Exploring surface charge dynamics: implications for AFM height measurements in 2D materials

• Mario Navarro-Rodriguez,
• Andres M. Somoza and
• Elisa Palacios-Lidon

Beilstein J. Nanotechnol. 2024, 15, 767–780, doi:10.3762/bjnano.15.64

• as an oscillating surface charge. For simplicity, we consider the case of an AC voltage (Vbias = VDC + VACcos(ωt)), although solutions will be very similar for small tip oscillation amplitudes, since only ftip(k) depends on z0 or V. In order to properly calculate them, we need to solve Equation 1

A cantilever-based, ultrahigh-vacuum, low-temperature scanning probe instrument for multidimensional scanning force microscopy

• Hao Liu,
• Zuned Ahmed,
• Sasa Vranjkovic,
• Manfred Parschau,
• Andrada-Oana Mandru and
• Hans J. Hug

Beilstein J. Nanotechnol. 2022, 13, 1120–1140, doi:10.3762/bjnano.13.95

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

• interaction force, the measurement observables, and the probe excitation parameters is defined by an average of the normal force along the sampling path over the oscillation cycle. Usually, it is tacitly assumed that tip oscillation and force data recording follows the same path perpendicular to the surface

• of a viscous damping layer, in-plane dissipation mechanisms have been found to cause systematic changes of the phase shift in amplitude-modulation AFM depending on the cantilever inclination [15]. Furthermore, it has been proposed to use the presence of a lateral component in the tip oscillation path

• an inclined tip oscillation, four cases are discussed. Common to all cases is that the data recording path, described by the oscillation centre positions remains oriented parallel to the -axis, that is, perpendicular to the surface as indicated by the dotted lines in Figure 3b and Figure 3c. This

Reducing molecular simulation time for AFM images based on super-resolution methods

• Zhipeng Dou,
• Jianqiang Qian,
• Yingzi Li,
• Rui Lin,
• Jianhai Wang,
• Peng Cheng and
• Zeyu Xu

Beilstein J. Nanotechnol. 2021, 12, 775–785, doi:10.3762/bjnano.12.61

• correct damping of the tip oscillation. In the simulation, the initial distance between the virtual atom and the sample surface Zc remains unchanged at a suitable distance. Then we employ the raster scanning method to construct the average interplay energy map of the sample surface in a calculation period

Determining amplitude and tilt of a lateral force microscopy sensor

• Oliver Gretz,
• Alfred J. Weymouth,
• Thomas Holzmann,
• Korbinian Pürckhauer and
• Franz J. Giessibl

Beilstein J. Nanotechnol. 2021, 12, 517–524, doi:10.3762/bjnano.12.42

• related to the sensor parameters and the weighted average of the force gradient over the tip oscillation, ⟨kts⟩(x0, z0), where x0 and z0 define the average tip position over one oscillation cycle [14]: Here, f0 is the resonance frequency of the sensor away from the surface and k is the stiffness of the

• sensor. The weighted average must also take into account the direction of the tip oscillation: where A is the oscillation amplitude. Extracting force and potential energy from the measured Δf is a complex inversion problem requiring deconvolution. Several deconvolution methods include a matrix inversion

• amplitude. In this paper we present a method to calibrate the amplitude and determine the tilt of the LFM sensor. The method is based on collecting STM data of a surface feature both without and with tip oscillation, as was proposed in [20]. The data without oscillation is used as input to a simulation that

Mapping the local dielectric constant of a biological nanostructured system

• Wescley Walison Valeriano,
• Rodrigo Ribeiro Andrade,
• Juan Pablo Vasco,
• Angelo Malachias,
• Bernardo Ruegger Almeida Neves,
• Paulo Sergio Soares Guimarães and
• Wagner Nunes Rodrigues

Beilstein J. Nanotechnol. 2021, 12, 139–150, doi:10.3762/bjnano.12.11

• oscillate, during the second pass, at the resonance frequency of the cantilever, f0. Variations in the local relative permittivity properties of the sample will lead to different tip–sample force gradients, which promote a shift Δf0 in the tip oscillation frequency [21][22] which is, approximately, where dF

Numerical analysis of vibration modes of a qPlus sensor with a long tip

• Kebei Chen,
• Zhenghui Liu,
• Yuchen Xie,
• Chunyu Zhang,
• Gengzhao Xu,
• Wentao Song and
• Ke Xu

