Multi-frequency atomic force microscopy: A system-theoretic approach

Multi-frequency atomic force microscopy (MF-AFM), employing the detection and/or excitation of multiple cantilever frequencies, has shown great promise in increasing the compositional sensitivity, and the spatial and temporal resolution of imaging. The multitude of frequency components generated in MF-AFM encode information about the tip-sample nonlinearity. For quantitative interpretation of the observables in MF-AFM operation, we propose a two-pronged approach combining special-purpose cantilevers and a system-theoretic modeling paradigm. This provides an excellent framework to understand and leverage the nonlinear dynamics of the interaction of a multi-eigenmodal cantilever with the nonlinear force potentials on the sample surface, to develop novel imaging methods. We describe experimental techniques for accurate in-situ identification of the cantilever (sensor/actuator) transfer functions, which are crucial components to understand the generation of MF-AFM observables. The modeling framework is verified with experiments and is shown to be able to predict several key features of MF-AFM operation.