Tendency in tip polarity changes in non-contact atomic force microscopy imaging on a fluorite surface

• Bob Kyeyune,
• Philipp Rahe and
• Michael Reichling

Beilstein J. Nanotechnol. 2025, 16, 944–950, doi:10.3762/bjnano.16.72

• was used. The NC-AFM was operated in the frequency-modulation mode with an oscillation amplitude of 7.4 nm, and images shown herein were acquired in the quasi constant-height mode [18]. Frequency shift values printed in the respective images correspond to the setpoint of the feedback loop. LT

• constant-height mode using an atom-tracking and feed-forward system for instantaneous drift compensation [29]. All frequency shift (Δf) images are presented with regions of strong attractive tip–sample interaction depicted as ‘bright’ and regions of weak attractive or repulsive interaction reproduced as

• ‘dark’. In NC-AFM, the frequency shift Δf is proportional to the weighted average of the tip–sample interaction force gradient [30]. Attractive forces mostly exhibiting a positive force gradient are considered as negative and yield a negative Δf according to a generally accepted convention. When

Nanoscale capacitance spectroscopy based on multifrequency electrostatic force microscopy

• Pascal N. Rohrbeck,
• Lukas D. Cavar,
• Franjo Weber,
• Peter G. Reichel,
• Mara Niebling and
• Stefan A. L. Weber

Beilstein J. Nanotechnol. 2025, 16, 637–651, doi:10.3762/bjnano.16.49

• ][71] as well as a heterodyne-based EFM mode [59][72][73][78]. By using a low-frequency modulation of a high-frequency electrostatic drive, the response can be picked up either via a frequency shift or by an electrostatic response at one of the cantilever’s resonance frequencies. Thus, the dielectric

ReactorAFM/STM – dynamic reactions on surfaces at elevated temperature and atmospheric pressure

• Tycho Roorda,
• Hamed Achour,
• Matthijs A. van Spronsen,
• Marta E. Cañas-Ventura,
• Sander B. Roobol,
• Willem Onderwaater,
• Mirthe Bergman,
• Peter van der Tuijn,
• Gertjan van Baarle,
• Johan W. Bakker,
• Joost W. M. Frenken and
• Irene M. N. Groot

Beilstein J. Nanotechnol. 2025, 16, 397–406, doi:10.3762/bjnano.16.30

• the tip interacts with the surface. Amplitude, frequency, and phase are measured. These signals are then fed into the electronics for monitoring and feedback options. The RHK software (R9 plus) allows for various user controls, that is, setpoint (frequency shift for AFM feedback or current for STM

• as in UHV and at RT; however, long waiting times are required and feedback might be lost because of the higher sensitivity to fluctuations in pressure and temperature while scanning. The images were taken in combined nc-AFM/STM mode using the frequency shift dF as feedback, while recording the

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

• et al. addresses the significantly increased precision of force spectroscopy measurements when performed with a quartz cantilever allowing to reduce the oscillation amplitude to values in the low picometer regime [2]. As the conversion of frequency-shift to force data critically depends on the

Local work function on graphene nanoribbons

• Daniel Rothhardt,
• Amina Kimouche,
• Tillmann Klamroth and
• Regina Hoffmann-Vogel

Beilstein J. Nanotechnol. 2024, 15, 1125–1131, doi:10.3762/bjnano.15.91

• performed measurements at different frequency shifts. We have then measured a force–distance curve to match each frequency shift to a distance to the sample surface (see Supporting Information File 1, Section II). We show the data in Figure 3c together with the calculated results. With this approach using

• , whereas the red, dashed green, and dashed yellow curves are fits to the data as described in the text. Supporting Information Supporting Information File 56: Additional information on the DFT calculations, on the force–distance data used for transforming frequency shift information into distance

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

• sample [38][39][40][41], or to typically electrostatic conservative forces [42]. In the latter case, using KPFM to minimize these forces mitigates the problem. Finally, if the driving excitation frequency is tracked to follow the resonance frequency shift induced by the tip–sample interactions, the

