Amplitude dependence of resonance frequency and its consequences for scanning probe microscopy

TL;DR

This paper demonstrates that the resonance frequency of probes in scanning probe microscopy depends on oscillation amplitude due to geometric effects, which can cause significant errors in quantifying tip-sample interactions if uncorrected.

Contribution

It reveals the amplitude dependence of resonance frequency as a systematic error source in SPM and emphasizes the need for correction to improve measurement accuracy.

Findings

Resonance frequency varies systematically with oscillation amplitude.

Amplitude dependence introduces errors in measured interaction potentials.

Correction of amplitude effects is necessary for high-resolution quantification.

Abstract

With recent advances in scanning probe microscopy (SPM), it is now routine to determine the atomic structure of surfaces and molecules while quantifying the local tip-sample interaction potentials. Such quantitative experiments are based on the accurate measurement of the resonance frequency shift due to the tip-sample interaction. Here, we experimentally show that the resonance frequency of oscillating probes used for SPM experiments change systematically as a function of oscillation amplitude under typical operating conditions. This change in resonance frequency is not due to tip-sample interactions, but rather due to the cantilever strain or geometric effects and thus the resonance frequency being a function of the oscillation amplitude. Our numerical calculations demonstrate that the amplitude dependence of the resonance frequency is an additional yet overlooked systematic error source that can result nonnegligible errors in measured interaction potentials and forces. Our experimental results and complementary numerical calculations reveal that the frequency shift due to this amplitude dependence needs to be corrected even for experiments with active oscillation amplitude control to be able to quantify the tip-sample interaction potentials and forces with milli-electron volt and pico-Newton resolutions.