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

• the framework focuses on a particular kind of sensor, it may be adapted to any high-k, high-Q nc-AFM probe used under similar conditions, such as silicon cantilevers and LERs. Keywords: low temperature; non-contact atomic force microscopy; qPlus sensors; quartz tuning fork; stiffness calibration

• , which forms the tip. The tip is electrically connected to an electrode that collects the tunneling current if scanning tunneling experiments are to be performed along with nc-AFM experiments. The qPlus sensors feature a resonance frequency of f1 ≃ 25 kHz and a most commonly reported stiffness of 1800 N

• ][57][58][59][60], leading to a set of a dozen distinct approaches. A “global calibration initiative” has even been launched by Sader [58][61]. Conversely, much less references are available for qPlus sensors [62][63][64][65][66][67], and, among these, none of them deals with the direct stiffness

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

• Sciences (CAS), Suzhou 215123, China CAS Key Laboratory of Nanophotonic Materials and Devices, Suzhou Institute of Nano-Tech and Nano-Bionics, Suzhou 215123, China 10.3762/bjnano.12.7 Abstract We study the oscillatory behavior of qPlus sensors with a long tilted tip by means of finite element simulations

• horizontally and vertically. The vibration characteristics of qPlus sensors with different tip sizes were studied. An optimized tip size was derived from obtained values of tip amplitude, ratio between vertical and lateral amplitude components, output current, and quality factor. For high spatial resolution

• . Here, we report a numerical study of the vibration modes of qPlus sensors. Eigenfrequencies, tip amplitudes, ratios between vertical and lateral amplitude components, output currents, and Q factor values as functions of the tip size of the qPlus sensor are systematically analyzed. Eventually, the

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

• experiments (5 and 77 K) with qPlus sensors as well as at room temperature using silicon cantilevers [22]. Although the NC-AFM tips were not functionalised, i.e., not specifically terminated with atoms or molecules for imaging, we find a very good agreement between the experimental data and probe particle

Optimizing qPlus sensor assemblies for simultaneous scanning tunneling and noncontact atomic force microscopy operation based on finite element method analysis

• Omur E. Dagdeviren and
• Udo D. Schwarz

Beilstein J. Nanotechnol. 2017, 8, 657–666, doi:10.3762/bjnano.8.70

• , low cost, a freedom in the selection of the materials used as local probes, and physical dimensions that allow experimentalists to assemble sensors right in their own labs with relative ease [19][22][23][24][25]. But even though this in-lab assembly of qPlus sensors is a manageable task, the small

• perturbation of the ideal vertical oscillation behavior using the finite element method (FEM). Building on an earlier study that quantified the performance of qPlus sensors without tips as a function of the location and amount of epoxy glue used to mount the fork onto its holder [26], we model in this work

• degree by which the oscillation deviates from movement in the vertical x–z axis (the “perturbation” Δy/Δz). To assess the significance of these changes on the sensing capabilities of the device, let us recall from the discussion in [26] that high-resolution measurements involving qPlus sensors are to

A simple method for the determination of qPlus sensor spring constants

• John Melcher,
• Julian Stirling and
• Gordon A. Shaw

Beilstein J. Nanotechnol. 2015, 6, 1733–1742, doi:10.3762/bjnano.6.177

• John Melcher Julian Stirling Gordon A. Shaw National Institute of Standards and Technology, Gaithersburg, MD 20899, USA 10.3762/bjnano.6.177 Abstract qPlus sensors are widely used to measure forces at the atomic scale, however, confidence in these measurements is limited by inconsistent reports

• possible for qPlus sensors [10], and other sensors with cantilevered geometries [11], to reach quality factors in excess of 106 without inertial cancelling. Several methods have been developed to reconstruct the tip–sample interaction force from the frequency shift of an oscillating tip in ncAFM [12][13

• based on quartz tuning forks [25][26][27][28][29], no comprehensive framework yet exists due to inconsistencies between results from different methods. qPlus sensors are stiff compared to traditional microcantilever sensors and present their own set of spring constant calibration challenges. A common

Nano-contact microscopy of supracrystals

• Adam Sweetman,
• Nicolas Goubet,
• Ioannis Lekkas,
• Marie Paule Pileni and
• Philip Moriarty

