Advanced atomic force microscopy techniques V

• Philipp Rahe,
• Ilko Bald,
• Nadine Hauptmann,
• Regina Hoffmann-Vogel,
• Harry Mönig and
• Michael Reichling

Beilstein J. Nanotechnol. 2025, 16, 54–56, doi:10.3762/bjnano.16.6

• 10.3762/bjnano.16.6 Keywords: AFM; atomic force microscopy; conductivity; drift correction; force spectroscopy; NC-AFM; non-contact atomic force microscopy; resistivity; tip–surface interaction; With the restrictions on travelling and social distancing lifted, we were delighted to continue two series of

• not involving any tip–surface interaction. The measurement of electrostatic properties at the nanoscale emerged as a most relevant subfield of atomic force microscopy, especially driven by electrostatic force microscopy (EFM), Kelvin probe force microscopy (KPFM), and closely related techniques

Dual-heterodyne Kelvin probe force microscopy

• Benjamin Grévin,
• Fatima Husainy,
• Dmitry Aldakov and
• Cyril Aumaître

Beilstein J. Nanotechnol. 2023, 14, 1068–1084, doi:10.3762/bjnano.14.88

• strictness, in the above, we should have written that ωac = ω1 − (ω0 + Δω0), where Δω0 stands for the cantilever frequency shift due to the tip–surface interaction. In heterodyne KPFM, the reference sideband that drives the modulated bias is indeed generated as follows. The frequency of the first source

• the cantilever. The frequency mixing effect will effectively generate a modulated electrostatic component at ω1 – phase-coherent with the demodulation chain – only and if only the frequency shift that the cantilever (at its first resonance mode) experiences in the tip–surface interaction is taken into

Intermodal coupling spectroscopy of mechanical modes in microcantilevers

• Ioan Ignat,
• Bernhard Schuster,
• Jonas Hafner,
• MinHee Kwon,
• Daniel Platz and
• Ulrich Schmid

Beilstein J. Nanotechnol. 2023, 14, 123–132, doi:10.3762/bjnano.14.13

• multifrequency AFM has improved both imaging contrast and the amount of extracted information from AFM experiments by exploiting the nonlinearity of the tip–surface interaction [32][33][34][35][36]. The methods applied excel in both their creativity and engineering prowess. A first example is on-resonance

Quantitative dynamic force microscopy with inclined tip oscillation

• Philipp Rahe,
• Daniel Heile,
• Reinhard Olbrich and
• Michael Reichling

Beilstein J. Nanotechnol. 2022, 13, 610–619, doi:10.3762/bjnano.13.53

• path perpendicular to the surface, provide quantitative information about the details of the tip–surface interaction when properly analysed [2]. Recently, a universal description of quantitative dynamic force microscopy based on the harmonic approximation has been developed [3], yielding three central

• displacement qs with turning points qs + A and qs − A (Figure 1d). The momentary tip position at time t can either be described as the displacement q(t) or as the position zts(t), whereby the lower turning point is the point of strongest tip–surface interaction. While the tip position and sensor dynamics can

Two dynamic modes to streamline challenging atomic force microscopy measurements

• Alexei G. Temiryazev,
• Andrey V. Krayev and
• Marina P. Temiryazeva

Beilstein J. Nanotechnol. 2021, 12, 1226–1236, doi:10.3762/bjnano.12.90

• classical contact mode, the friction force can be measured; when using off-resonance dynamic modes, stiffness and adhesion in the samples can be determined. Obviously, in determining the mechanical properties, the force of tip–surface interaction should be somewhat greater than that required if the task is

Protruding hydrogen atoms as markers for the molecular orientation of a metallocene

• Linda Laflör,
• Michael Reichling and
• Philipp Rahe

Beilstein J. Nanotechnol. 2020, 11, 1432–1438, doi:10.3762/bjnano.11.127

• arranged along the CaF2 direction, resembling one molecular row of the superstructure that was observed in the experiments. All simulated Δf data are shown with a colour code representing a strong attractive tip–surface interaction as bright and a weak attractive or repulsive interaction as dark to allow

• between experiment and simulation might also reflect a more general feature of repulsive mode imaging. While the tip–surface interaction force curves in the attractive region differ significantly from each other for different tip-terminating species, the force curves in the repulsive region are so steep

Friction force microscopy of tribochemistry and interfacial ageing for the SiO_x/Si/Au system

