Accurate, explicit formulae for higher harmonic force spectroscopy by frequency modulation-AFM

• Kfir Kuchuk and
• Uri Sivan

Beilstein J. Nanotechnol. 2015, 6, 149–156, doi:10.3762/bjnano.6.14

• conservative and dissipative forces in terms of an arbitrary single harmonic. Additionally, we show that in frequency modulation-AFM (FM-AFM) each harmonic carries complete information on the force, obviating the need for multi-harmonic analysis. Finally, we show that higher harmonics may indeed be used to

• reconstruct short range forces more accurately than the fundamental harmonic when the oscillation amplitude is small compared with the interaction range. Keywords: atomic force spectroscopy; higher harmonic FM-AFM; Introduction AFM measurements are presently utilized to generate atomic resolution [1][2], 3D

• resonance frequency. In frequency modulation-AFM (FM-AFM), the force is usually reconstructed from the resonance frequency shift, which in the small amplitude regime is proportional to the derivative of the force with respect to tip–surface distance. Similarly, it has been recognized that higher harmonics

Dissipation signals due to lateral tip oscillations in FM-AFM

• Michael Klocke and
• Dietrich E. Wolf

Beilstein J. Nanotechnol. 2014, 5, 2048–2057, doi:10.3762/bjnano.5.213

• force microscopy (AFM); frequency-modulated atomic force microscopy (FM-AFM); energy dissipation; Introduction The usage of scanning probe microscopes requires an understanding of the physical processes during the scan, otherwise images can be misinterpreted. Due to the importance of frequency

• -modulated atomic force microscopy (FM-AFM), the physical processes involved have been studied intensively in the past [1]. This includes the relation between tip–surface interaction and frequency-shift [2], as well as features such as the energy dissipation during the scan [3], which is an interesting side

• -effect of the FM-AFM principle. The height (the topography) of a point on the surface is measured by shifting the probe such that the resonant frequency of the cantilever oscillation is detuned by a given amount due to surface–tip interactions. The amplitude is kept constant, which requires to drive the

Probing viscoelastic surfaces with bimodal tapping-mode atomic force microscopy: Underlying physics and observables for a standard linear solid model

• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 1649–1663, doi:10.3762/bjnano.5.176

• and Garcia [11][12], which is the most common, but some of the discussion is also applicable to bimodal methods involving frequency-modulation (FM-AFM [3][9][18][27]. Characterization of viscoelastic surfaces with AFM Viscoelastic characterization is generally performed with contact-mode-based methods

• ][35][36] methods. Within multi-frequency AFM, Lozano et al. analyzed the behavior of Vts and Pts for the original bimodal AFM method, which uses an open loop drive to excite the higher eigenmode [32][37]. Naitoh and coworkers reported bimodal experiments by using FM-AFM to drive both eigenmodes, in

• , constant-excitation FM-AFM and constant-amplitude FM-AFM [27]. Even more recently Herruzo et al. [9] succeeded for the first time in inverting the conservative tip–sample interaction force curve along with a depth-dependent, direction-independent tip–sample dissipation coefficient by using bimodal FM-AFM

Trade-offs in sensitivity and sampling depth in bimodal atomic force microscopy and comparison to the trimodal case

• Babak Eslami,
• Daniel Ebeling and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 1144–1151, doi:10.3762/bjnano.5.125

• generally smaller than that of the fundamental mode, it can be made more sensitive to compositional contrast, as previously discussed by Rodriguez and Garcia [12]. The two eigenmodes can also be driven using the frequency modulation scheme (FM-AFM [4][15][16][17]), and it is also possible to simultaneously

Impact of thermal frequency drift on highest precision force microscopy using quartz-based force sensors at low temperatures

• Florian Pielmeier,
• Daniel Meuer,
• Daniel Schmid,
• Christoph Strunk and
• Franz J. Giessibl

Beilstein J. Nanotechnol. 2014, 5, 407–412, doi:10.3762/bjnano.5.48

• Florian Pielmeier Daniel Meuer Daniel Schmid Christoph Strunk Franz J. Giessibl Institute of Experimental and Applied Physics, University of Regensburg, D-93053 Regensburg, Germany 10.3762/bjnano.5.48 Abstract In frequency modulation atomic force microscopy (FM-AFM) the stability of the

• ]. In FM-AFM the frequency shift Δf = f – f0 of a mechanical oscillator with stiffness k upon tip–sample interaction is measured, while the oscillation amplitude A is kept constant. For quantitative force measurements the uncertainty in the force gradient is crucial [7]. Frequency shift and force

