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

• stiffness calibration of a particular type of qPlus sensor in UHV and at 9.8 K by means of thermal noise measurements. The stiffness calibration of such high-k sensors, featuring high quality factors (Q) as well, requires to master both the acquisition parameters and the data post-processing. Our approach

• optical detection setup. Nc-AFM experiments are then mostly performed with quartz sensors, essentially implemented according to two geometries: quartz tuning fork (QTF) [19] or length-extensional resonator (LER) [20][21][22]. The commercial versions of these probes are the qPlus sensor (Scienta-Omicron

• qPlus sensor. The discussion is restricted to probes with a rectangular cross section (length l, thickness t, width w are such that l ≫ t and l ≫ w) treated in the Euler–Bernoulli model of the embedded beam, extensively detailed, for example, in [35] (cf. also Supporting Information File 1). The

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

• superconducting cavity read-out scheme is intrinsically low noise. Compared to other low-temperature AFM probes, such as the qPlus sensor [42], our versatile design allows for achieving a wide variety of the parameters of the mechanical mode (force transducer) with a much lower effective mass and, consequently

Topographic signatures and manipulations of Fe atoms, CO molecules and NaCl islands on superconducting Pb(111)

• Carl Drechsel,
• Philipp D’Astolfo,
• Jung-Ching Liu,
• Thilo Glatzel,
• Rémy Pawlak and
• Ernst Meyer

Beilstein J. Nanotechnol. 2022, 13, 1–9, doi:10.3762/bjnano.13.1

• [47] operated in the frequency-modulation mode (resonance frequency f0 ≈ 25 kHz, spring constant k ≈ 1800 N/m, quality factor Q ≈ 14000, and oscillation amplitude A ≈ 0.5 Å). The tip mounted to the qPlus sensor consists of a 25 μm-thick PtIr wire, shortened and sharpened with a focused ion beam. A

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

• , CH-1015 Lausanne, Switzerland II. Institute of Physics, RWTH Aachen University, D-52074 Aachen, Germany 10.3762/bjnano.12.46 Abstract Combined scanning tunnelling and atomic force microscopy using a qPlus sensor enables the measurement of electronic and mechanic properties of two-dimensional

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

• ]. This has been used to achieve atomic resolution of a sample that is laterally stiff and vertically soft [5]. It has also been used under ultrahigh-vacuum conditions [6] as well as in liquid to yield atomic resolution [7]. Also in 2002, Giessibl and co-workers performed LFM using a qPlus sensor as shown

• 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

• , Germany) operating in ultra-high vacuum at 5.6 K equipped with a qPlus sensor [25]. The sensor was equipped with an etched tungsten tip, which was repeatedly poked into a Cu(111) surface to generate well-defined tip apex configurations. Cu(111) was cleaned by standard sputtering and annealing cycles

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

• . The vibration modes of a qPlus sensor with a long tip are quite different from those of a cantilever with a short tip. Flexural vibration of the tungsten tip will occur. The tip can no longer be considered as a rigid body that moves with the prong of the tuning fork. Instead, it oscillates both

• the optimal diameter was found to be 0.1 mm. Keywords: finite element method; long tilted tip; noncontact atomic force microscopy; qPlus sensor; quartz tuning fork; simulations; Introduction Quartz tuning forks are widely used in the watch industry because of their low frequency offset over a wide

• temperature range [1]. In addition, quartz tuning forks have a high elastic constant, a high quality factor (Q factor), and are self-sensing due to the piezoelectric effect [1]. Therefore, a quartz tuning fork can be used as a force sensor. The central part of the “qPlus sensor” is a quartz tuning fork of

Ion mobility and material transport on KBr in air as a function of the relative humidity

• Dominik J. Kirpal,
• Korbinian Pürckhauer,
• Alfred J. Weymouth and
• Franz J. Giessibl

Beilstein J. Nanotechnol. 2019, 10, 2084–2093, doi:10.3762/bjnano.10.203

• relationship between humidity, water coverage and movement speed, however, is complex. In this study we investigated the surface of KBr, a salt crystal, by using frequency-modulation atomic force microscopy (FM-AFM) using a qPlus sensor [9][10][11]. The aim of our experiments is a qualitative and quantitative

• range for each experiment. Experimental For the experiments we used a custom-designed AFM equipped with a qPlus sensor. The qPlus sensor is a stiff (k = 1800 N/m) self-sensing quartz sensor with a resonance frequency around f0 = 32 kHz. It has enabled unprecedented results in low-temperature AFM, such

