Modeling of eccentric nanoneedle in trolling-mode atomic force microscope

Limitations on installation of a standard TR-AFM nanoneedle can have unpredictable effects on dynamics of system. Therefore, it is crucial to pay close attention to the position and geometry of mounted nanoneedle when deriving the mathematical model. During TR-AFM fabrication process, the nanoneedle may not always deposit precisely at the middle of AFM tip, which would result in coupled bending-torsion modes in the dynamical operation of system. In this paper, we investigate the effect of eccentric nanoneedle in dynamic response of TR-AFM. To address this issue, a continuous mathematical model is developed. This model accounts for eccentric nanoneedle which can address the couplings in nonlinear vibration. Hamilton's principle is used to derive equations of motion and then assumed mode method (AMM) is utilized. This model is capable of simulating the cantilever dynamics under complicated nanoneedle tip-sample interactions. Displacements of different components of system for various eccentricity are determined. It is found that nanoneedle eccentricity has noticeable effects on microbeam torsion angle and out of plane nanoneedle tip displacement.