• gradient are related via where is the averaged force gradient between tip and sample, which can be deconvolved into kts [8]. Four noise contributions limit the accuracy of the Δf measurement, which are inherent to FM-AFM [7]. Deflection detector noise [1][9][10][11] is proportional to the measurement

Frequency, amplitude, and phase measurements in contact resonance atomic force microscopies

• Gheorghe Stan and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 278–288, doi:10.3762/bjnano.5.30

• ), respectively [15][16][17][18][19][20]. In the last ten years, intermittent-contact measurements have been enhanced through multifrequency excitation methods [21][22][23][24][25][26][27]. In multifrequency AFM, the fundamental cantilever eigenmode is typically controlled in conventional AM- or FM-AFM mode for

• sensitivity. However, with the exception of small-amplitude FM-AFM [28][29] in which the tip–sample force gradient can be measured directly, the mapping of Vts and Pts in intermittent-contact imaging generally only provides a qualitative map of surface viscoelasticity. In this work the focus is on the CR-AFM

Multiple regimes of operation in bimodal AFM: understanding the energy of cantilever eigenmodes

• Daniel Kiracofe,
• Arvind Raman and
• Dalia Yablon

Beilstein J. Nanotechnol. 2013, 4, 385–393, doi:10.3762/bjnano.4.45

• not possible to separately identify the conservative (e.g., elastic) and dissipative (e.g., viscous) components of the tip–sample interaction by using the first eigenmode phase (in contrast to FM-AFM imaging, or higher eigenmode imaging in bimodal AFM). Instead, the first eigenmode phase gives

Bimodal atomic force microscopy driving the higher eigenmode in frequency-modulation mode: Implementation, advantages, disadvantages and comparison to the open-loop case

• Daniel Ebeling and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2013, 4, 198–207, doi:10.3762/bjnano.4.20

• fundamental eigenmode is driven by using the amplitude-modulation technique (AM-AFM) while a higher eigenmode is driven by using either the constant-excitation or the constant-amplitude variant of the frequency-modulation (FM-AFM) technique. We also offer a comparison to the original bimodal AFM method, in

• type, instrumentation availability and user skill level. General appeal of frequency shift and relationship to phase contrast The first question that emerges when discussing AM-FM concerns the reasoning behind the use of FM-AFM, which has in the past been mostly reserved for vacuum operation, with a

• few exceptions in liquid imaging [16][17] and spectroscopy experiments in air as well as in liquid [18][19][20][21]. Historically, FM-AFM addressed the limitation brought about by the large transient times observed in classical AM-AFM, where the oscillation amplitude is used as an input signal for the

Interpreting motion and force for narrow-band intermodulation atomic force microscopy

• Daniel Platz,
• Daniel Forchheimer,
• Erik A. Tholén and
• David B. Haviland

Beilstein J. Nanotechnol. 2013, 4, 45–56, doi:10.3762/bjnano.4.5

• -modulation AFM (FM-AFM) and amplitude-modulation AFM (AM-AFM) FI and FQ are usually probed by a slow variation of the probe height h with fixed oscillation amplitude at each height. To measure FI and FQ in FM-AFM the oscillation frequency shift and the drive force are recorded as the static probe height is

• values of the force quadratures [13]. In contrast to FM-AFM, the oscillation amplitude is free to change during the measurement and thus the AM-AFM measurement path in the h–A plane is more complicated. The path shown in Figure 6 was obtained by simulating the AM-AFM tip dynamics with cvode. In the

• ]. This instability is frequently observed in experiments, and it makes the reconstruction of tip–surface forces rather difficult. In contrast to FM-AFM and AM-AFM, ImAFM allows for a measurement of FI and FQ at fixed static probe height, along a straight path parallel to the A axis in the h–A plane, as

Thermal noise limit for ultra-high vacuum noncontact atomic force microscopy

• Jannis Lübbe,
• Matthias Temmen,
• Sebastian Rode,
• Philipp Rahe,
• Angelika Kühnle and
• Michael Reichling

Beilstein J. Nanotechnol. 2013, 4, 32–44, doi:10.3762/bjnano.4.4

• for high-Q cantilevers. Combining Equation 1 and Equation 3 yields a simple yet accurate expression for the power spectral density of the total displacement noise in an FM-AFM system operated under high-Q conditions [4]: To obtain the noise power spectral density of the frequency-shift signal present

Spring constant of a tuning-fork sensor for dynamic force microscopy

• Dennis van Vörden,
• Manfred Lange,
• Merlin Schmuck,
• Nico Schmidt and
• Rolf Möller