• per hour. The humidity was continuously measured and, if needed, adjusted during the measurement process. All AFM experiments were performed in the frequency-modulation mode with a qPlus sensor with a resonance frequency of 29 to 33 kHz and a stiffness of k = 1.8 kN/m. Typical image parameters were an

Nitrous oxide as an effective AFM tip functionalization: a comparative study

• Taras Chutora,
• Bruno de la Torre,
• Pingo Mutombo,
• Jack Hellerstedt,
• Jaromír Kopeček,
• Pavel Jelínek and
• Martin Švec

Beilstein J. Nanotechnol. 2019, 10, 315–321, doi:10.3762/bjnano.10.30

• with exposures of 0.5–1.7 L. AFM measurements were performed with a qPlus sensor (resonance frequency ca. 30 kHz; k ≈ 1800 N/m), using an oscillation amplitude of 50 pm. Prior to functionalization, the Pt tip was repeatedly indented into the Au(111) substrate several nanometers deep for sharpening and

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

• location and orientation of the tip will be modified along with the amount of epoxy used for attaching the tip. In panels (b–e) of Figure 1, we then establish some benchmark values for the qPlus sensor with tips. Figure 1b visualizes the mesh distributions used for the calculations. As before, mesh

• %. Results and Discussion Effect of attaching a tip to the free prong of the tuning fork In this section, we are investigating how different choices to attach the tip to the free prong of the qPlus sensor affect the evolution of the spring constant k, the first eigenfrequency f0, the quality factor Q, and

• more than 2% even for straight up tip orientations (φ = 0°) and may reach values of 8% for small epoxy amounts and large tip tilts. Effect of a wire for collecting the tunneling current In many qPlus sensor designs, a separate wire connects to the metallic probe tip to allow for an independent

Length-extension resonator as a force sensor for high-resolution frequency-modulation atomic force microscopy in air

• Hannes Beyer,
• Tino Wagner and
• Andreas Stemmer

Beilstein J. Nanotechnol. 2016, 7, 432–438, doi:10.3762/bjnano.7.38

• [4][5]. Recently, atomic resolution has been achieved with a qPlus sensor in air on potassium bromide and graphite [2][6]. In this paper, we demonstrate the suitability of the piezoelectric self-sensing length-extension resonator (LER) [7][8] for high-resolution FM-AFM imaging in air. The LER has a

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

• of the spring constant of the sensor and complications from finite tip heights. Here we combine a numerical investigation of the force reconstruction with an experimental characterization of the flexural mechanics of the qPlus sensor. Numerical studies reveal significant errors in reconstructed force

• approach has been to estimate the spring constant from plane view geometry and the Young’s modulus of the appropriate crystallographic orientation. In this case, the qPlus sensor is treated as a uniform, rectangular cantilever and the spring constant is predicted from Euler–Bernoulli beam theory [1][7

• , we develop a rigorous mathematical model for the qPlus sensor with a finite tip. The effect of the parasitic tip motion on the reconstructed interaction force is examined quantitatively from the perspective of two-dimensional grid spectroscopy. In addition, we use a traceable nanoindenter to

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

• of the tuning fork due to variations in the tip–sample interaction are tracked and, via the formula introduced by Sader and Jarvis [18], can be converted to force or potential energy measurements. The qPlus sensor facilitates, in principle, a straight-forward method of acquiring tunnelling current

Patterning a hydrogen-bonded molecular monolayer with a hand-controlled scanning probe microscope

• Matthew F. B. Green,
• Taner Esat,
• Christian Wagner,
• Philipp Leinen,
• Alexander Grötsch,
• F. Stefan Tautz and
• Ruslan Temirov

Beilstein J. Nanotechnol. 2014, 5, 1926–1932, doi:10.3762/bjnano.5.203

• used a qPlus sensor [17] manufactured by CREATEC. The AFM/STM tip was made from a 0.3 mm long and 15 μm thick PtIr wire glued to the tuning fork of the qPlus sensor, and sharpened with a gallium focused ion beam (FIB). The resulting resonance frequency of the qPlus sensor was f0 = 30,300 Hz with a

• quality factor of Q ≈ 70,000. Contacting and manipulation were performed with the qPlus sensor oscillating with an amplitude of A0 ≈ 0.2–0.3 Å. Interactions in the junction were monitored by measuring the frequency shift Δf(z) ≈ −(f0/2k0)dFz/dz, where k0 = 1800 N/m is the stiffness of the quartz tuning

