Josephson dynamics and Shapiro steps at high transmissions: current bias regime

• Artem V. Galaktionov and
• Andrei D. Zaikin

Beilstein J. Nanotechnol. 2024, 15, 51–56, doi:10.3762/bjnano.15.5

• , equivalently, ω = (k/n)ωJ, where k and n are positive integer numbers. The values k ≥ 2 correspond to the presence of higher harmonics of the Josephson current emerging because of a possibly non-sinusoidal current–phase relation, whereas the numbers n ≥ 2 account for multiphoton processes, which may become non

Comparing the performance of single and multifrequency Kelvin probe force microscopy techniques in air and water

• Jason I. Kilpatrick,
• Emrullah Kargin and
• Brian J. Rodriguez

Beilstein J. Nanotechnol. 2022, 13, 922–943, doi:10.3762/bjnano.13.82

• leading to artefacts in the measurements. For multifrequency techniques, this nonlinear motion of the cantilever due to tapping the surface can induce motion of the lever at higher harmonics and distort the frequency response characteristics of the system [104][105][106]. Under large amplitude conditions

Cantilever signature of tip detachment during contact resonance AFM

• Devin Kalafut,
• Ryan Wagner,
• Maria Jose Cadena,
• Anil Bajaj and
• Arvind Raman

Beilstein J. Nanotechnol. 2021, 12, 1286–1296, doi:10.3762/bjnano.12.96

• Figure 2f, the probe tip motion is more complex and even paths above the sample surface. Not surprisingly, the frequency domain of the slope amplitudes echo the complexity and reveal higher harmonics, or dynamics at multiples of the operating frequency, at play. This is crucial because the lock-in

• amplifier used to monitor the photodiode output during frequency sweeps is set to only observe dynamics coinciding with the drive frequency. In the standard measurement configuration, any other frequency content, for example higher harmonics of cantilever motion, are not observed. Finally, we turn to

• amplitude, though the probe tip may remain in contact with the sample, the presence of higher harmonics and nonlinear softening of the resonance peak distorts measurements and should be taken as a signal of caution. If the operating amplitude continues to increase, it may exceed a threshold above which

Optically and electrically driven nanoantennas

• Monika Fleischer,
• Dai Zhang and
• Alfred J. Meixner

Beilstein J. Nanotechnol. 2020, 11, 1542–1545, doi:10.3762/bjnano.11.136

• . However, owing to the polarization and far-field interference, a silencing of the SHG is observed for decreasing gap sizes [53]. This effect is further studied in [54] using the surface integral equation method. On the other hand, the generation of higher harmonics by a dielectric nanostructure can be

Design of V-shaped cantilevers for enhanced multifrequency AFM measurements

• Mehrnoosh Damircheli and
• Babak Eslami

Beilstein J. Nanotechnol. 2020, 11, 1525–1541, doi:10.3762/bjnano.11.135

• vibrational and dynamic properties. The ideal situation for achieving the best contrast in multifrequency or higher-mode AFM would be using AFM cantilevers with higher eigenmode frequencies equal or close to the higher harmonics [28][29][30]. This can be achieved by modifying the AFM cantilever designs. For

• example, it was shown that, by modifying the mass distribution and geometry of a rectangular cantilever, the ratio between the second eigenmode and the first eigenmode frequency decreases, which increases the chance of having self-excitation for higher harmonics [31][32][33]. By modifying the cantilever

Scanning tunneling microscopy and spectroscopy of rubrene on clean and graphene-covered metal surfaces

• Karl Rothe,
• Alexander Mehler,
• Nicolas Néel and
• Jörg Kröger

Beilstein J. Nanotechnol. 2020, 11, 1157–1167, doi:10.3762/bjnano.11.100

• electronically decouple 2,5-bis(3-dodecylthiophen-2-yl)thieno[3,2-b]thiophene from the metal surface [10]. A rich vibronic fine structure was observed in the HOMO spectroscopic signature induced by several fundamental vibrational modes of the molecule together with their higher harmonics and combination