• Christiane Petzold,
• Marcus Koch and
• Roland Bennewitz

Beilstein J. Nanotechnol. 2018, 9, 1647–1658, doi:10.3762/bjnano.9.157

• we did not observe any static friction peak, overall no contact ageing was found for these non-reactive contacts in vacuum. Occasionally, we observed first signs of a stronger tip–surface interaction at varying positions and scan velocities, prevalently at the turning points of the scanning motion

Robust procedure for creating and characterizing the atomic structure of scanning tunneling microscope tips

• Sumit Tewari,
• Koen M. Bastiaans,
• Milan P. Allan and
• Jan M. van Ruitenbeek

Beilstein J. Nanotechnol. 2017, 8, 2389–2395, doi:10.3762/bjnano.8.238

• –surface interaction will be dominated by Au at both sides, while the PtIr base provides better mechanical stability. All the measurements reported here were performed at temperatures between 2 and 4.2 K. Conductance traces Using this STM setup we applied training procedures for the tip apex following the

• 20 nm, as obtained by grinding and mechanical polishing. PtIr tips are among the most commonly used tips in STM experiments as opposed to Au tip used in reference [25]. We exploit the fact that the tips become covered with the Au sample material at the apex. We anticipate that the nanoscale tip

Functional dependence of resonant harmonics on nanomechanical parameters in dynamic mode atomic force microscopy

• Federico Gramazio,
• Matteo Lorenzoni,
• Francesc Pérez-Murano,
• Enrique Rull Trinidad,
• Urs Staufer and
• Jordi Fraxedas

Beilstein J. Nanotechnol. 2017, 8, 883–891, doi:10.3762/bjnano.8.90

• simplified expression is: where kc stands for the cantilever stiffness, z is the distance between the cantilever base and the sample surface and Tn(u) = cos(ncos−1(u)). Note that An decreases for increasing order number (n) and kc values. The tip–surface interaction Fts can be expressed as a function of

• factors of the 2nd flexural eigenmode have been approximated by the known relationships 6.27f, 6.272kc and 6.27Q, respectively, corresponding to a massless tip [29]. As mentioned above, we have used the DMT model to describe the tip–surface interaction and the tip has been approximated by a hemisphere

Correlative infrared nanospectroscopic and nanomechanical imaging of block copolymer microdomains

• Benjamin Pollard and
• Markus B. Raschke

Beilstein J. Nanotechnol. 2016, 7, 605–612, doi:10.3762/bjnano.7.53

• with the tip–surface interaction, while for inelastic deformation, energy is transferred into the sample itself [32] or to the surface water layer through the formation and rupture of the capillary neck at different distances [30]. In the case of PS-b-PMMA, the positive correlation between dissipation

Kelvin probe force microscopy for local characterisation of active nanoelectronic devices

• Tino Wagner,
• Hannes Beyer,
• Patrick Reissner,
• Philipp Mensch,
• Heike Riel,
• Bernd Gotsmann and
• Andreas Stemmer

Beilstein J. Nanotechnol. 2015, 6, 2193–2206, doi:10.3762/bjnano.6.225

• distances and single-scan techniques on structured surfaces, where the tip–surface interaction is not limited to the apex. In order to address the topography crosstalk due to C'', Lee et al. [34] suggested to use a feedback signal normalised to the 2ωm sideband, thus rendering the CPD tracking error

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

• generated by the nonlinear tip–surface interaction (to be distinguished from higher flexural modes of the cantilever) are related to higher derivatives of the force, and thus carry additional information on the interaction [5][6][7][8][9][10][11]. Broad implementation of force spectroscopy by analysing

• –surface interaction Here, k is the effective cantilever spring constant, ω0 is the fundamental resonance frequency in the absence of tip–surface interaction, q(t) is the tip position, γ is the damping coefficient, and F0 and ω are the amplitude and frequency of the driving force, respectively. As the

• cantilever is brought close to a surface, the tip–surface interaction forces shift the resonance frequency. The relation between the frequency shift and Fts, in the case where the force depends only on tip position, was first derived by Giessibl as [14] Here, Δω is the frequency shift, a is the oscillation

High-frequency multimodal atomic force microscopy

• Adrian P. Nievergelt,
• Jonathan D. Adams,
• Pascal D. Odermatt and
• Georg E. Fantner

Beilstein J. Nanotechnol. 2014, 5, 2459–2467, doi:10.3762/bjnano.5.255

• scanner feedback loop is then closed by enforcing a higher drive amplitude than the free drive amplitude. As the tip–sample distance decreases, the force interaction becomes stronger and energy is lost from the cantilever oscillation. By using this technique, the non-monotonic tip–surface interaction