Beilstein J. Nanotechnol. 2015, 6, 1229–1236, doi:10.3762/bjnano.6.126

• experiments were undertaken. The scanning probe data in this paper were acquired using an Omicron Nanotechnology combined low temperature STM/DFM operating under UHV conditions at cryogenic temperatures (78 K, with liquid nitrogen cooling). Commercial qPlus sensors from Omicron with an electrochemically

Calibration of quartz tuning fork spring constants for non-contact atomic force microscopy: direct mechanical measurements and simulations

• Jens Falter,
• Marvin Stiefermann,
• Gernot Langewisch,
• Philipp Schurig,
• Hendrik Hölscher,
• Harald Fuchs and
• André Schirmeisen

Beilstein J. Nanotechnol. 2014, 5, 507–516, doi:10.3762/bjnano.5.59

• tuning forks. However, the underlying models of these calculations are barely in agreement with the actual geometry of real “qPlus” sensors, in which the force is applied through a metal wire glued onto the free prong. Therefore, the force application point is defined by the position of the glue point

• findings motivated our detailed analysis of the mechanical tuning fork properties by FEM using the software Comsol Multiphysics (V 4.1a). In addition to the measurement of “custom-made qPlus” sensors, we also measured the spring constant of “qPlus” sensors from Omicron NanoScience GmbH, Taunusstein. The

• Young’s modulus ETorrSeal,RT = 4000 GPa. As our custom-build “qPlus” sensors are cured out in an oven, the value of ETorrSeal = 6000 GPa was used in our FEM simulations for the epoxy glue. The geometry of the simulated model is depicted in Figure 4 in more detail. The sophisticated geometry of different

Impact of thermal frequency drift on highest precision force microscopy using quartz-based force sensors at low temperatures

• Florian Pielmeier,
• Daniel Meuer,
• Daniel Schmid,
• Christoph Strunk and
• Franz J. Giessibl

Beilstein J. Nanotechnol. 2014, 5, 407–412, doi:10.3762/bjnano.5.48

• for the frequency change with temperature of TF and qPlus sensors The same result is obtained for the LER geometry. For X cut crystalline quartz no change in vs within a precision of 0.1 ppm was observed below 10 K [23][24][25]. The measured values of below 10 K are in the order of 0.01 ppm/K [21

• were investigated to directly evaluate and compare the influence of thermal frequency drift on the force gradient noise. Two coupled oscillators, a LER (Figure 1a) and a TF (Figure 1b) both without tip, were used for direct comparison. Two standard qPlus sensors were built with quartz TFs, one without

• tip (S, Figure 1c) and one with a tip (St, Figure 1d). Finally, custom designed quartz cantilevers, are used to build qPlus sensors with standard and smaller beam dimensions (C and Ct, Figure 1e, Figure 1f). At the end of the prong of sensor Ct is a small appendix for easier accommodation of tips

Uncertainties in forces extracted from non-contact atomic force microscopy measurements by fitting of long-range background forces

• Adam Sweetman and
• Andrew Stannard

Beilstein J. Nanotechnol. 2014, 5, 386–393, doi:10.3762/bjnano.5.45

• transferred into the scan head and left to cool before imaging. Commercial qPlus sensors from Omicron with electrochemically etched tungsten wire glued to one tine of the tuning fork were introduced into the scan head without any further preparation. We typically recorded resonant frequencies of f0 ≈ 25 kHz

Optimal geometry for a quartz multipurpose SPM sensor

• Julian Stirling

Beilstein J. Nanotechnol. 2013, 4, 370–376, doi:10.3762/bjnano.4.43

• increasing the tip length is a reduction in lateral spring constant, which comes at the price of lower eigenfrequencies. A tip length of 1mm would provide eigenfrequencies of f1 = 11.8 kHz and f2 = 17.2 kHz, with klat= 1.50 kN·m−1. These frequencies are of the same order of magnitude as qPlus sensors with

• between Alat and Aantinode is on the order of 2. Other detection parameters are also of the same order of magnitude as for a qPlus sensor. Thus, as qPlus sensors have achieved imaging with amplitudes as low as 20 pm [16], similar amplitudes are in theory possible for the LFM mode of the symmetric sensor

