Signal generation in dynamic interferometric displacement detection

• Knarik Khachatryan,
• Simon Anter,
• Michael Reichling and
• Alexander von Schmidsfeld

Beilstein J. Nanotechnol. 2024, 15, 1070–1076, doi:10.3762/bjnano.15.87

• measurements of DC and AC signals with a bandwidth of 200 MHz. The interferometer is precisely aligned via a tube piezo controlled by the R9 control system (RHK Technology Inc., Troy, MI, USA). Cantilever excitation with a sine wave voltage with a well-defined amplitude Vexc and overall experiment control is

• accomplished by a HF2LI (Zurich Instruments, Zürich, Switzerland). Experiments are performed with the freely oscillating cantilever. Therefore, the cantilever excitation frequency fexc is set to the eigenfrequency of the cantilever, which is determined by taking a resonance curve before each experiment. By

• amplitude Vexc ramped from 0 to 7 V. This voltage is reduced by a 100:1 voltage divider before it is applied to the excitation piezo. For each amplitude, 512 traces of Vsig are taken and averaged, where the start of sampling is triggered by the zero crossing of the low-noise sinusoidal cantilever excitation

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

• that the modulation frequency of the light source is set high enough, it becomes possible to “stabilize” the static bending in a steady state, and photothermal cantilever excitation can be avoided (by setting the optical modulation at a frequency that differs from the cantilever resonance eigenmodes

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

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. Experimental and Theoretical Methods Atomic force microscopy For the AFM experiments we used a modified commercial atomic force microscope [22] with custom photothermal cantilever excitation [23] and a custom three-dimensional scanning and data acquisition mode [24] in the frequency-modulation

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

• Fourier analysis to implement ICM current measurements. Fourier analysis is commonly used in ICM-AFM experiments due to the periodic nature of the cantilever excitation and response. For example, in amplitude-modulation AFM (AM-AFM), the most common ICM-AFM method, a lock-in amplifier is used to track the

• current amplifiers to overload and may dominate all other current signals, and this issue would be ever present regardless of the application and regardless of the type of tip used. This might be eliminated through alternate cantilever excitation methods, such as laser-based thermal excitation, although

Nanoscale spatial mapping of mechanical properties through dynamic atomic force microscopy

• Zahra Abooalizadeh,
• Leszek Josef Sudak and
• Philip Egberts

Beilstein J. Nanotechnol. 2019, 10, 1332–1347, doi:10.3762/bjnano.10.132

• amplitude determined on a silicon surface. In the next step we brought the cantilever in contact with the HOPG surface without changing the cantilever excitation frequency and amplitude to maintain the same drive force. The drive force was maintained constant during the scanning of the HOPG surface. Knowing

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

• improvements in bandwidth or resonance frequency of all of the components constituting the tip–sample distance regulation loop, such as the cantilever, cantilever excitation unit, cantilever deflection sensor, scanner, feedback controller, and phase-locked loop (PLL) circuit. In particular, the PLL circuit is

• signal is output from the PLL and used for tip–sample distance feedback control. Meanwhile, the VCO output is employed to excite cantilever oscillations, forming the cantilever excitation loop depicted in Figure 1a. Similarly to a general lock-in amplifier, an M-PLL utilizes a multiplication-based PC

• a wide input range has a high latency at its pass band. This high latency results in a slow cantilever excitation loop response time. Therefore, in spite of the fast response of the phase feedback loop, the investigated S-PLL circuit was not suitable for high-speed FM-AFM operation. One of the most

Electrostatically actuated encased cantilevers

• Benoit X. E. Desbiolles,
• Gabriela Furlan,
• Adam M. Schwartzberg,
• Paul D. Ashby and
• Dominik Ziegler

Beilstein J. Nanotechnol. 2018, 9, 1381–1389, doi:10.3762/bjnano.9.130

• implementation remains difficult because alignment of an electrode is generally cumbersome and electrostatic forces frequently convoluted with the tip–sample interaction where changes in capacitance gradient due to topographical features influence cantilever excitation. An optically transparent electrode [20] or