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

• -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

• the origin of the coordinate system. The mass point representing the cantilever, including the tip, carries a charge of −q. The tip–surface interaction then reads Although this force model is quite simple and might not be as well justified as commonly used models, it provides an important feature

• transfer is essentially given by the phase of the lateral oscillation, when the tip leaves the tip–surface interaction region. If we extend the model to a second cycle, we see that the amplification also depends on the phase when the tip enters the interaction region. In Figure 4, interaction times are

Dynamic calibration of higher eigenmode parameters of a cantilever in atomic force microscopy by using tip–surface interactions

• Stanislav S. Borysov,
• Daniel Forchheimer and
• David B. Haviland

Beilstein J. Nanotechnol. 2014, 5, 1899–1904, doi:10.3762/bjnano.5.200

• force reconstruction technique and does not require any prior knowledge of the eigenmode shape or the particular form of the tip–surface interaction. The calibration method proposed requires a single-point force measurement by using a multimodal drive and its accuracy is independent of the unknown

• calibration method is similar to that described in [29], in which stiffness of the second eigenmode is experimentally defined by using consecutive measurements of the frequency shift caused by the tip–surface interaction for different eigenmodes. In contrast, we propose a simultaneous one-point measurement by

• soft and stiff cantilevers, but works best when nonlinearities are weak. Thus the amplitude contraction of the engaged cantilever oscillations with respect to the free motion should be about 10–20%. Choose a particular model for the tip–surface interaction and solve nonlinear system Equation 4 for

Uncertainties in forces extracted from non-contact atomic force microscopy measurements by fitting of long-range background forces

• Adam Sweetman and
• Andrew Stannard

Beilstein J. Nanotechnol. 2014, 5, 386–393, doi:10.3762/bjnano.5.45

• calculated values. We also note that during the review process we became aware of a forthcoming publication by Kuhn et al. [26] which rigorously explores the uncertainties and consistency of the long-range background fitting method for a number of different tip–surface interaction models in the case where no

Noise performance of frequency modulation Kelvin force microscopy

• Heinrich Diesinger,
• Dominique Deresmes and
• Thierry Mélin

Beilstein J. Nanotechnol. 2014, 5, 1–18, doi:10.3762/bjnano.5.1

• the distance control loop does not interfere with the Kelvin control loop. First, it must not modify, by tip–surface interaction, the PLL response, e.g., by modifying Q via dissipation; second, it must not respond periodically to the frequency modulations caused by the Kelvin loop. This means that

Structural development and energy dissipation in simulated silicon apices

• Samuel Paul Jarvis,
• Lev Kantorovich and
• Philip Moriarty

Beilstein J. Nanotechnol. 2013, 4, 941–948, doi:10.3762/bjnano.4.106

• rotational degree of freedom can have as measurable an impact on the tip–surface interaction as a completely different tip structure. Keywords: apex structure; atomic force microscopy; DFT; dissipation; hysteresis; NC-AFM; silicon; spectroscopy; tip structure; Introduction The theoretical treatment of

• , which pulls the apex downwards into a narrower shape. The geometry shown in Figure 3f is taken at the same z position as (d), during retraction from the surface. From the calculated geometries we can see that the tip structures in (d) and (f) differ, thus modifying the tip–surface interaction, which in

• appears to protrude at a large angle relative to the surface normal. This structure would likely lead to a complicated tip-surface interaction [40]. To test the stability of the D2b tip a further calculation was carried out, just as for the D2a structure, over the same deposited silicon atom. In this case

Polynomial force approximations and multifrequency atomic force microscopy

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

Beilstein J. Nanotechnol. 2013, 4, 352–360, doi:10.3762/bjnano.4.41

• time dependence of the tip–surface force Fts can be considered as an implicit time dependence, since it is assumed that the tip–surface interaction depends on the instantaneous tip position z and velocity , which are functions of time. In Fourier space Equation 1 becomes where the linear response

• experimental data. As the field of multifrequency AFM continues to evolve, new alternative data-representation schemes can help to simplify analysis and extract more specific properties of the tip–surface interaction. The force-quadrature picture is such a scheme, which decouples information about the tip

• –surface interaction from the actual tip motion. We showed how the general idea behind approximative force reconstruction can be adapted to the force-quadrature picture, and we introduced an efficient way to extract the polynomial coefficients from the force quadratures. We hope that in the future

