Characterization of surface stiffness and probe-sample dissipation using the band excitation method of atomic force microscopy: a numerical analysis

Recently Jesse and co-workers introduced the band excitation atomic force microscopy (BE-AFM) method (Jesse et al 2007 Nanotechnology 18 435503), in which the cantilever probe is excited in a continuum frequency band in order to measure its response at all frequencies in the band. Analysis of the cantilever response using the damped harmonic oscillator model provides information on the stiffness and level of dissipation at the tip-sample junction as the sample is scanned. Since its introduction, this method has been used in magnetic, electromechanical, thermal and molecular unfolding applications, among others, and has given rise to a new family of scanning probe microscopy techniques. Additionally, the concept is applicable to any field in which measurement of the frequency response of harmonic oscillators is relevant. In this paper we present an analytical and numerical analysis of the excitation signals used in BE-AFM, as well as of the cantilever response under different conditions. Our analysis is performed within the context of viscoelastic characterization. We discuss subtleties in the cantilever dynamics, provide guidelines for implementing the method effectively and illustrate the use of simulation in interpreting the results.