• maintain the system at resonance and track the frequency shift, a wide-bandwidth PLL (0.5–32 kHz) was enabled. In this operation mode, the amplitude signal carries information about dissipative interactions, as conservative forces only modify the resonant frequency. KPFM was operated in the frequency

• capacitance signal was also recorded, as explained in [61]. Spectroscopy data were acquired using a variant of the 3D-mode dynamic force spectroscopy [62], explained in detail in [63]. Briefly, force, frequency shift, amplitude, and phase channels are recorded simultaneously at a fixed sample point as a

Stiffness calibration of qPlus sensors at low temperature through thermal noise measurements

• Laurent Nony,
• Sylvain Clair,
• Daniel Uehli,
• Aitziber Herrero,
• Jean-Marc Themlin,
• Andrea Campos,
• Franck Para,
• Alessandro Pioda and
• Christian Loppacher

Beilstein J. Nanotechnol. 2024, 15, 580–602, doi:10.3762/bjnano.15.50

• to perform frequency shift spectroscopy to quantitatively evaluate the tip–sample interaction forces and potentials above individual atoms or molecules. The stiffness of the probe, k, is then required to perform the frequency shift-to-force conversion. However, this quantity is generally known with

• resonance frequency remains unchanged, f1. When the tip is in the range of attractive interatomic forces Fint(r), that is, for tip–surface separations r 1 nm, non-linear effects modify the oscillator dynamics, which shifts its resonance frequency down to lower values < f1. The resulting frequency shift Δf

• the recent works to perform the frequency shift-to-force conversion (see, e.g., the supplementary material of [8] and [9]), is not necessarily compatible with that of modern ones. Furthermore, because the detailed geometry of each tip is never the same (regarding, e.g., diameter and length), and

Unveiling the nature of atomic defects in graphene on a metal surface

• Karl Rothe,
• Nicolas Néel and
• Jörg Kröger

Beilstein J. Nanotechnol. 2024, 15, 416–425, doi:10.3762/bjnano.15.37

• frequency shift [39][40]. Topographic STM and AFM data were processed using WSxM [41]. Results and Discussion Scanning tunneling microscopy and spectroscopy findings After gentle Ar+ ion bombardment, graphene-covered Ir(111) gives rise to STM images as depicted in Figure 1a. The periodic superstructure of

• resonance frequency shift from (a) −48 to −13 Hz and (c) −36 to −18 Hz as well as changes in the tunneling current from (b) 4 to 19 nA and (d) 4 to 7 nA. (e, f) Variation of Δf with tip displacement Δz (tip approach from left to right) on intact graphene (cross in (a) and (c)). The vertical arrow marks the

Determining by Raman spectroscopy the average thickness and N-layer-specific surface coverages of MoS₂ thin films with domains much smaller than the laser spot size

• Felipe Wasem Klein,
• Jean-Roch Huntzinger,
• Vincent Astié,
• Damien Voiry,
• Romain Parret,
• Houssine Makhlouf,
• Sandrine Juillaguet,
• Jean-Manuel Decams,
• Sylvie Contreras,
• Périne Landois,
• Ahmed-Azmi Zahab,
• Jean-Louis Sauvajol and
• Matthieu Paillet

Beilstein J. Nanotechnol. 2024, 15, 279–296, doi:10.3762/bjnano.15.26

• monotonically, reversibly, and quasi-linearly with Pλ (see inset of Figure 1). For MoS2, we found an increase rate of 25–30 °C/mW for monolayers (1L-MoS2) and 40–45 °C/mW for bilayers (2L-MoS2). Usual effects of sample heating are the frequency shift of the phonon modes and their concomitant broadening. In

Design, fabrication, and characterization of kinetic-inductive force sensors for scanning probe applications

• August K. Roos,
• Ermes Scarano,
• Elisabet K. Arvidsson,
• Erik Holmgren and
• David B. Haviland

Beilstein J. Nanotechnol. 2024, 15, 242–255, doi:10.3762/bjnano.15.23

• hierarchy is the value of the single-photon electromechanical coupling strength, characterizing the microwave frequency shift G per zero-point motion (in the z direction) of the mechanical mode zzpf. The shift will depend as where the last term requires a microscopic theory of the effect of strain on the

