple perturbation formula, originally derived in the context of scattering theory of electromagnetic waves, can be used to obtain the capacitance and the electrostatic force between a metallic tip and an inhomogeneous dielectric sample. For inhomogeneous thin dielectric films, the scanning probe signal is shown to be proportional to the convolution between an effective surface profile and a response function of the microscope. This provides a rigorous framework to address the resolution issue and the inverse problem.