• be attached to the tungsten tip, as is often done for qPlus sensors. This is inadvisable as it also breaks the symmetry of the sensor. Another method would be to add a thin insulating layer to the top side of the resonator and on top of that a new electrode, such as the method developed by Nauga

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

• measurements [3], the spring constant is often left unmeasured and is assumed to be k ≈ 1800 N·m−1 from the geometry of the bare tine [10]. Measurements of the spring constants of qPlus sensors have produced conflicting results [4][13], which highlights the need for more detailed analysis. Tung et al. [11

• motion normal to the surface even in the first eigenmode. This differs from previous work considering the lateral motion of qPlus sensors, such as Heyde et al. [14], as the lateral motion arises directly from the eigenmode used for imaging, rather than a parallel or torsional eigenmode. As such the

• , thermal tuning of qPlus sensors with spring constants on the order of 2 kN·m−1 remains a challenging experimental task as the rms amplitude of thermal excitation at 300 K is ≈1.4 pm. For well-calibrated force measurements, the dynamic spring constant for the excited eigenmode ki must be calculated. By

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

• methods that can be used for estimating the stiffness of qPlus sensors. The first method is based on continuum theory of elasticity. The second (Cleveland’s method) uses the change in the eigenfrequency that is induced by the loading of small masses. Finally, the stiffness is obtained by analysis of the

• . This method is based on gluing small pieces of a tungsten wire; the mass is obtained from the volume of the wire, which is measured by optical microscopy. To facilitate detection of oscillation eigenfrequencies under ambient conditions, we designed and built a device for testing qPlus sensors

• simultaneous STM and AFM signals with atomic resolution on a metal surface [14]. At the same time F. J. Giessibl introduced so-called qPlus sensors [15], which allow simultaneous acquisition of the tunneling current and the forces with a small oscillation amplitude. This method increases substantially the

Simultaneous current, force and dissipation measurements on the Si(111) 7×7 surface with an optimized qPlus AFM/STM technique

• Zsolt Majzik,
• Martin Setvín,
• Andreas Bettac,
• Albrecht Feltz,
• Vladimír Cháb and
• Pavel Jelínek

Beilstein J. Nanotechnol. 2012, 3, 249–259, doi:10.3762/bjnano.3.28

• number of successful simultaneous AFM/STM measurements with coated Si-cantilevers [21][22][23][24], qPlus sensors [25][26][27][28] and length-extensional quartz resonators [16][29]. The possibility of measuring the interaction forces simultaneously with the flow of electrons between the tip and the

• voltage and the sample holder is grounded. NanoSurf EasyPLL is used for the FM demodulation and the Omicron MATRIX control system for the data acquisition. The qPlus sensors were built from commercially available tuning forks from Micro Crystal, originally packed in the SMD package MS1V-T1K. The original

qPlus magnetic force microscopy in frequency-modulation mode with millihertz resolution

• Maximilian Schneiderbauer,
• Daniel Wastl and
• Franz J. Giessibl

Beilstein J. Nanotechnol. 2012, 3, 174–178, doi:10.3762/bjnano.3.18

• perform magnetic force microscopy with qPlus sensors, even under ambient conditions. State-of-the-art low-temperature magnetic force microscopy has been applied to measure the Barkhausen effect, yielding a frequency-shift contrast of 0.7 Hz for a cantilever with f0 = 195 kHz and k = 47 Nm−1 [22], which

• corresponds to a magnetic force gradient of 340 μNm−1. At low temperatures we expect that the noise in our MFM measurements will decrease dramatically due to an increase in Q, a decrease in nq (Equation 2–Equation 4), and a decrease in thermal frequency drift, therefore we trust that qPlus sensors will become

Effect of the tip state during qPlus noncontact atomic force microscopy of Si(100) at 5 K: Probing the probe

• Adam Sweetman,
• Sam Jarvis,
• Rosanna Danza and
• Philip Moriarty

Beilstein J. Nanotechnol. 2012, 3, 25–32, doi:10.3762/bjnano.3.3

• 1200 °C, and then slow cooling from 900 °C to room temperature before being placed into the scan head. We introduced commercial qPlus sensors (Omicron GmbH), with an electrochemically etched tungsten wire attached to one tine of the tuning fork, into the scan head without any ex situ tip treatment. The