Small amplitude Dynamic AFM: quantifying interactions with different tip   detection and excitation schemes in presence of additional resonances
  Quantifying the tip-sample interaction at the nanoscale in Amplitude Modulation mode AFM is challenging, especially when measuring in liquids. Here, we derive formulas for the tip-sample conservative and dissipative interactions and investigate the effect that spurious resonances have on the measured interaction. Both direct and acoustic excitation are considered. We also highlight the differences between measuring directly the tip position or the cantilever deflection. We show that, when probing the tip-sample forces, the acoustically excited cantilever behavior is insensitive to spurious resonances as long as the measured signal corresponds to the tip position, or if the excitation force is correctly taken into account. Since the effective excitation force may depend on the presence of such spurious resonances, we consider the cases where the frequency is kept constant during the measurement so that the proportionality between excitation signal and actual excitation force is kept constant. With the present work we show the advantages that result from the use of a calibration method based on the acquisition of approach-retract curves. Optical beam deflection based AFMs benefit from the use of this calibration method, especially in presence of spurious resonances in the cantilever transfer function. 
Luca Costa, Mario S Rodrigues
physics.ins-det cond-mat.mtrl-sci