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

• discuss a possible approach to develop an intermittent-contact conductive AFM mode based on Fourier analysis, whereby the measured current response consists of higher harmonics of the cantilever oscillation frequency. Such an approach may enable the characterization of soft samples with less damage than

• significant instrumentation challenges are anticipated, the modelling results are promising and suggest that Fourier-based higher-harmonics current measurement may enable the development of a reliable intermittent-contact conductive AFM method. Keywords: atomic force microscopy (AFM); conductivity; current

• plus its higher harmonics, with the an values representing the amplitudes of those harmonics. For instance, a1 corresponds to the fundamental frequency of the cantilever response, which is typically tracked using a lock-in amplifier and modulated during a standard dynamic AFM experiment. As outlined in

A review of demodulation techniques for multifrequency atomic force microscopy

• David M. Harcombe,
• Michael G. Ruppert and
• Andrew J. Fleming

Beilstein J. Nanotechnol. 2020, 11, 76–91, doi:10.3762/bjnano.11.8

• within dynamic mode AFM. It involves studying multiple frequency components in the cantilever oscillation during tip–sample interactions [13]. Observing higher eigenmodes of the cantilever [14], higher harmonics of the fundamental resonance [15] and intermodulation products [16] have been shown to

• inherently greater demodulation challenges. Strong OMR is required as higher harmonics are separated by nf0, much closer than the approx. 6f0 second eigenmode spacing [61]. In addition, harmonic content from tip–sample interactions scales with approx. 1/n2[13]. Therefore, the signals of interest are detected

• driven at its fundamental resonance frequency, during imaging its deflection signal contains additional frequency components. These include higher harmonics and intermodulation products excited by non-linear tip–sample forces during contact. Second-harmonic amplitude images captured by both demodulators

Kelvin probe force microscopy work function characterization of transition metal oxide crystals under ongoing reduction and oxidation

• Dominik Wrana,
• Karol Cieślik,
• Wojciech Belza,
• Christian Rodenbücher,
• Krzysztof Szot and
• Franciszek Krok

Beilstein J. Nanotechnol. 2019, 10, 1596–1607, doi:10.3762/bjnano.10.155

• correlate directly with the work function differences as provided by the KPFM measurements taken at the very same area. This was possible by forcing the same conductive contact AFM tip to oscillate at higher harmonics to enter the FM-KPFM mode (more details can be found in [29]). Figure 2d,e presents the

• noncontact mode measurements (with a Kelvin loop) using the very same tip, maintaining oscillations at the higher harmonics of the fundamental frequency (≈75 kHz). Hence, in order to record current and CPD maps from the very same sample area, KPFM measurements were first performed with the soft cantilever

• forced to oscillate at higher harmonics, then the tip was retracted tens of nanometers from the surface, all feedback loops were turned down and a contact mode AFM scan was performed when approached with a single loop maintaining a deflection set point of 10–30 mV. The high conductivity of both TiO and

Quantitative comparison of wideband low-latency phase-locked loop circuit designs for high-speed frequency modulation atomic force microscopy

• Kazuki Miyata and
• Takeshi Fukuma

Beilstein J. Nanotechnol. 2018, 9, 1844–1855, doi:10.3762/bjnano.9.176

• and a reference signal. In a multiplication-based PC, a low-pass filter (LPF) is employed to eliminate higher harmonics generated by the multiplication of an input signal and a reference signal. However, a LPF has a relatively high latency (i.e., long time delay) at its pass band, often limiting the

Lyapunov estimation for high-speed demodulation in multifrequency atomic force microscopy

• David M. Harcombe,
• Michael G. Ruppert,
• Michael R. P. Ragazzon and
• Andrew J. Fleming

Beilstein J. Nanotechnol. 2018, 9, 490–498, doi:10.3762/bjnano.9.47

• stiffness, elasticity and adhesiveness [10]. The acquisition of these observables requires tracking the amplitude and phase of additional frequencies of interest. These include higher harmonics of the fundamental frequency [11], higher flexural eigenmodes [12] and intermodulation products [13]. Higher