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

• for such a measurement is shown in Figure 2. In order to validate this measurement method we assembled a test sensor similar to the “qPlus” sensor setup. In the same way as in a “qPlus” sensor, a quartz tuning fork was glued onto a Macor body, and a tungsten wire with a diameter of dW-wire = 50 μm was

• “qPlus” sensor in the FEM software as realistic as possible, including gluing points as well as a metal tip. As for the tuning fork, an isotropic Young’s modulus of Equartz = 78.9 GPa was used. To obtain a realistic value of the Young’s modulus of the glue for the FEM simulations, three samples made from

• “qPlus” sensor configuration, the wire-tip is attached at the side causing a torque around the axis of the beam in addition to the bending of the prong. To evaluate the influence of the torsion, the simulation was repeated with the tip positioned at the center of the prong (indeed some experimentalists

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

• principle. The frequency variation with temperature T for all sensors is negative up to 30 K and on the order of 1 ppm/K, up to 13 K, where a distinct kink appears, it is linear. Furthermore, we characterize a new type of miniaturized qPlus sensor and confirm the theoretically predicted reduction in

• detector noise. Keywords: AFM; frequency drift; length extensional resonator; needle sensor; qPlus sensor; quartz; Findings Frequency modulation atomic force microscopy [1] has become an essential tool for surface scientist‘s to study chemical and magnetic interactions at the atomic scale [2][3][4][5][6

The role of surface corrugation and tip oscillation in single-molecule manipulation with a non-contact atomic force microscope

• Christian Wagner,
• Norman Fournier,
• F. Stefan Tautz and
• Ruslan Temirov

Beilstein J. Nanotechnol. 2014, 5, 202–209, doi:10.3762/bjnano.5.22

• -molecule manipulation has particularly promising potential to yield new insights. We recently reported experiments, in which 3,4,9,10-perylene-tetracarboxylic-dianhydride (PTCDA) molecules were lifted with a qPlus-sensor and analyzed these experiments by using force-field simulations. Irrespective of the

• the qPlus sensor [6][11][24]. Figure 1a, which exhibits an example of such a measurement, reveals that the qPlus sensor oscillating with the amplitude of AqPlus = 0.2–0.3 Å can indeed measure the stiffness ∂Fz/∂z(z) of the junction continuously through all stages of the manipulation experiment. Since

• in the manipulation experiment). In particular, the superior stiffness of the qPlus sensor results in the absence of any systematic hysteresis between the stiffness curves measured in the “lift” and “put” parts of the manipulation cycle. As a result, the measurement of Δf shown in Figure 1a exhibits

Optimal geometry for a quartz multipurpose SPM sensor

• Julian Stirling

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

• ] respectively, into a wide range of specialised sensors. The most common NC-AFM sensors: silicon microcantilvers [5], and quartz sensors such as the qPlus sensor (tuning fork) [6] or KolibriSensor® [7], have all been used for combined AFM/STM [7][8][9]. Combined AFM/LFM sensors have been constructed from

• silicon cantilevers, by exciting torsional modes to generate the lateral motion needed for the LFM [10]. The qPlus sensor has been used as an LFM by rotating the tip on the end of the quartz tuning fork [11], but no combined AFM/LFM qPlus system has been developed due to the magnitude of the torsion

• . For quartz sensors the obvious choice of cantilever is the standard qPlus sensor with a normal spring constant of approximately 1.8 kN·m−1. [17][18] For commercially available silicon cantilevers the spring constants are usually less than 50 N·m−1, with resonant frequencies of 200–300 kHz. The

High-resolution dynamic atomic force microscopy in liquids with different feedback architectures

• John Melcher,
• David Martínez-Martín,
• Miriam Jaafar,
• Julio Gómez-Herrero and
• Arvind Raman

Beilstein J. Nanotechnol. 2013, 4, 153–163, doi:10.3762/bjnano.4.15

• possibility that force resolution is not necessarily the limiting factor for imaging resolution. The highest resolution images are achieved with the qPlus sensor in [47], which has the lowest force resolution amongst the references in vacuum. If the force sensitivity meets some minimal requirements, the

• typically low, the force sensitivity can be preserved by using soft probes with small amplitudes. Remarkably, it is possible for a probe in liquid to have a force sensitivity on par with the qPlus sensor in vacuum. Moreover, we find that the reduction in both attractive forces and quality factors that

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

• bandwidth larger than the thermal-limit bandwidth. Note that the thermal-noise contribution of AL 3 is even larger than the total noise of the other cantilevers. These results are compared to typical values for a qPlus sensor with parameters taken from [11]. The thermal noise δfth of the qPlus sensor is an

