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Intermodulation 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.
KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
KTH, School of Engineering Sciences (SCI), Applied Physics.ORCID iD: 0000-0001-8534-6577
2008 (English)In: Applied Physics Letters, ISSN 0003-6951, E-ISSN 1077-3118, Vol. 92, 153106- p.Article in journal (Refereed) Published
Abstract [en]

A mode of atomic force microscopy ͑AFM͒ is demonstrated where an oscillating AFM cantileverhaving linear response is driven with two frequencies in the vicinity of a resonance. Newfrequencies in the response, known as intermodulation products, are generated when the linearity ofthe cantilever response is perturbed by the nonlinear tip-surface interaction. A rich structure of theintermodulation products is observed as a function of the probe-surface separation, indicating thatit is possible to extract much more detailed information about the tip-surface interaction than ispossible with the standard amplitude and phase imaging methods.

Place, publisher, year, edition, pages
2008. Vol. 92, 153106- p.
Keyword [en]
Atomic force microscopy, Nonlinear oscillations, Cantilevers; Surfaces; Tip
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:kth:diva-11551DOI: 10.1063/1.2909569ISI: 000255117100081Scopus ID: 2-s2.0-42349116023OAI: oai:DiVA.org:kth-11551DiVA: diva2:277681
Note

QC 20100812

Available from: 2009-11-20 Created: 2009-11-19 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Intermodulation in microresonators: for microwave amplification and nanoscale surface analysis
Open this publication in new window or tab >>Intermodulation in microresonators: for microwave amplification and nanoscale surface analysis
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This work explores the effects of weak nonlinearity on harmonic oscillators.Two particular systems are studied experimentally: A superconductingresonator formed from a coplanar waveguide that oscillates at microwave frequencies,and the cantilever of an atomic force microscope (AFM) vibratingat ultrasonic frequencies. Both of these systems are described in the introduction,followed by a theory chapter giving a general theoretical framework for nonlinear oscillators. Basic properties of nonlinear oscillators, such asbifurcation and intermodulation, are explained using simple models. Experimental methods, including cryogenic and microwave measurement techniques,are described in some detail.

The nonlinear superconducting resonator is studied for use as a parametric amplifier. A strong drive tone, called the pump, drives the oscillator nearthe point of bifurcation. A second, much weaker drive signal that is slightlydetuned from the pump, will cause energy to move from the pump to the signal, giving signal amplification. We have measured a signal gain greaterthan 22 dB in a bandwidth of 30 kHz, for a resonator pumped at 7.6 GHz.This type of amplifier is phase-sensitive, meaning that signals in phase withthe pump will be amplified, but signals in quadrature phase of the pump will be deamplified. Phase-sensitivity has important implications on the amplifier’snoise properties. With a parametric amplifier, a signal can be amplified without any additional noise being added by the amplifier, something that is fundamentally impossible for a standard amplifier.

The vibrating AFM cantilever becomes a nonlinear oscillator when it is interacting with a surface. When driven with two frequencies, the amplitudeand phase of the cantilever’s response will develop mixing products, or intermodulation products, that are very sensitive to the exact form of the nonlinearity. Very small changes in the surface properties will be detectable when measuring the intermodulation products. Simultaneously measuring many intermodulation products, or acquiring an intermodulation spectrum,allows one to reconstruct the tip-surface interaction. Intermodulation AFM increases the sensitivity of the measurement or the contrast of the acquiredimages, and provides a means of rapidly measuring the nonlinear tip-surface interaction. The method promises to enhance the functionality of the AFM beyond simple topography measurement, towards quantitative analysis of the chemical or material properties of the surface.

Place, publisher, year, edition, pages
Stockholm: KTH, 2009. v, 106 p.
Series
Trita-FYS, ISSN 0280-316X ; 2009:66
Keyword
Superconductivity, Atomic Force Microscopy, Nonlinear oscillators, Parametric amplification
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-11593 (URN)978-91-7415-508-2 (ISBN)
Public defence
2009-12-11, FB54, AlbaNova University Center, Roslagstullsbacken 21,, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

QC 20100812

Available from: 2009-12-04 Created: 2009-11-20 Last updated: 2012-08-30Bibliographically approved
2. 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.
Series
Trita-FYS, ISSN 0280-316X ; 2013:21
Keyword
oscillator, force spectroscopy, atomic force microscopy, intermodulation, multifrequency, inverse problem, high quality factor
National Category
Nano Technology
Identifiers
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)
Opponent
Supervisors
Note

QC 20130527

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

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Publisher's full textScopushttp://link.aip.org/link/?APPLAB/92/153106/1

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Platz, DanielHaviland, David

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