The Relation between Resonance Curves and Tip-Surface Interaction Potential in Noncontact Atomic-Force Microscopy

We present a perturbation theory which enables us to understand the physics of the cantilever-forced vibration in noncontact-mode atomic-force microscopy. Analytical expressions of the resonance curve and frequency shift are given. This theory is applied to the model system with a van der Waals tip-surface interaction potential. Based on this case study, it is elucidated how the resonance frequency shift is analytically described by an integral of the tip-surface interaction force over the traverse of the tip around the turning point. This quantity is rather sensitive to the interaction potential. We can see by this method how the dynamical instability occurs and significantly influences the observation of the resonance peak. Calculated resonance curves and frequency shifts agree fairly well with those obtained by a numerical integration of equation of motion outside the bistable region.