Beilstein J. Nanotechnol. 2021, 12, 82–92, doi:10.3762/bjnano.12.7

• output current and of Atfz with respect to the tip length are not necessarily synchronous. Tip oscillation and SEM observation Since the tip swings around the end of the tuning fork prong, Atip is different from Atfz. We should focus on the vibration of the tip apex itself. Figure 6 gives Atip and the

• higher ratio corresponds to a higher proportion of the oscillation parallel to the X direction. In contrast, a smaller ratio means the tip oscillation is close to the ideal tapping mode. In the in-phase mode, Ax/Az for all tip diameters increases with respect to the tip length. However, the increase of

Current measurements in the intermittent-contact mode of atomic force microscopy using the Fourier method: a feasibility analysis

• Berkin Uluutku and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2020, 11, 453–465, doi:10.3762/bjnano.11.37

• dynamic current measurements, this manuscript discusses three different cases: (i) a noncontact dynamic current measurement where the cantilever follows an ideal sinusoidal trajectory, (ii) a similar case, but considering a more realistic trajectory where the tip oscillation is perturbed by the presence

• repulsive interaction (the simulation parameters are provided in Table 2). The higher harmonic amplitudes of the tip oscillation are much smaller than the first harmonic amplitude but do nonetheless influence the current response. b) Comparison of the power spectrum of the current for the realistic

Development of a new hybrid approach combining AFM and SEM for the nanoparticle dimensional metrology

• Loïc Crouzier,
• Alexandra Delvallée,
• Sébastien Ducourtieux,
• Laurent Devoille,
• Guillaume Noircler,
• Christian Ulysse,
• Olivier Taché,
• Elodie Barruet,
• Christophe Tromas and
• Nicolas Feltin

Beilstein J. Nanotechnol. 2019, 10, 1523–1536, doi:10.3762/bjnano.10.150

• resonance frequency is 300 kHz and the nominal radius of curvature of the tip is roughly 7 nm. The nominal stiffness of the cantilever is 42 N/m. For all measurements, the tip oscillation amplitude was about 40 nm. The amplitude setpoint was fixed very high and near the free amplitude (80%) value to prevent

Influence of dielectric layer thickness and roughness on topographic effects in magnetic force microscopy

• Alexander Krivcov,
• Jasmin Ehrler,
• Marc Fuhrmann,
• Tanja Junkers and
• Hildegard Möbius

Beilstein J. Nanotechnol. 2019, 10, 1056–1064, doi:10.3762/bjnano.10.106

• Bruker Dimension Icon atomic force microscope. The topography of the samples was measured in tapping mode and the phase images in interleave mode at a certain lift height. The changes in amplitude indicate the topography changes in tapping mode. The amplitude of the tip oscillation is 50 nm in order to

Artifacts in time-resolved Kelvin probe force microscopy

• Sascha Sadewasser,
• Nicoleta Nicoara and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2018, 9, 1272–1281, doi:10.3762/bjnano.9.119

• tip oscillation at the ac-detection frequency (fac) is extracted. This simulation is repeated for up to 30 different dc voltages in a range between −3 V < Vdc < +3 V. The expected v-shaped dependence according to Equation 3 is observed, where the minimum is extracted, which corresponds to the VCPD

• –cantilever motion is affected by this driving force, leading to an imperfect compensation of the electrostatically excited oscillation in some cases. Figure 1c shows the tip oscillation for three different cases. For pulses applied at the same frequency as the ac bias, the oscillation amplitude can be

• complexity of the driving forces, whereby the usual KPFM driving forces (Fdc, Fac, and F2ac) are convoluted with the voltage pulse, makes it difficult to draw analytical generalizations beyond the observation of the value of the FFT at the detection frequency. Figure 1e shows the obtained tip oscillation

High-stress study of bioinspired multifunctional PEDOT:PSS/nanoclay nanocomposites using AFM, SEM and numerical simulation

• Alfredo J. Diaz,
• Hanaul Noh,
• Tobias Meier and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2017, 8, 2069–2082, doi:10.3762/bjnano.8.207

• free cantilever resonance frequency, is directly related to stiffness (larger stiffness leads to larger frequency and vice-versa) [49], while the quality factor maps the sample damping of the cantilever tip oscillation (greater dissipation leads to lower quality factor and vice-versa) [50]. The contact

Dynamic of cold-atom tips in anharmonic potentials

• Tobias Menold,
• Peter Federsel,
• Carola Rogulj,
• Hendrik Hölscher,
• József Fortágh and
• Andreas Günther