• that we characterized in Figure 2d (k ≈ 4 N·m−1) we achieved an amplitude of ca. 25 nm with drive voltages of 4 V. Bandwidth limits Capacitive excitation has a higher bandwidth than other cantilever excitation techniques. The parasitic capacitance spanning the tip-side of the entire silicon chip (C3

Imaging of viscoelastic soft matter with small indentation using higher eigenmodes in single-eigenmode amplitude-modulation atomic force microscopy

• Miead Nikfarjam,
• Enrique A. López-Guerra,
• Santiago D. Solares and
• Babak Eslami

Beilstein J. Nanotechnol. 2018, 9, 1116–1122, doi:10.3762/bjnano.9.103

• environments, which we have not considered in this study, but where many soft samples are imaged. Some of these effects include mass loading of the cantilever, excitation of higher cantilever eigenmodes, and the inability to accurately track the tip motion for piezoelectrically excited cantilevers [31][32][33

Material property analytical relations for the case of an AFM probe tapping a viscoelastic surface containing multiple characteristic times

• Enrique A. López-Guerra and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2017, 8, 2230–2244, doi:10.3762/bjnano.8.223

• tip–sample position, A is the tapping amplitude, ω is the excitation frequency, and Asin(ωt) = z(t) is the instantaneous tip deflection. We have omitted the phase term, usually expressed as a phase lag between cantilever excitation and response, due to the sample-oriented analytical approach that we

Noise in NC-AFM measurements with significant tip–sample interaction

• Jannis Lübbe,
• Matthias Temmen,
• Philipp Rahe and
• Michael Reichling

Beilstein J. Nanotechnol. 2016, 7, 1885–1904, doi:10.3762/bjnano.7.181

• of tip–sample interaction and the cantilever eigenfrequency f0. Furthermore, the demodulator provides the cantilever excitation signal with frequency fexc that is nominally identical to the current resonance frequency fr of the cantilever. The frequency shift noise power spectral density DΔf(fm

• ) depends on the filter and loop settings of the PLL demodulator expressed by its frequency response function Hfilter(fm), where fm represents the frequencies of the modulation side bands measured relative to the resonance frequency fr [11]. Thus, the cantilever excitation signal contains noise from both

• . The control loop within the PLL demodulator (not shown in Figure 2) is discussed in appendix C.2. In this frequency control loop feedback path, displacement noise propagating from the PLL to the cantilever excitation is weighted by the reciprocal of the quality factor Q0. This factor defines the ratio

Understanding interferometry for micro-cantilever displacement detection

• Alexander von Schmidsfeld,
• Tobias Nörenberg,
• Matthias Temmen and
• Michael Reichling

Beilstein J. Nanotechnol. 2016, 7, 841–851, doi:10.3762/bjnano.7.76

• all further details of the NC-AFM setup are described in [12]. The cantilever, I, with its support chip is mounted on a dove-tail cantilever holder, II, clamped into position inside two side braces on a piezo stage, III, facilitating cantilever excitation. The cantilever holder has an angle of α = 15

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

• mechanisms dominates, and those, where both occur simultaneously. Adhesion hysteresis was found at and around the tip position, where the apex atom of the tip faces a substrate ion of opposite charge. These correspond to binding sites of the ionic crystal. Lateral cantilever excitation was found in an

Efficiency improvement in the cantilever photothermal excitation method using a photothermal conversion layer

• Natsumi Inada,
• Hitoshi Asakawa,
• Taiki Kobayashi and
• Takeshi Fukuma

Beilstein J. Nanotechnol. 2016, 7, 409–417, doi:10.3762/bjnano.7.36

• /bjnano.7.36 Abstract Photothermal excitation is a cantilever excitation method that enables stable and accurate operation for dynamic-mode AFM measurements. However, the low excitation efficiency of the method has often limited its application in practical studies. In this study, we propose a method for

• than 2 h without any indication of possible contamination from the coating. The proposed method, using a PTC layer made of colloidal graphite, greatly enhances photothermal excitation efficiency even for a relatively stiff cantilever in liquid. Keywords: atomic force microscopy; cantilever excitation

