Multimodal analysis of force spectroscopy based on a transfer function study of micro-cantilevers

Quantitative force spectroscopy experiments require a comprehensive knowledge of the frequency response characteristics of the micro-cantilever. To establish a generic theoretical model an analytical mathematical description of the cantilever dynamics in force spectroscopy was developed using a transfer function approach. This study allows for quantitative evaluation of force spectroscopy experiments and analysis of stability and controllability of an atomic force microscope (AFM). The model accounts for the dynamic characteristics of the extended cantilever beam and for elastic sample properties. The system dynamics were investigated using an exact system-theoretic approach. The step and frequency responses are given for force spectroscopy experiments in different experimental configurations. The transfer function approach used in this study allows us to investigate very significant dynamic aspects that simple first mode approximations cannot capture. Only extended beam models account for both poles and zeros of the transfer function and can thus reproduce important features that are related to the zero dynamics. These features include pole-zero cancellations or non-minimum phase response. The possibility of non-minimum phase response in AFM is highly important for the design of inverse filters. The presence of zeros in the right half of the Laplace plane immediately implies that the inverse system is unstable.