Small amplitude Dynamic AFM: quantifying interactions with different tip detection and excitation schemes in presence of additional resonances

TL;DR

This paper develops formulas to quantify tip-sample interactions in amplitude modulation AFM, analyzing the effects of spurious resonances and excitation schemes, and proposes calibration methods to improve measurement accuracy especially in liquids.

Contribution

It introduces new formulas for conservative and dissipative interactions and compares measurement schemes, highlighting calibration benefits in the presence of spurious resonances.

Findings

Acoustic excitation is insensitive to spurious resonances when measuring tip position.

Calibration using approach-retract curves improves accuracy in the presence of resonances.

Optical beam deflection AFMs benefit from the proposed calibration method.

Abstract

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.