Theory of electrostatic probe microscopy: A simple perturbative approach

A theoretical approach to electrostatic scanning probe microscopy is presen ted. We show that a simple perturbation formula, originally derived in the context of scattering theory of electromagnetic waves, can be used to obtai n 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 be tween an effective surface profile and a response function of the microscop e. This provides a rigorous framework to address the resolution issue and t he inverse problem. (C) 2000 American Institute of Physics. [S0003-6951(00) 04820-8].