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Polynomial force approximations and multifrequency atomic force microscopy
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
2013 (English)In: Beilstein Journal of Nanotechnology, ISSN 2190-4286, Vol. 4, no 1, 352-360 p.Article in journal (Refereed) Published
Abstract [en]

We present polynomial force reconstruction from experimental intermodulation atomic force microscopy (ImAFM) data. We study the tip-surface force during a slow surface approach and compare the results with amplitude-dependence force spectroscopy (ADFS). Based on polynomial force reconstruction we generate high-resolution surface-property maps of polymer blend samples. The polynomial method is described as a special example of a more general approximative force reconstruction, where the aim is to determine model parameters that best approximate the measured force spectrum. This approximative approach is not limited to spectral data, and we demonstrate how it can be adapted to a force quadrature picture.

Place, publisher, year, edition, pages
2013. Vol. 4, no 1, 352-360 p.
Keyword [en]
AFM, Atomic force microscopy, Force spectroscopy, Intermodulation, Multifrequency, Polynomial
National Category
Nano Technology
URN: urn:nbn:se:kth:diva-122572DOI: 10.3762/bjnano.4.41ISI: 000320048600001ScopusID: 2-s2.0-84880255850OAI: diva2:622850
Swedish Research CouncilVinnovaKnut and Alice Wallenberg Foundation

QC 20131204. Updated from accepted to published.

Available from: 2013-05-23 Created: 2013-05-23 Last updated: 2013-12-04Bibliographically 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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