Optimization of the excitation frequency for high probe sensitivity in single-eigenmode and bimodal tapping-mode AFM

The cantilever excitation frequency and tip free oscillation amplitude are two critical imaging parameters in amplitude-modulation atomic force microscopy (AM-AFM, often referred to as tapping-mode AFM). In general, the excitation frequency is selected to be 'near' the measured resonance frequency of the probe, but there is no established systematic approach for making that choice. In this work we show that the choice of excitation frequency can play a very significant role in the characterization of viscoelastic materials, even when considering small deviations with respect to the resonance frequency. Additionally, we offer an analytical expression, verified through experiments and numerical simulations, which offers guidance for selecting the drive frequency that maximizes probe sensitivity. Our approach is illustrated experimentally through single-eigenmode and bimodal AFM measurements performed on spin-coated Nafion(®) proton exchange thin films. We find that very often, the phase contrast channel is optimized by selecting an excitation frequency that is not necessarily at or near the free resonance frequency.