Measurements of dichroic bow-tie antenna arrays with integrated cold-electron bolometers using YBCO oscillators

• Leonid S. Revin,
• Dmitry A. Pimanov,
• Alexander V. Chiginev,
• Anton V. Blagodatkin,
• Viktor O. Zbrozhek,
• Andrey V. Samartsev,
• Anastasia N. Orlova,
• Dmitry V. Masterov,
• Alexey E. Parafin,
• Victoria Yu. Safonova,
• Anna V. Gordeeva,
• Andrey L. Pankratov,
• Leonid S. Kuzmin,
• Anatolie S. Sidorenko,
• Silvia Masi and
• Paolo de Bernardis

Beilstein J. Nanotechnol. 2024, 15, 26–36, doi:10.3762/bjnano.15.3

• of frequency bands between arrays of antennas can be seen. We should note here that a certain frequency shift of the channels is due to improper Si substrate thickness (available in the clean room at that time), which was about 0.29 mm instead of the optimized 0.26 mm (see modelling results in Figure

• measured with a YBCO Josephson junction oscillator show narrow peaks with band separation at 205 GHz for the 210 GHz array and at 225 GHz for the 240 GHz array. It is demonstrated that the undesired frequency shift is mainly due to improper Si substrate thickness in these test samples. The NEP level in the

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

High–low Kelvin probe force spectroscopy for measuring the interface state density

• Ryo Izumi,
• Masato Miyazaki,
• Yan Jun Li and
• Yasuhiro Sugawara

Beilstein J. Nanotechnol. 2023, 14, 175–189, doi:10.3762/bjnano.14.18

• vibration cos 2πf0t, f0 ± fm components of the electrostatic force Fele,L(f0 ± fm) appear: When the electrostatic force is detected by the FM method, the electrostatic force Fele,L(f0 ± fm) is demodulated into the fm component of the frequency shift ΔfL(fm), which is expressed as where k is the spring

• constant of the cantilever. This equation indicates that the slope of the dependence of the fm component of the frequency shift ΔfL(fm) on the DC bias voltage Vdc (ΔfL(fm)–Vdc curve) is proportional to the capacitance inside the semiconductor at a low-frequency AC bias (CD + Cit). High KPFS Next, we

• vibration cos2πf0t, the f0 + fm component of the electrostatic force Fele,H(f0 + fm) appears: In the depletion region, In the accumulation and inversion regions, In the FM method, the electrostatic force Fele,H(f0 + fm) is demodulated into the fm component of the frequency shift ΔfH(fm). The resulting fm

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

• frequency shift, as it was measured without the thermal stabilisation technique described above. Keeping the pump constant while sweeping the signal tone over the second mode, we have an example of the strong coupling regime, seen in Figure 3b. As soon as the pump is turned on, there are two distinguishable

• minimum decreases with the pump as expected, yet the two hybridized peaks are asymmetric in their lineshape. The one on the left exhibits a shear drop in amplitude towards the dip, while the right one misses such feature. Last, T1–F4 has a frequency shift. This is not uncommon in the measured data as F1

• –T3, F1–F3, and F3–F4 show it as well. Heating effects would cause a quadratic shift with respect to the pump voltage, dominated by the thermal length extension of the cantilever, either up or down due to the extra signal used for compensation. In contrast, the frequency shift of T1–F4 is linear. A

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

• frequency shift map acquired in the work of Albers et al. [14] with a volume of 1.6 × 0.8 × 0.12 nm3 and 256 × 119 × 61 pixels required a total acquisition time of 40 h, that is, it was measured with a pixel bandwidth of only 12.9 pixels per second. While to date most atomic-resolution studies under UHV

• islands on top (see section “Results and Discussion”). There is a third noise source, namely the oscillator noise given by Equation 3, which is, however, relevant only for low-quality factor conditions [59]. An experimental evaluation of the measured frequency shift noise revealed that it depends as on

Optimizing PMMA solutions to suppress contamination in the transfer of CVD graphene for batch production