• a sharp tip and a sample. Therefore, an excitation method of cantilever oscillations is an important technique in dynamic-mode AFM. Acoustic excitation is the most widely used method for cantilever excitation in dynamic-mode AFM. The method is used in many commercially available AFM systems because

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

• morphology during the scan. Obviously, the cantilever excitation plays a central role in AM-AFM. Conventionally, mechanical vibration of the cantilever holder is provided through the excitation of a small piezoelectric element (dither). The setup is widely employed in many commercial and custom-made AFMs and

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

• topography as well as mechanical properties. Nevertheless, instrument bandwidth limitations on cantilever excitation and readout have restricted the ability of multifrequency techniques to fully benefit from small cantilevers. We present an approach for cantilever excitation and deflection readout with a

• our system for noise performance will decrease the baseline noise value further [35]. Dissipation imaging Bimodal imaging The capability for clean, high-frequency cantilever excitation, and low-noise, high-frequency deflection readout provide a powerful platform for extending multifrequency techniques

• potential is mapped onto a monotonic function. By controlling for a constant energy loss in this way, soft imaging with very small amplitudes down to 100 pm can be realized; however, an unclean cantilever excitation can negatively impact the imaging. Our photothermal readout head provides the capability for

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

• of higher eigenmodes and multiple-impact regimes [21][26], mass loading and fluid-borne cantilever excitation [19][23][24], discrepancies between the photodetector signal and the actual tip position for base-excited cantilever systems [24][28] and non-ideal spectroscopy curves (for example, curved

Determining cantilever stiffness from thermal noise

• Jannis Lübbe,
• Matthias Temmen,
• Philipp Rahe,
• Angelika Kühnle and
• Michael Reichling

Beilstein J. Nanotechnol. 2013, 4, 227–233, doi:10.3762/bjnano.4.23

• Qn can quite easily be determined with high precision by a cantilever excitation experiment [12], the thermal method discussed here is hitherto the only one to yield valid results for the modal stiffness kn. The strength of the thermal method is that it is solely based on the equipartition theorem

• precisely be determined from an in situ cantilever excitation experiment [12], the latter function can be assumed to be 1 if the filter transfer function is reasonably well-behaved as a function of frequency and a sufficiently large PLL bandwidth is chosen [6]. Results shown in Figure 3 demonstrate that the

• noise is most interesting for cantilever excitation at higher oscillation modes where the projection of the displacement noise into the low frequency region by the PLL demodulator is especially convenient. Respective results obtained for cantilevers P 5 and AF 11 are shown in Table 2. For cantilever P 5

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

• the noise contributions of the thermal cantilever excitation and the detection system yield different spectral characteristics. The detection bandwidth B and, consequently, the noise propagation characteristics depend on the PLL amplitude response GPLL = Gfilter × Gdemod, which can usually be

• thermal cantilever excitation. The noise contribution of the detection system can be obtained from the white-noise floor of the measured spectra. The knowledge of the detection-system transfer functions allows one to predict the frequency-shift noise from the measured displacement noise, and by inversion

Wavelet cross-correlation and phase analysis of a free cantilever subjected to band excitation

• Francesco Banfi and
• Gabriele Ferrini

Beilstein J. Nanotechnol. 2012, 3, 294–300, doi:10.3762/bjnano.3.33

• ], impulsive cantilever excitation [5] or thermal-noise excitation [6][7][8][9]. Thermal noise analysis has been performed, with the aid of wavelet transforms, to characterize the time–frequency response of a thermally excited cantilever in dynamic force spectroscopy [10][11][12]. In these previous works, the

Tip-sample interactions on graphite studied using the wavelet transform

• Giovanna Malegori and
• Gabriele Ferrini

Beilstein J. Nanotechnol. 2010, 1, 172–181, doi:10.3762/bjnano.1.21

• contact. The discontinuous appearance of the signal in the time-frequency representation is due to the statistical nature of the cantilever excitation. The thermal contact of the cantilever with a reservoir at temperature T implies that its mean potential energy (where Arms is the root mean square