Numerical modelling for atomic-force-microscopy-based impedance imaging

Abstract

This paper is motivated by the pioneering work of O'Hayre et al. and of Kalinin and Bonnell who brought together the imaging modalities of atomic force microscopy (AFM) and electrical impedance spectroscopy. With the intention to assist in the further development of AFM-impedance imaging by enhancing its quantitative spatial resolution, a numerical model is provided on the basis of a finite element method which can be used to simulate the impedance measurements. The model facilitates the contact impedance at the interface between the tip of the atomic force microscope's cantilever and the upper surface of the sample. Based on this model, a formula is derived for the linearized sensitivity of the measurement as a spatial function that relates the value of electric potential recorded at the tip to the electrical properties of the sample underneath it. The performed numerical simulations suggest that the sensitivity functions of adjacently captured impedance measurements overlap, and this introduces linear dependences in the acquired data, ultimately reducing the spatial resolution of the reconstructed image. © 2005, Institution of Mechanical Engineers. All rights reserved.