State-space model of freely vibrating and surface-coupled cantilever dynamics in atomic force microscopy
Physical Review B 69(8): 085412
The dynamics of the microcantilever in atomic force microscopy (AFM) is represented by a multiple-degrees-of-freedom state-space model and is discussed within the framework of system theory. The cantilever dynamics is modeled as a linear time-invariant system with a nonlinear output feedback due to the tip-sample interaction. This allows one to use the same model to analyze different aspects of atomic force microscopy such as the dynamics of contact-mode or the dynamics of tapping-mode AFM. The state-space approach to the dynamic response of the AFM cantilever allows for numerically efficient simulations. We show that not only the eigenfrequency but also the modal damping of a cantilever interacting with a surface strongly depends on the contact stiffness. This is important for a quantitative characterization of elastic sample properties. Additionally, our model shows the presence of higher harmonics in tapping-mode AFM. The excitation of higher eigenmodes can strongly distort the system response. The results illustrate that higher eigenmodes have to be considered in the analysis of dynamic AFM.