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

• , providing deeper insight into the tip–surface interaction. We demonstrate the capabilities of ImAFM approach measurements on a polystyrene polymer surface. Keywords: atomic force microscopy; AFM; frequency combs; force spectroscopy; high-quality-factor resonators; intermodulation; multifrequency

• the sensitivity and gain of the motion-detection system. To mitigate these problems, we have developed narrow-band intermodulation AFM (ImAFM), which analyzes the response only near the first flexural eigenmode. In general ImAFM utilizes frequency mixing due to the nonlinear tip–surface interaction. A

• so-called virial of the tip–surface force, which is only affected by the conservative part of the tip–surface interaction [34], whereas FQ is related to the energy dissipated by the tip–surface interaction [11]. We note that, through their dependence on tip position z and velocity , the force

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

• ) consists of cantilever thermal noise, tip–surface-interaction noise and instrumental noise from the detection and signal processing systems. We investigate how the displacement-noise spectral density dz at the input of the frequency demodulator propagates to the frequency-shift-noise spectral density dΔf

• at the demodulator output in dependence of cantilever properties and settings of the signal processing electronics in the limit of a negligible tip–surface interaction and a measurement under ultrahigh-vacuum conditions. For a quantification of the noise figures, we calibrate the cantilever

• by the amplitude feedback loop. Signal processing in NC-AFM involves the demodulation of the periodic cantilever-displacement signal Vz(t) as well as filtering in the frequency domain to yield the frequency shift Δf(t) carrying the information on the tip–surface interaction [1]. Demodulation is

Characterization of the mechanical properties of qPlus sensors

• Jan Berger,
• Martin Švec,
• Martin Müller,
• Martin Ledinský,
• Antonín Fejfar,
• Pavel Jelínek and
• Zsolt Majzik

Beilstein J. Nanotechnol. 2013, 4, 1–9, doi:10.3762/bjnano.4.1

• affect experimental force measurements. The force can be expressed by using the Sader formula [35] as follows where Δν is the frequency shift, νr is the resonant frequency, k is the stiffness of the sensor, A is the amplitude of oscillation, F is the tip–surface interaction force, x is the tip–surface

Mapping mechanical properties of organic thin films by force-modulation microscopy in aqueous media

• Jianming Zhang,
• Zehra Parlak,
• Carleen M. Bowers,
• Terrence Oas and
• Stefan Zauscher

Beilstein J. Nanotechnol. 2012, 3, 464–474, doi:10.3762/bjnano.3.53

• attributed to hydrodynamic lubrication forces that increase with increasing proximity of the tip to the surface [49]. In regime B, the amplitude of the first harmonic decreases, while that of the second harmonic increases, reflecting the increasing nonlinearity of the initial tip–surface interaction and the

Models of the interaction of metal tips with insulating surfaces

• Thomas Trevethan,
• Matthew Watkins and
• Alexander L. Shluger

Beilstein J. Nanotechnol. 2012, 3, 329–335, doi:10.3762/bjnano.3.37

• regions of the tip–surface interaction with high stability, in particular the “near contact” region of separation where the tip apex atom and surface are separated by only a few angstroms (i.e., the typical range of chemical bonds). However, the nature of the force between the tip and the surface is

• characterize in situ, i.e., in UHV and through the tip–surface interaction. The use of metal-coated tips meets both of these requirements. Firstly, coating a standard silicon tip with a layer of metal can be achieved in the UHV chamber by evaporation (assuming that the metal bonds effectively to the oxide

• chromium and tungsten, which are chosen due to their common use in scanning-probe experiments. For several different combinations of tip and surface, we determine the tip–surface force field and the origin of the tip–surface interaction at close approach. These calculations employ cluster-tip models and

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

• , the image depicts the regulation of the tip–surface separation that is required to maintain constant Δfset. Therefore, beyond the known influence of (i) the tip–surface interaction regime (attractive versus repulsive; the attractive regime is such that H > Hmin, and the repulsive regime is such that H

• < Hmin, where Hmin corresponds to H at Δfmin, i.e., the minimum in the frequency shift versus tip–surface separation (H) curve) and (ii) the chemical nature of the tip–surface interaction on the contrast formation of the resulting images, the measured images may as well depend on the acquisition mode. To

• surface in the frozen-atoms mode and at constant height, Hset = 4.3 Å, where H is the distance between the topmost surface plane and the terminating atom of the tip apex. At this distance, the tip oscillates in the attractive part of the tip–surface interaction force curve. This is the reason why the