Interpreting motion and force for narrow-band intermodulation atomic force microscopy

TL;DR

This paper introduces a novel analysis method for intermodulation atomic force microscopy (ImAFM) that extracts detailed tip-surface force components as functions of both probe height and oscillation amplitude, enhancing understanding of surface interactions.

Contribution

The paper presents a new time domain analysis of ImAFM that reconstructs force components' dependence on amplitude and probe height from single measurements, advancing surface force characterization.

Findings

Force components depend on both probe height and oscillation amplitude.

Single measurement can reconstruct amplitude-dependent force components.

Demonstrated method on polystyrene surface.

Abstract

Intermodulation atomic force microscopy (ImAFM) is a mode of dynamic atomic force microscopy that probes the nonlinear tip-surface force by measurement of the mixing of multiple tones in a frequency comb. A high $Q$ cantilever resonance and a suitable drive comb will result in tip motion described by a narrow-band frequency comb. We show by a separation of time scales, that such motion is equivalent to rapid oscillations at the cantilever resonance with a slow amplitude and phase or frequency modulation. With this time domain perspective we analyze single oscillation cycles in ImAFM to extract the Fourier components of the tip-surface force that are in-phase with tip motion ($F_I$) and quadrature to the motion ($F_Q$). Traditionally, these force components have been considered as a function of the static probe height only. Here we show that $F_I$ and $F_Q$ actually depend on both static probe height and oscillation amplitude. We demonstrate on simulated data how to reconstruct the amplitude dependence of $F_I$ and $F_Q$ from a single ImAFM measurement. Furthermore, we introduce ImAFM approach measurements with which we reconstruct the full amplitude and probe height dependence of the force components $F_I$ and $F_Q$, providing deeper insight into the tip-surface interaction. We demonstrate the capabilities of ImAFM approach measurements on a polystyrene polymer surface.