Beilstein J. Nanotechnol. 2012, 3, 809–816, doi:10.3762/bjnano.3.90

• , offering several advantages compared to the standard microfabricated silicon-based cantilevers [1][2]. Frequency-modulation atomic force microscopy (FM-AFM) with a tuning-fork sensor has had a major impact on fundamental and scientific research, e.g., by resolving the structure of a molecule [3] or even

• determining the structure of an unknown organic molecule [4]. In FM-AFM, the motion of the sensor is given in very good approximation by a harmonic oscillator. For the limit of small amplitudes the measurement of the frequency shift provides the average force gradient caused by the interaction between the tip

Drive-amplitude-modulation atomic force microscopy: From vacuum to liquids

• Miriam Jaafar,
• David Martínez-Martín,
• Mariano Cuenca,
• John Melcher,
• Arvind Raman and
• Julio Gómez-Herrero

Beilstein J. Nanotechnol. 2012, 3, 336–344, doi:10.3762/bjnano.3.38

• high quality factor Q of the cantilevers in vacuum, which present a settling time given by τcl= Q/(πf0). Frequency-modulation AFM (FM-AFM, also known as noncontact AFM) [9] is the classical alternative to AM allowing atomic resolution in UHV chambers [10] at higher scanning rates. FM-AFM has recently

• been extended to operate in other media with lower Q, with remarkable success [11]. However, FM-AFM has a well-known drawback: The transition from noncontact to contact causes an instability in the feedback control [12], which is particularly important for inhomogeneous surfaces in which, for example

Graphite, graphene on SiC, and graphene nanoribbons: Calculated images with a numerical FM-AFM

• Fabien Castanié,
• Laurent Nony,
• Sébastien Gauthier and
• Xavier Bouju

Beilstein J. Nanotechnol. 2012, 3, 301–311, doi:10.3762/bjnano.3.34

• tackled FM-AFM image calculations of three types of graphitic structures, namely a graphite surface, a graphene sheet on a silicon carbide substrate with a Si-terminated surface, and finally, a graphene nanoribbon. We compared static structures, meaning that all the tip and sample atoms are kept frozen in

• demonstrates the stability of our n-AFM to image a non-perfectly planar substrate exhibiting a geometrical step as well as a material step. Keywords: calculations; FM-AFM; graphene; graphite; image; nanoribbon; Introduction In the family of atomic force microscopy (AFM) techniques, the frequency-modulation

• fork and provides a stiff probe capable of being approached close enough to the sample without touching the surface [62]. When the probe is oscillating above the sample, one of the characteristics of an experimental FM-AFM setup is the presence of several feedback loops to pilot the probe based on the

Simultaneous current, force and dissipation measurements on the Si(111) 7×7 surface with an optimized qPlus AFM/STM technique

• Zsolt Majzik,
• Martin Setvín,
• Andreas Bettac,
• Albrecht Feltz,
• Vladimír Cháb and
• Pavel Jelínek

Beilstein J. Nanotechnol. 2012, 3, 249–259, doi:10.3762/bjnano.3.28

• , and reliable interpretation of the atomic contrast becomes very difficult. The next milestone in AFM history was the introduction of the frequency-modulation (FM)-AFM technique by Albrecht and co-workers [4]. By applying this method Giessibl demonstrated the possibility of achieving true atomic

• resolution on the prototypical Si(111) 7×7 surface [5]. Among others, this seminal work initiated a fast progression of the FM-AFM technique over the past decade [6][7]. At the beginning, mainly silicon-based cantilevers oscillating with large amplitudes (tens of nanometers) were used, because they possess

• simultaneous AFM/STM experiments seems to be a natural choice. Consequently, a new kind of sensor was introduced, based on a quartz resonator, into the field of FM-AFM. So far, the most popular and reasonable way to reach the desired small amplitudes is to replace the microfabricated (Si) cantilevers by stiff

Analysis of force-deconvolution methods in frequency-modulation atomic force microscopy

• Joachim Welker,
• Esther Illek and
• Franz J. Giessibl

Beilstein J. Nanotechnol. 2012, 3, 238–248, doi:10.3762/bjnano.3.27

• molecules. However, all these remarkable results have to rely on inversion methods as the force is not directly measured in the dynamic modes of an AFM. For high-resolution atomic force microscopy commonly the frequency-modulation (FM) technique is used [6]. In FM-AFM the direct observable is the frequency

