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 using noncontact frequency modulation atomic force microscopy is 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 is 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 in 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.
Highlights
IntroductionResonant structures are widely used as accurate measurement devices in fields of science ranging from biological chemical detection to gravitational waves or quantum mechanical systems [1,2,3,4,5]
Resonant structures are widely used as accurate measurement devices in fields of science ranging from biological chemical detection to gravitational waves or quantum mechanical systems [1,2,3,4,5].oscillating structures play a transducer role in atomic force microscopy (AFM) and related techniques [6,7]
The frequency modulation AFM (FM-AFM) technique tracks the change in the resonance frequency of the cantilever, ∆f, under the influence of the attractive surface forces while keeping the oscillation amplitude ‘constant’ [8]
Summary
Resonant structures are widely used as accurate measurement devices in fields of science ranging from biological chemical detection to gravitational waves or quantum mechanical systems [1,2,3,4,5]. The currently reported experimental work can be summarized as the quantitative measurement of internal structures of molecules and chemical bonds in a molecule [21], the quantitative assessment of intermolecular interactions [22], the quantification of stiffness and the interaction with lateral force microscopy of molecules with sub milli-electron volt resolution for potential energy and zepto-Newton resolution for the torsional stiffness [23], and van der Waals interactions of isolated atoms with sub-milli-electron volt potential energy resolutions [24]. Our experiments and numerical calculations address the amplitude dependence of the resonance frequency as an important yet overlooked systematic error source which can impede the accurate measurement of the tip-sample interaction potential and force with milli-electron volt and pico-Newton resolutions. The systematic error due to the amplitude dependence of the resonance frequency should be corrected for meaningful and accurate data acquisition
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