• and also converge. Results and Discussion Hardware The Lyapunov filter was implemented on a high-speed FPGA to achieve the necessary sample rate for accessing higher harmonics during imaging. A Xilinx Kintex-7 KC705 evaluation board (model: XC7K325T) paired with a DC-coupled high-speed 4DSP input

• higher harmonics and minor intermodulation products are present. These are due to non-linear atomic forces exciting the cantilever during contact. Amplitude imaging results are shown in Figure 9. As the sixth and seventh harmonics are closely spaced to the second resonance frequency of the cantilever

Material discrimination and mixture ratio estimation in nanocomposites via harmonic atomic force microscopy

• Weijie Zhang,
• Yuhang Chen,
• Xicheng Xia and
• Jiaru Chu

Beilstein J. Nanotechnol. 2017, 8, 2771–2780, doi:10.3762/bjnano.8.276

• threshold of approximately 0.24, the amplitude difference starts to decrease. Such a characteristic has also been noted in a previous publication. The higher harmonics were found to have an inverted U-shape dependence on the tip–sample gap [32]. Despite the deviation in the quantitative values, the

Comprehensive investigation of the electronic excitation of W(CO)₆ by photoabsorption and theoretical analysis in the energy region from 3.9 to 10.8 eV

• Mónica Mendes,
• Khrystyna Regeta,
• Filipe Ferreira da Silva,
• Nykola C. Jones,
• Søren Vrønning Hoffmann,
• Gustavo García,
• Chantal Daniel and
• Paulo Limão-Vieira

Beilstein J. Nanotechnol. 2017, 8, 2208–2218, doi:10.3762/bjnano.8.220

• cell is evacuated using a scroll pump to prevent any absorption of oxygen from the air for measurements below 200 nm (energies above 6.20 eV). For measurements above 220 nm, air is allowed into this gap to let oxygen absorb higher harmonics of light (at half the chosen wavelength) that may be passing

A review of demodulation techniques for amplitude-modulation atomic force microscopy

• Michael G. Ruppert,
• David M. Harcombe,
• Michael R. P. Ragazzon,
• S. O. Reza Moheimani and
• Andrew J. Fleming

Beilstein J. Nanotechnol. 2017, 8, 1407–1426, doi:10.3762/bjnano.8.142

• . However, this also increases the noise bandwidth. On the other hand, in multifrequency AFM applications, the sensitivity to other frequency components is of greatest concern. These applications may include multiple eigenmode contributions [20][21][22], higher harmonics [23][24][25], and multi-tone near

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

• Microelectrónica de Barcelona (IMB-CNM, CSIC), Campus UAB, 08193 Bellaterra, Barcelona, Spain Technical University of Delft, Mekelweg 2, 2628CD Delft, The Netherlands 10.3762/bjnano.8.90 Abstract We present a combined theoretical and experimental study of the dependence of resonant higher harmonics of rectangular

• cannot be oversimplified and flexural eigenmodes must be considered, in particular when they are located close to one of the harmonics [11]. Here, we report a combined theoretical and experimental study on the functional dependence of the amplitudes of higher harmonics on relevant parameters such as the

• ) with kc ≈ 44 N/m and 300 ≤ f0 ≤ 400 kHz, OTESPA-R3 (Bruker) with kc ≈ 25 N/m and 200 ≤ f0 ≤ 400 kHz, and PPP-FMR (Nanosensors) with kc ≈ 3 N/m and 70 ≤ f0 ≤ 80 kHz, where f0 stands for the resonance frequency. The amplitudes of the higher harmonics were registered using an internal lock-in amplifier

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

• perturbation theory in combination with the Poincaré–Lindstedt method to avoid secular terms [41]. With αi = αi(x0,ω0,ε) being the contributions of the base frequency (i = 1) and higher harmonics (i > 1) to the particle dynamics [41][42], the solution reads which is a periodic function in time with the

• contain not only the fundamental frequency but also higher harmonics (see Equation 9). Following the above considerations and neglecting particle interactions, the dynamics of a cold-atom tip in an anharmonic potential can be understood as superposition of all single particle oscillations. Figure 2