Beilstein J. Nanotechnol. 2016, 7, 1543–1555, doi:10.3762/bjnano.7.148

• -control. Keywords: anharmonic motion; cold-atom scanning probe microscopy; dephasing; dynamic mode; tip oscillation; Introduction The development of novel scanning probe techniques has lead to tremendous improvements in investigating nanomaterials [1]. Starting with conventional force and tunneling

• measurement shows that this minimum position is slightly displaced from the maximum of the spectral response, which is likely due to the trap’s anharmonicity and particle collisions. Comparing experiment to theory To verify that the damping of the experimentally observed tip oscillation is solely due to the

• external potential. Moreover, the tip oscillation is excited similar to within the experiment, along one of the trap’s principal axes and including particle collisions. In addition, we use a more elaborate implementation of our detection scheme. The basic principles of the numerical simulation, the tip

Coupled molecular and cantilever dynamics model for frequency-modulated atomic force microscopy

• Michael Klocke and
• Dietrich E. Wolf

Beilstein J. Nanotechnol. 2016, 7, 708–720, doi:10.3762/bjnano.7.63

• bending mode of the cantilever. This potential is applied to each atom of the tip. As the simulated tip mass M is only a small portion of the real cantilever, the experimental values for kz would lead to an enormously enhanced frequency of the tip oscillation . To obtain a correct frequency of the

Nanoscale effects in the characterization of viscoelastic materials with atomic force microscopy: coupling of a quasi-three-dimensional standard linear solid model with in-plane surface interactions

• Santiago D. Solares

Beilstein J. Nanotechnol. 2016, 7, 554–571, doi:10.3762/bjnano.7.49

• be significantly influenced by in-plane surface forces. A final subtle observation can be made based on Figure 8c, which indicates that in-plane surface effects lead to changes in the tip oscillation amplitude. This is not unexpected, but is a reminder that topographical measurements in AFM are

A simple and efficient quasi 3-dimensional viscoelastic model and software for simulation of tapping-mode atomic force microscopy

• Santiago D. Solares

Beilstein J. Nanotechnol. 2015, 6, 2233–2241, doi:10.3762/bjnano.6.229

• spring in parallel with a damper. This is appropriate (i) when the tip oscillation amplitude is very small, since in this regime the small segment of the force curve that is involved can be treated as quasi-linear, and (ii) when the tip and sample are in permanent contact (that is, the tip does not

Capillary and van der Waals interactions on CaF₂ crystals from amplitude modulation AFM force reconstruction profiles under ambient conditions

• Annalisa Calò,
• Oriol Vidal Robles,
• Sergio Santos and
• Albert Verdaguer

Beilstein J. Nanotechnol. 2015, 6, 809–819, doi:10.3762/bjnano.6.84

• on the crystal surface (b). Zscale is 3 nm for both images. (b, Inset). Topographic profile corresponding to the white line in the image in (b). (a,b) Reconstructed force curves on top of the terrace in Figure 1a (a) and on top of the bigger water patch in Figure 1b (b); free amplitude of tip

• oscillation: A0 = 23 nm. Raw and smooth data are, respectively, indicated as solid circles in grey and as continuous lines in blue. (c) F vs separation curves acquired in contact mode on a wet CaF2 crystal. The extension and retraction paths are indicated, respectively, in blue and in grey only in (c). (a,c

Influence of spurious resonances on the interaction force in dynamic AFM

• Luca Costa and
• Mario S. Rodrigues

Beilstein J. Nanotechnol. 2015, 6, 420–427, doi:10.3762/bjnano.6.42

• the whole system has a specific transfer function, and assuming only that all the forces involved are additive. However, one should note that if we talk of the interaction stiffness, ki, this contains the implicit assumption that the interaction force, Fi, in the vicinity of the tip oscillation can be

• the tip oscillation, as in Note that the amplitude of Fliquid may be a function of the excitation frequency and in particular present resonances, but because we fixed the excitation frequency, this does not matter. If c1 and c2 are the proportionality constants between the excitation signal and kxb

Dynamic force microscopy simulator (dForce): A tool for planning and understanding tapping and bimodal AFM experiments

• Horacio V. Guzman,
• Pablo D. Garcia and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2015, 6, 369–379, doi:10.3762/bjnano.6.36