• present the results of the simulation showing a nontrivial amplitude dependence of the deconvolution quality and discuss the origin of the variations in deconvolution quality. Forces and frequency shifts in FM-AFM In FM-AFM the force is not directly proportional to the measured frequency shift, but

• , Equation 10) for an FM-AFM force sensor. The calculated frequency-shift curves are deconvoluted back to a force curve FS/M by using the Sader–Jarvis (S) and the matrix (M) method, respectively. In order to compare the two deconvolution methods for different force laws, we need a measure for the

A measurement of the hysteresis loop in force-spectroscopy curves using a tuning-fork atomic force microscope

• Manfred Lange,
• Dennis van Vörden and
• Rolf Möller

Beilstein J. Nanotechnol. 2012, 3, 207–212, doi:10.3762/bjnano.3.23

• 77 K with a home-built low-temperature tuning-fork-based AFM (LT-TF-AFM) [9]. When a conductive sample is used, scanning tunneling microscopy (STM) and FM-AFM measurements may be combined. The use of a tuning fork as a sensor allows an oscillation amplitude in the subnanometer regime to be used, due

• 77 K under ultrahigh vacuum (UHV) conditions. Measurements were performed using a home-built LT-TF-AFM [9], which is able to operate both as an STM and as an FM-AFM. The tuning fork is used in the qPlus configuration [22]. The oscillation amplitude of the tuning fork can be chosen in the subnanometer

Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus

• Elena T. Herruzo and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2012, 3, 198–206, doi:10.3762/bjnano.3.22

• between observables and forces is difficult to deduce. Since the observable quantities in dynamic modes are averaged over many cycles of oscillation (amplitude and phase shift for amplitude modulation AFM (AM-AFM) [20][21], and frequency shift and dissipation for FM-AFM [22][23]), it is not

• straightforward to obtain an analytical relationship between observables and forces. It is known that in FM-AFM the frequency shift of the first mode can be directly related to the gradient of the force when the amplitude is much smaller than the typical length scale of the interaction. For larger amplitudes, the

• frequency shift is related to the virial of the force [24][25]. Sader and Jarvis have proposed an alternative interpretation of FM-AFM in terms of fractional calculus [26][27]. They showed that the frequency shift can be interpreted as a fractional differential operator, where the order of differentiation

Quantitative multichannel NC-AFM data analysis of graphene growth on SiC(0001)

• Christian Held,
• Thomas Seyller and
• Roland Bennewitz

Beilstein J. Nanotechnol. 2012, 3, 179–185, doi:10.3762/bjnano.3.19

• decomposition in ultrahigh vacuum and in an argon atmosphere are compared and the respective growth mechanisms discussed. Keywords: FM-AFM; graphene; 6H-SiC(0001); KPFM; SPM; Introduction Graphene grows epitaxially on the Si face of 6H-SiC(0001) by thermal decomposition in vacuum or an inert atmosphere

qPlus magnetic force microscopy in frequency-modulation mode with millihertz resolution

• Maximilian Schneiderbauer,
• Daniel Wastl and
• Franz J. Giessibl

Beilstein J. Nanotechnol. 2012, 3, 174–178, doi:10.3762/bjnano.3.18

• (FM-AFM) the measured frequency shift Δf is proportional to an averaged force gradient with kts = −∂Fts/∂z; Fts is the force acting between tip and sample within one oscillation period; the z-direction is perpendicular to the sample surface. Within the gradient approximation, Δf is given by: To

• determine the sensitivity of the experimental setup, and thus the minimum detectable averaged force gradient , one has to calculate the frequency noise of the setup δ(Δf). In FM-AFM setups δ(Δf) is a sum of three uncorrelated noise sources [13][14]: Thermal noise deflection-detector noise and oscillator

• perform lift-mode experiments for MFM. The lift mode is a two-pass technique that enables a separation of topographic and, here, magnetic signals. In the first pass, a line is scanned in FM-AFM to obtain the topography of the surface. With the second pass, this previously acquired topographic trace is

Defects in oxide surfaces studied by atomic force and scanning tunneling microscopy

• Thomas König,
• Georg H. Simon,
• Lars Heinke,
• Leonid Lichtenstein and
• Markus Heyde

Beilstein J. Nanotechnol. 2011, 2, 1–14, doi:10.3762/bjnano.2.1

• atomic force microscopy (FM-AFM) or dynamic force microscopy (DFM). For the stability of tip and sample as well as for the reduction of piezo creep, piezo hysteresis, thermal drift and noise level, the setup was operated in ultrahigh vacuum (UHV) at low temperature (5 K). The resulting high stability