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

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

• atoms were used as probe particles and frequency-shift Δf data were calculated for an oscillation amplitude of 0.5 nm. Lateral and vertical stiffness were chosen as 0.5 and 20 N/m, respectively. FDCA molecular models in the DFT-optimised geometries (using geo 1 and geo 2 from [22], see Figure 1a,b) were

• frequency-shift images were acquired at different tip–sample distances, see Figure 2b–e. Data were acquired above a region where several FDCA molecules were arranged along the direction (see STM data in Figure 2a), with a molecular separation determined by the CaF2(111) lattice periodicity of 669 pm. Upon

• Figure 3b for geo 2. Conclusion We have investigated the origin of the dumbbell shape, which is observed when imaging FDCA molecules on CaF2(111) surfaces with NC-AFM. Based on a comparison of experimental constant-height frequency-shift data with image calculations using the probe particle model, we

Atomic defect classification of the H–Si(100) surface through multi-mode scanning probe microscopy

• Jeremiah Croshaw,
• Thomas Dienel,
• Taleana Huff and
• Robert Wolkow

Beilstein J. Nanotechnol. 2020, 11, 1346–1360, doi:10.3762/bjnano.11.119

• -functionalized tips. A true measurement of the force interaction between the tip and sample can be visualized with frequency-shift maps generated by non-contact AFM [28]. In our work, we observe two different imaging modes that we denote as dark (Figure 1g) and bright contrast AFM (Figure 1h), based on the

• , where the height-dependent frequency shift spectra (Δf(z)) taken above select positions on the surface (see Figure 1g,h for positions), shows significantly different character for each tip termination. To highlight the termination-dependent reactivity, frequency shift difference spectra [42] were

• artificially saturated from a 2.4 nA range to better show the H–Si atoms of the surface relative to the DB. A full-scale image of the DB is shown in Supporting Information File 1, Figure S8. Finally, AFM analysis in Figure 2a-5 and Figure 2a-6 presents the DB as a large negative frequency shift, with both tip

Measurement of electrostatic tip–sample interactions by time-domain Kelvin probe force microscopy

• Christian Ritz,
• Tino Wagner and
• Andreas Stemmer

Beilstein J. Nanotechnol. 2020, 11, 911–921, doi:10.3762/bjnano.11.76

• an alternative approach to find the surface potential without lock-in detection. Our method operates directly on the frequency-shift signal measured in frequency-modulated atomic force microscopy and continuously estimates the electrostatic influence due to the applied voltage modulation. This

• results in a continuous measurement of the local surface potential, the capacitance gradient, and the frequency shift induced by surface topography. In contrast to conventional techniques, the detection of the topography-induced frequency shift enables the compensation of all electrostatic influences

• . Another possibility for compensating the remaining frequency shift is the use of two-pass methods with feed-forward compensation techniques [20][21]. In this paper, we present a time-domain (TD) controller for KFM as a single-pass solution to the problem outlined above. Our method uses a Kalman filter as

Three-dimensional solvation structure of ethanol on carbonate minerals

• Hagen Söngen,
• Ygor Morais Jaques,
• Peter Spijker,
• Christoph Marutschke,
• Stefanie Klassen,
• Ilka Hermes,
• Ralf Bechstein,
• Lidija Zivanovic,
• John Tracey,
• Adam S. Foster and
• Angelika Kühnle

Beilstein J. Nanotechnol. 2020, 11, 891–898, doi:10.3762/bjnano.11.74

• nature of our findings. Results and Discussion AFM results A vertical slice of the frequency shift (Δνexc) obtained at the calcite (10.4)–ethanol interface is shown in Figure 1a. The average over all data shown in the slice is given as a vertical profile (i.e., as function of the z-piezo displacement zp

• ) in Figure 1b. The corresponding data for the magnesite-ethanol interface is shown in a similar fashion in the second row of Figure 1 (panels c and d). In both cases, the frequency shift exhibits local minima and maxima. Close to the surface (at the bottom), laterally alternating local maxima with a

• approximation” [19][20]. We note that it is relevant to discuss whether this approximation holds true for ethanol as well. However, in this work, we assume that a single ethanol molecule probes the solvation structure. In this model, the frequency shift modulation is approximately proportional to the solvent

Light–matter interactions in two-dimensional layered WSe₂ for gauging evolution of phonon dynamics

• Avra S. Bandyopadhyay,
• Chandan Biswas and
• Anupama B. Kaul

Beilstein J. Nanotechnol. 2020, 11, 782–797, doi:10.3762/bjnano.11.63

• frequency shift, ΔωT of the and A1g Raman active modes for 1L WSe2 with increasing T. The results were fit linearly using Equation 7 from which the slope χT was computed to be about −0.0145 cm−1/K and −0.0168 cm−1/K for the and A1g modes, respectively. The nonlinear perturbation of Raman shift for the

Quantitative determination of the interaction potential between two surfaces using frequency-modulated atomic force microscopy

• Nicholas Chan,
• Carrie Lin,
• Tevis Jacobs,
• Robert W. Carpick and
• Philip Egberts

Beilstein J. Nanotechnol. 2020, 11, 729–739, doi:10.3762/bjnano.11.60

• topography, among other parameters. In order to determine the interaction force behavior as a function of the separation distance, we measured the frequency shift of the oscillating cantilever as a function of the separation distance (Δf–d curves) between a silicon AFM probe and a diamond sample. An

• analytical relationship between the resonance frequency shift and the tip–sample interaction force in FM-AFM was first derived by Giessibl [42] and is seen in the following equation: In Equation 1, Δf represents the change in the primary flexural resonance frequency of the cantilever near the surface, fres

• topographic imaging of the surface, the tip–sample contact potential difference was determined by measuring the probe frequency shift as a function of the sample bias voltage. A DC bias was then applied to the sample surface for all subsequent measurements to compensate for this potential difference. Initial

Implementation of data-cube pump–probe KPFM on organic solar cells

• Benjamin Grévin,
• Olivier Bardagot and
• Renaud Demadrille

Beilstein J. Nanotechnol. 2020, 11, 323–337, doi:10.3762/bjnano.11.24

• are detected by demodulating the modulated component (ωmod) of the frequency-shift signal (Δf) with the LIA. The reference bias modulation voltage (Vmod, ωmod) and the compensation voltage generated by the KPFM feedback loop (VKPFM) are internally summed by the SPM unit. To generate the modulated bias

• = −CPD [39]. The KPFM data are presented as Vdc images also referred to as KPFM potential or SP images for simplicity. A lock-in amplifier (Signal Recovery 7280) was used to measure simultaneously the modulation of the frequency shift at the electrostatic excitation frequency. The ‘in-phase’ amplitude of

• feeding the frequency-shift signal (Δf) from the SPM phase-lock loop to the LIA input (KPFM operated in frequency-modulation mode). Using the SPM unit (block 1), the reference bias modulation voltage (Vmod, ωmod) is added to the compensation voltage generated by the KPFM feedback loop. The sum is