• Chun-Da Liao,
• Andrea Capasso,
• Tiago Queirós,
• Telma Domingues,
• Fatima Cerqueira,
• Nicoleta Nicoara,
• Jérôme Borme,
• Paulo Freitas and
• Pedro Alpuim

Beilstein J. Nanotechnol. 2022, 13, 796–806, doi:10.3762/bjnano.13.70

• sp2 carbon atoms [23], and its position displays a blueshift as the charge carrier concentration rises. That is, the frequency shift of the G band is proportional to |EF|, which sets the carrier concentration. Due to the method and materials employed for the graphene transfer being the same except for

Direct measurement of surface photovoltage by AC bias Kelvin probe force microscopy

• Masato Miyazaki,
• Yasuhiro Sugawara and
• Yan Jun Li

Beilstein J. Nanotechnol. 2022, 13, 712–720, doi:10.3762/bjnano.13.63

• , the value should typically be larger than 100 mV. AC-KPFM in FM mode In the FM mode, AC-KPFM measures the modulated frequency shift with frequency ωm, which is driven by the modulated electrostatic force For a small oscillation amplitude, under a modulated laser can be approximately expressed as

• frequency ωm and a DC bias VDC were applied to the sample. The laser power was modulated to a square waveform by a chopper at frequency ωm, synchronized to the AC bias. VAC is controlled to nullify the modulated frequency shift (Equation 12), yielding the SPV value. We used a digital lock-in amplifier

• ). Results and Discussion First, we detected the SPV signal with AC-KPFM in the FM mode. Figure 2a shows the spectrum of the frequency shift Δf under modulated UV laser illumination with frequency fm = 100 Hz. The peak appeared at 100 Hz only when the tip approached the sample. Here, VDC was set to −300 mV

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

• equations that link the physical interaction parameters force and damping with the measurement observables static deflection qs, oscillation amplitude A, and phase φ as well as the excitation parameters frequency fexc and force Fexc. This theory specifically predicts the distant-dependent frequency shift

• of a tip moved perpendicular to a surface for a given force curve. Inversion formulae are available that allow for the extraction of the interaction force from measured frequency-shift data [4][5]. A tacit assumption of all prevalent algorithms for force inversion is that the axis of data acquisition

• appropriate data analysis procedures. We demonstrate these consequences by simulating the frequency shift Δf = fexc − f0 in the frequency-modulated AFM mode for different cases using a Morse potential as a model that describes the interaction between two atoms at a distance d by the parameters Eb = 0.371 aJ

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

• frequency fr. This frequency shift is proportional to the force gradient and has a nonmonotonic dependence on z [4][12][13][14]. This dependence can be directly observed if resonance conditions are maintained, for example, if we use a phase-locked loop and constantly keep the driving frequency at resonance

• amplitude [15]. The two possible resonant frequencies correspond to different distances between the probe and the sample. The condition under which the frequency shift is negative is called the net-attractive regime, and correspondingly, positive frequency shift is called net-repulsive regime. Switching

Local stiffness and work function variations of hexagonal boron nitride on Cu(111)

• Abhishek Grewal,
• Yuqi Wang,
• Matthias Münks,
• Klaus Kern and
• Markus Ternes

Beilstein J. Nanotechnol. 2021, 12, 559–565, doi:10.3762/bjnano.12.46

• 6.1 eV [35], which can be modulated by the Moiré pattern [30]. We analyse the substrate using STM topography, dI/dV, and frequency shift, Δf, AFM maps under low (in-gap) and high (conduction band onset) bias conditions (see Figure 2). Due to h-BN being insulating, no spectroscopic contribution is

• , independent method to detect the variation in Φ. For this we record the frequency shift, Δf, of the resonance frequency of the cantilever oscillating perpendicular to the surface as a function of the bias voltage (see Figure 3b). At the extrema of the parabolic Δf curves, the electrostatic force is minimised

