Tip-surface interactions in dynamic atomic force microscopy

TL;DR

This paper introduces a new method for analyzing tip-surface interactions in dynamic AFM by representing forces in phase space and using amplitude dependence to reconstruct conservative and dissipative forces, enhancing understanding of nanoscale interactions.

Contribution

It presents a novel force spectroscopy approach that captures velocity and trajectory dependence in tip-surface interactions within narrow band dynamic AFM.

Findings

Force disk representation in phase space effectively describes interactions.

Amplitude dependence reveals qualitative force characteristics.

Simulated data demonstrates accurate force reconstruction.

Abstract

In atomic force microscopy (AFM) tip-surface interactions are usually considered as functions of the tip position only, so-called force curves. However, tip-surface interactions often depend on the tip velocity and the past tip trajectory. Here, we introduce a compact and general description of these interactions appropriate to dynamic AFM where the measurement of force is restricted to a narrow frequency band. We represent the tip-surface interaction in terms of a force disk in the phase space of position and velocity. Determination of the amplitude dependence of tip-surface forces at a fixed static probe height allows for a comprehensive treatment of conservative and dissipative interactions. We illuminate the fundamental limitations of force reconstruction with narrow band dynamic AFM and we show how the amplitude dependence of the Fourier component of the force at the tip oscillation frequency, gives qualitative insight into the detailed nature of the tip-surface interaction. With minimal assumptions this amplitude dependence force spectroscopy allows for a quantitative reconstruction of the effective conservative tip-surface force as well as a position-dependent damping factor. We demonstrate this reconstruction on simulated intermodulation AFM data.