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Tip-surface interactions in dynamic atomic forcemicroscopy
KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.ORCID iD: 0000-0002-5923-0279
KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.ORCID iD: 0000-0003-0675-974X
KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.ORCID iD: 0000-0001-8534-6577
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In atomic force microscopy (AFM) tip-surface interactions are usuallyconsidered 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 interactionsappropriate to dynamic AFM where the measurement of force is restricted toa narrow frequency band. We represent the tip-surface interaction in termsof a force disk in the phase space of position and velocity. Determination ofthe amplitude dependence of tip-surface forces at a fixed static probe heightallows for a comprehensive treatment of conservative and dissipative interactions.We illuminate the fundamental limitations of force reconstruction with narrowband dynamic AFM and we show how the amplitude dependence of the F ouriercomponent of the force at the tip oscillation frequency, gives qualitative insight intothe detailed nature of the tip-surface interaction. With minimal assumptions thisamplitude dependence force spectroscopy allows for a quantitative reconstruction ofthe effective conservative tip-surface force as well as a position-dependent dampingfactor. We demonstrate this reconstruction on simulated intermodulation AFMdata.

Keyword [en]
atomic force microscopy, measurement of force, mechanical resonators, MEMS/NEMS, dissipation, intermodulation
National Category
Nano Technology
URN: urn:nbn:se:kth:diva-122581OAI: diva2:622854
Swedish Research CouncilVinnova

QS 2013

Available from: 2013-05-23 Created: 2013-05-23 Last updated: 2013-05-27Bibliographically approved
In thesis
1. Reconstructing force from harmonic motion
Open this publication in new window or tab >>Reconstructing force from harmonic motion
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

High-quality factor oscillators are often used in measurements of verysmall force since they exhibit an enhanced sensitivity in the narrow frequencyband around resonance. Forces containing frequencies outside this frequencyband are often not detectable and the total force acting on the oscillatorremains unknown. In this thesis we present methods to eciently use theavailable bandwidth around resonance to reconstruct the force from partialspectral information.We apply the methods to dynamic atomic force microscopy (AFM) wherea tip at the end of a small micro-cantilever oscillates close to a sample surface.By reconstructing the force between the tip and the surface we can deducedierent properties of the surface. In contrast, in conventional AFM only oneof the many frequency components of the time-dependent tip-surface forceallowing for only qualitative conclusions about the tip-surface force.To increase the number of measurable frequency components we developed Intermodulation AFM (ImAFM). ImAFM utilizes frequency mixing ofa multifrequency drive scheme which generates many frequencies in the response to the nonlinear character of the tip-surface interaction. ImAFM,amplitude-modulated AFM and frequency-modulated AFM can be considered as special cases of narrow-band AFM, where the tip motion can bedescribed by a rapidly oscillating part and a slowly-varying envelope function. Using the concept of force quadratures, each rapid oscillation cycle canbe analyzed individually and ImAFM measurements can be interpreted as arapid measurement of the dependence of the force quadratures on the oscillation amplitude or frequency. To explore the limits of the force quadraturesdescription we introduce the force disk which is a complete description of thetip-surface force in narrow-band AFM at xed static probe height.We present a polynomial force reconstruction method for multifrequencyAFM data. The polynomial force reconstruction is a linear approximativeforce reconstruction method which is based on nding the parameters of amodel force which best approximates the tip-surface force. Another classof reconstruction methods are integral techniques which aim to invert theintegral relation between the tip-surface force and the measured spectraldata. We present an integral method, amplitude-dependence force spectroscopy (ADFS), which reconstructs the conservative tip-surface force fromthe amplitude-dependence of the force quadratures. Together with ImAFMwe use ADFS to combine high-resolution AFM imaging at high speeds withhighly accurate force measurements in each point of an image. For the measurement of dissipative forces we discuss how methods from tomography canbe used to reconstruct forces that are a function of both tip position andvelocity.The methods developed in this thesis are not limited to dynamic AFM andwe describe them in the general context of a harmonic oscillator subject to anexternal force. We hope that theses methods contribute to the transformationof AFM from a qualitative imaging modality into quantitative microscopy andwe hope that they nd application in other measurements which exploit theenhanced sensitivity of a high-quality factor oscillator.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. v, 91 p.
Trita-FYS, ISSN 0280-316X ; 2013:21
oscillator, force spectroscopy, atomic force microscopy, intermodulation, multifrequency, inverse problem, high quality factor
National Category
Nano Technology
urn:nbn:se:kth:diva-122583 (URN)978-91-7501-792-1 (ISBN)
Public defence
2013-06-14, FA31, Albanova University Center, Roslagstullsbacken 21, Stockholm, 13:00 (English)

QC 20130527

Available from: 2013-05-27 Created: 2013-05-23 Last updated: 2013-05-27Bibliographically approved

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