• = 100 pA and V = 10 mV. We then record the frequency shift Δf with respect to f0 while V is swept at constant tip height. Vertical stiffness: The 3D Δf data (8 × 8 × 0.27 nm3), evaluated in this work, are obtained by taking 28 2D maps at successively increased tip–sample separation (Δz = 10 pm) starting

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

• atomic force microscopy (AFM) is a non-contact atomic force microscopy technique where the frequency shift (Δf) of an oscillating tip is detected [1]. The frequency shift is a measure of the total force gradient acting on the tip, which includes both long-range and short-range contributions. A typical

• molecular adsorbate [11][12]. Moreover, other methods, including the use of a long tip on a qPlus sensor that oscillates laterally at a higher flexural mode are also possible [13]. In LFM or normal AFM, the recorded frequency shift Δf is related to the force gradient kts in the direction of the tip

• oscillation. For a sensor oscillating in the x-direction, where F is the component of force in the x-direction and U is the potential energy. In general, the relevant force gradient at a spatial coordinate (x, z) for a tip oscillating at an angle θ with respect to the x-direction is: The frequency shift is

Reconstruction of a 2D layer of KBr on Ir(111) and electromechanical alteration by graphene

• Zhao Liu,
• Antoine Hinaut,
• Stefan Peeters,
• Sebastian Scherb,
• Ernst Meyer,
• Maria Clelia Righi and
• Thilo Glatzel

Beilstein J. Nanotechnol. 2021, 12, 432–439, doi:10.3762/bjnano.12.35

• frequency shift, which is related to short-range interaction forces and highlights, therefore, the atomic periodicity [50]. The topography shows not only the cubic KBr lattice but also the hexagonal graphene moiré, which shines through the KBr layer and has dimensions (2.42 nm) similar to those of the pure

• a constant amplitude and controlled by the frequency shift. Bimodal AFM was used to combine the first flexural resonance (frequency of f1 ≈ 165 kHz, amplitude of A1 = 2–8 nm and a typical quality factor of Q1 = 30,000) or the second flexural resonance (frequency of f2 ≈ 1 MHz, amplitude of A2 = 200

• AC excitation bias to the sample [51]. The frequency of the excitation was set to fAC = 210 Hz and the amplitude to UAC = 700 mV, while the oscillation amplitude of the frequency shift Δf1(fAC) was compensated by controlling the applied DC voltage. Computational methods DFT calculations were

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

• and VDC is the applied tip–sample bias. From Equation 1 and Equation 2 we have: This equation relates the frequency shift Δf0 to the applied bias voltage VDC and is the measured EFM signal. The bias-independent term in Equation 3 is defined as α, given by Since f0, K and VDC are well determined, local

• variations of the measured frequency shift Δf0 are associated with changes in the second derivative of the capacitance in Equation 3 and Equation 4. The capacitance depends both on the geometry and on the relative permittivity of the medium. Hence, we only need to use a suitable capacitance model to be able

• the coefficient α For the experiments we use an atomic force microscope in the EFM mode, which measures the frequency shift for each bias voltage at each position of the sample. We varied the bias voltage from −10 V to +10 V, in steps of 1 V. Plotting the frequency shift as a function of the bias

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

• and fq in the in-phase mode (Figure 3 and Figure 6). We found a 0.05 mm tip has the best performance when the tip length is 0.65 mm in the anti-phase mode. However, Ax/Az in the anti-phase mode is 2.36, that is, φ is 23°. In frequency modulation-atomic force microscopy (FM-AFM), the frequency shift Δf

Direct observation of the Si(110)-(16×2) surface reconstruction by atomic force microscopy

• Tatsuya Yamamoto,
• Ryo Izumi,
• Kazushi Miki,
• Takahiro Yamasaki,
• Yasuhiro Sugawara and
• Yan Jun Li

Beilstein J. Nanotechnol. 2020, 11, 1750–1756, doi:10.3762/bjnano.11.157

• keep the frequency shift constant. When the imaging became unstable, a bias voltage was applied between the tip and sample to eliminate the electrostatic force between the tip and sample. As a sample, p-doped Si(110) with a resistivity of 1–5 Ω·cm was used, which was cleaned by cycles of flushing at