• regimes in AM-AFM is a direct consequence of the nonlinear character of the tip–surface force [11][46]. The amplitude versus the average tip–surface distance zc curve shows a sudden increase at zc = 9.3 nm (Figure 3a).This increase marks the transition between a tip oscillation dominated by attractive

• forces to a tip oscillation dominated by repulsive forces. The increase in the amplitude curve is also reflected in the phase shift curve (Figure 3b) where the phase shift changes from about 110° to 65°. The initial values of the deflection, position and velocity determine the zc value where the jump

• . Bimodal AFM tip motion. The tip oscillation (blue), instantaneous force (red) and velocity (green) are shown. Notice that in this particular case the period of the oscillation is 6 times the period of the first mode. Data obtained at zc = 9 nm. Material contrast in bimodal AFM. Phase shift as a function

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

• value fset, by changing z0 accordingly. Here, T is the actual period of the normal tip oscillation, which due to the attraction by the substrate is larger than 2π/ωz. Afterwards, we displace the tip by small amounts Δx0 and determine the topography signal z0(x0) for the same reduced frequency shift. The

Challenges and complexities of multifrequency atomic force microscopy in liquid environments

• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 298–307, doi:10.3762/bjnano.5.33

• deflection (this can be approximated as tip position minus base position), not tip position. Figure 9 illustrates the photodetector readings that would be obtained for different values of the quality factor for a given second eigenmode tip oscillation (labeled as “Real”). Clearly spectroscopic measurements

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

• acoustic microscopy (AFAM) configuration [3]), such that the tip oscillation amplitude and its phase with respect to the excitation can be measured and converted into a loss and storage modulus. In contact resonance AFM (CR-AFM) [3][4][5][6][7][8][9] a similar setup is used, supplying the sinusoidal

The role of surface corrugation and tip oscillation in single-molecule manipulation with a non-contact atomic force microscope

• Christian Wagner,
• Norman Fournier,
• F. Stefan Tautz and
• Ruslan Temirov

Beilstein J. Nanotechnol. 2014, 5, 202–209, doi:10.3762/bjnano.5.22

• tip elasticity, and the tip oscillation amplitude. In short, we simulate a full tip oscillation cycle at each step of the manipulation process and calculate the frequency shift by solving the equation of motion of the tip. The new model correctly reproduces previously unexplained key features of the

• of the tip oscillation is 200 ps, which corresponds to a frequency resolution of about 0.2 Hz. Note that the motion of the tip during one oscillation cycle is strictly vertical, whereas the overall motion of the tip during the retraction–relaxation steps might also involve a lateral displacement of

• the tip. Results and Discussion To understand how the refinement of the mechanical model of the junction influences the outcome of the simulations we perform several different simulation runs with tip oscillation and surface corrugation. In the first run we make the tip infinitely stiff (ktip = ∞) and

Manipulation of nanoparticles of different shapes inside a scanning electron microscope

• Boris Polyakov,
• Sergei Vlassov,
• Leonid M. Dorogin,
• Jelena Butikova,
• Mikk Antsov,
• Sven Oras,
• Rünno Lõhmus and
• Ilmar Kink

Beilstein J. Nanotechnol. 2014, 5, 133–140, doi:10.3762/bjnano.5.13

• voltage were 20–50 mV and the corresponding tip oscillation amplitude was in order of 100 nm. The tip oscillated parallel to the sample surface, i.e., in the shear mode [20]. The QTF force sensors were calibrated on a reference contact mode AFM cantilever (NT-MDT, CSG11), which was previously calibrated

• ). During the manipulation, the tip moved parallel to the surface along a straight line without feedback loop. At the end of every manipulation event the tip was abruptly retracted from the NP to avoid sticking of the particle to the tip. Two different modes of the tip oscillation direction were used in

• S5, Supporting Information File 1) the NP often moved aside affected by the tip oscillation (Figure 5). Moreover, the force necessary to displace a NP can be overestimated due to an unaccounted amount of energy dissipated in a shear interaction between the tip and the NP. For the parallel tip

Peak forces and lateral resolution in amplitude modulation force microscopy in liquid

• Horacio V. Guzman and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2013, 4, 852–859, doi:10.3762/bjnano.4.96

• nm has been obtained with the point-mass model while for A0 = 10 nm we have used the extended Euler–Bernoulli model. Figure 1 shows one period of the tip oscillation and the corresponding force. The peak force is defined as the maximum force point in the dashed line curves. The curves show a purely