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

• . Keywords: amplitude calibration; displacement detection; force microscopy; interferometer signal; NC-AFM; Introduction Optical interferometry is a reliable technique utilizing light waves to measure distance and displacement with high precision [1][2]. With the light wavelength as the length standard, a

• the calibration of the cantilever oscillation amplitude, we exemplify the fit procedure and accuracy limits for the fit parameter A. Amplitude calibration means to relate the cantilever oscillation amplitude A to the voltage Vexc to yield the calibration factor S = A/Vexc [18]. An accurate calibration

• yields a compensation of positive and negative deviations from the straight line. To obtain limits for the precision and accuracy of the result for the amplitude calibration factor, we consider four contributions to the error in S, which are expressed in the following formula of error propagation for the

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

• ][14][15][16]. The amplitude calibration in nc-AFM using the so-called constant-γ method is well documented and reasonably accurate [16][17][18], even if recently reported methods seem more accurate [16]. Conversely, it seems that the direct stiffness calibration of nc-AFM probes in UHV and at low

• constant-γ calibration procedure of the oscillation amplitude in nc-AFM mode [16][17][18]. The accuracy of the calibration is cross-checked in STM mode, which guarantees an accuracy of 5% in the amplitude calibration. A dedicated software data acquisition module implemented by SPECS into the Nanonis MIMEA

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

• frequency-modulation atomic force microscopy, the tip oscillates parallel to the surface. Existing amplitude calibration methods are not applicable for mechanically excited LFM sensors at low temperature. Moreover, a slight angular offset of the oscillation direction (tilt) has a significant influence on

• for a given amplitude and tilt. Finally, the amplitude and tilt are determined by fitting the simulation output to the data with oscillation. Keywords: frequency-modulation atomic force microscopy; lateral force microscopy; amplitude calibration; tilt estimation; Introduction Frequency-modulation

• both with oscillation and without as the CO bends faster than the cantilever moves. At the heights where we performed the amplitude calibration, we did not observe a LFM signal, meaning that the lateral forces were insignificant. Also, the excitation frequency of the frustrated translational mode is in

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

• , or vacuum environments. Keywords: amplitude calibration; atomic force microscopy; electrostatic excitation; encased cantilevers; liquid AFM; Introduction Dynamic atomic force microscopy requires excitation of the cantilever oscillation. Most commonly, this is achieved using a dither piezo built

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

• thermal calibration method [39]. For amplitude calibration the inverse optical lever sensitivity in units of nm/V was determined via a noncontact method proposed by M. J. Higgins et al. [36]. The noise level of the AFM optical detector was less than 60 μV, which corresponds to an amplitude noise of

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

• ambient conditions. The time evolution is expressed in terms of sequentially acquired images. The free oscillation amplitude was set to 30 nm and setpoint to Asp = 27 nm, respectively. The missing points 3, 4 and 5 correspond to approach curves taken for amplitude calibration. The continuous blue lines

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

• convert voltage signals delivered by the instruments to physical units. The detection sensitivity for the herein presented data is determined to 52.5 nm/V from an amplitude calibration (see [19] and Supporting Information of [11]). A PLLpro2 control system (RHK Technology, Inc., Troy, MI, USA) is used

• excitation calibration factors and , respectively, where is determined by an amplitude calibration as described in [19] while is determined from measuring the oscillation amplitude in resonance for a given excitation voltage Vexc. Assuming Q0 = A/Aexc = allows a straightforward calculation of from known

• parameters of a well-characterised system. Note that by rewriting this formula to , we can fully describe Hac without performing an amplitude calibration measurement. The characteristics of the loop are defined by two parameters, the gain PA and the integral cutoff IA. Assuming that the cantilever is a

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

• oscillation amplitude of λ/8. The measured maximum voltage in combination with the wavelength is used for amplitude calibration by applying an arcsine function to account for the approximately sinusoidal modulation of the interferometric fringes as a function of d. For a cavity with low , this is a good

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

• different amplitude calibration factors for the corresponding modes. However, due to the length of only 40 μm and 35 μm, for the high-frequency cantilevers AP 5 and AL 3, the laser adjustment becomes difficult, yielding only 77 μW and 18 μW laser power on the PSD compared to about 100 μW for other

• output of the demodulator and demonstrated that predictions based on the demodulator transfer function and filtering are well reproduced by experiments. For a quantitative analysis of the noise, a precise amplitude calibration of the detection system relating electrical signals to the mechanical

Calculation of the effect of tip geometry on noncontact atomic force microscopy using a qPlus sensor

• Julian Stirling and
• Gordon A. Shaw

Beilstein J. Nanotechnol. 2013, 4, 10–19, doi:10.3762/bjnano.4.2

• images and spectra can be generated to theoretically calculate the effect; however, one must carefully consider both the amplitude calibration and the methods for calculating frequency shifts from a potential before continuing. Effect on frequency shift Under the assumption that the direction of motion

• for tip motion parallel to the cantilever oscillation. However, if lateral forces are present, then these will also affect the frequency shift. Effect on calibration Amplitude calibration in qPlus AFM is usually performed by measuring the z extension needed to maintain a constant value for [10]. As

Characterization of the mechanical properties of qPlus sensors

• Jan Berger,
• Martin Švec,
• Martin Müller,
• Martin Ledinský,
• Antonín Fejfar,
• Pavel Jelínek and
• Zsolt Majzik

Beilstein J. Nanotechnol. 2013, 4, 1–9, doi:10.3762/bjnano.4.1

• , namely the amplitude calibration (see Equation 8). The other two methods do not depend on the amplitude calibration. They depend only on size measurements, which can be calibrated with very high accuracy by using optical or electron microscopes. Therefore, we suppose that the overall error in the force