• different outcoupling positions x0 = 0 and x0 = σx for a small oscillation amplitude A = 0.5σx. The results are well described by the approximation from Equation 17. This changes for larger oscillation amplitudes, where higher harmonics must be taken into account as shown in Figure 4b for a cloud with

Adiabatic superconducting cells for ultra-low-power artificial neural networks

• Andrey E. Schegolev,
• Nikolay V. Klenov,
• Igor I. Soloviev and
• Maxim V. Tereshonok

Beilstein J. Nanotechnol. 2016, 7, 1397–1403, doi:10.3762/bjnano.7.130

• is non-sinusoidal and amplitudes of its higher harmonics increase with increasing inductance, lq. A sigmoid function is most suitable mathematically for the solution of the image or pattern recognition problems by means of MLP. One can provide this form of a flux-to-current transformation by

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

• several harmonic potentials corresponding to the different modes of the cantilever, and by effective masses of part of the simulated atoms, as described in the next paragraphs. The bending mode of the cantilever (in the absence of the substrate) can be regarded as a harmonic oscillation. Higher harmonics

Active multi-point microrheology of cytoskeletal networks

• Tobias Paust,
• Tobias Neckernuss,
• Lina Katinka Mertens,
• Ines Martin,
• Michael Beil,
• Paul Walther,
• Thomas Schimmel and
• Othmar Marti

Beilstein J. Nanotechnol. 2016, 7, 484–491, doi:10.3762/bjnano.7.42

• recorded motions of a group of particles located and connected to each other in the viscoelastic medium, it is possible to determine the transfer tensor of motion, the relationship of response amplitudes, phase shifts and frequency changes to higher harmonics with the help of the lock-in technique. A

• resulted in the uncertainties. To improve the results and decrease the error it might be recommended to additionally investigate the amplitudes of the higher harmonics of the measurement. If those amplitudes are comparable to the first harmonic, nonlinear effects play a role, which complicate the

Charge and heat transport in soft nanosystems in the presence of time-dependent perturbations

• Alberto Nocera,
• Carmine Antonio Perroni,
• Vincenzo Marigliano Ramaglia and
• Vittorio Cataudella

Beilstein J. Nanotechnol. 2016, 7, 439–464, doi:10.3762/bjnano.7.39

Large area scanning probe microscope in ultra-high vacuum demonstrated for electrostatic force measurements on high-voltage devices

• Urs Gysin,
• Thilo Glatzel,
• Thomas Schmölzer,
• Adolf Schöner,
• Sergey Reshanov,
• Holger Bartolf and
• Ernst Meyer

Beilstein J. Nanotechnol. 2015, 6, 2485–2497, doi:10.3762/bjnano.6.258

• measurements, such as Kelvin probe force microscopy, scanning capacitance force microscopy, scanning spreading resistance microscopy, and also electrostatic force microscopy at higher harmonics. The instrument incorporates beside a standard beam deflection detection system a closed loop scanner with a scan

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

• materials it is more difficult to achieve high resolution. The phase shift (Figure 4b) decreases more rapidly with the average distance in the stiffer material. The amplitude spectrum shows that strength of the higher harmonics also depends on the material. Higher components are observed in the stiffer

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

• 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

• higher harmonics has been nevertheless impeded by the lack of a closed-form expression for the force in terms of measured quantities, namely, the lack of a higher harmonics analogue of the Sader–Jarvis formula for the fundamental harmonic [12][13]. In the present letter we fill this gap by providing such

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

• to a nonlinear force on at least two frequencies and gives a response in the frequency domain not only at these drive frequencies and their higher harmonics but also at their linear combinations (n and m are integers) called intermodulation products (IMPs). Use of the small base frequency results

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

• excitation for a single eigenmode [21][22], band excitation single- or dual-mode characterization [23][24] and techniques based on the observation of higher harmonics and their inversion to obtain force distance curves [25][26]. Most of the discussion in this paper is based on the AM-OL method of Rodriguez