• order of magnitude below the values for the cantilevers. Including the noise of the detection system, δftot of the qPlus sensor is nearly identical to the thermal noise δfth obtained for cantilever D 5 (curve not shown) and, therefore, only half of the noise level of the best cantilevers. For a valid

• δγtot is quite close to that of cantilever D 5. On the other hand, the qPlus sensor has a noise level δγ more than two orders above the results for the cantilevers due to its exceptional k/f0 ratio. Therefore, the advantageous noise figures of the qPlus sensor documented in Figure 8a can only be

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

• qPlus atomic force microscopy the tip length can in principle approach the length of the cantilever. We present a detailed mathematical model of the effects this has on the dynamic properties of the qPlus sensor. The resulting, experimentally confirmed motion of the tip apex is shown to have a large

• and molecular interactions [6][7]. As with all forms of AFM, image resolution and force measurements ultimately depend on the structure of the last few angstroms of the tip apex [1][2][4][6][7][8][9]. The qPlus sensor is unusual for an AFM sensor in that it is constructed from a quartz tuning fork and

• for the deflection, elastic potential energy, and spring constant of the tine of a qPlus sensor, for an arbitrary tip geometry. Furthermore, we derive the resulting lateral component of the motion of the tip apex, showing it, both theoretically and experimentally, to be comparable to the amplitude of

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

• the tuning fork is assumed to behave like a simple harmonic oscillator. The normal stiffness of the qPlus sensor can be related by the equipartition theorem to its thermal energy during vibration, leading to the relationship where Ath is the amplitude of the thermal motion of the free prong, kB is the

• from the volume of the wire. The wire can be easily removed after the measurement without destroying the sensor. Home-made qPlus sensor consists of the following parts: (1) base stage (from Omicron–Oxford instruments), (2) ceramic plate, (3) copper shield that is glued to the ceramic plate (4

Models of the interaction of metal tips with insulating surfaces

• Thomas Trevethan,
• Matthew Watkins and
• Alexander L. Shluger

Beilstein J. Nanotechnol. 2012, 3, 329–335, doi:10.3762/bjnano.3.37

• fact, in many cases atomic-resolution images are only obtained after the tip has been deliberately crashed into the surface, implying that the tip apex is formed from surface species [1][2]. The development of NC-AFM based on a quartz tuning fork (qPlus sensor) instead of a silicon cantilever has led

Graphite, graphene on SiC, and graphene nanoribbons: Calculated images with a numerical FM-AFM

• Fabien Castanié,
• Laurent Nony,
• Sébastien Gauthier and
• Xavier Bouju

Beilstein J. Nanotechnol. 2012, 3, 301–311, doi:10.3762/bjnano.3.34

• -AFM users equipped, for example, with a qPlus sensor. Nevertheless, calculations are necessary to fully interpret experimental images in some specific cases. In this context, we developed a numerical AFM (n-AFM) able to be used in different modes and under different usage conditions. Results: Here, we

• functionalized tip, that is, with a CO molecule attached to the tip apex acting as a supertip [60]. Most of the mentioned studies were based on a technical improvement consisting of the use of a tuning fork of the qPlus sensor type [61]. This sensor is an AFM tip that is fixed to one branch of a quartz tuning

• amplitude constant and equal to a predefined setpoint. Large-amplitude (typically 10–20 nm) to small-amplitude (of the order of 0.02 nm to mimic a qPlus sensor [62]) settings are available with the n-AFM. The DC allows the regulation of the tip–sample distance based on minimizing the difference between Δf

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

• .3.28 Abstract We present the results of simultaneous scanning-tunneling and frequency-modulated dynamic atomic force microscopy measurements with a qPlus setup. The qPlus sensor is a purely electrical sensor based on a quartz tuning fork. If both the tunneling current and the force signal are to be

• parts of the qPlus sensor are large enough for assembly of the sensor simply by hand. Let us note that using a length-extensional resonator is another interesting alternative to the qPlus configuration [15][16]. The comparison of their performance is still an open issue in the community [13]. Probably

• deflection signal due to the coupling between the channels. The prevention of the cross-talk phenomena In a joint project with Omicron Nanotechnology, we evaluated the crosstalk in the qPlus sensor. We suggested several improvements in order to keep the capacitive couplings as low as possible. First, we

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

• gradients of the interactions responsible for atomic contrast and those causing domain contrast are orders of magnitude apart, ranging from up to 100 Nm−1 for atomic interactions down to 0.0001 Nm−1 for magnetic dipole interactions. Here, we show that this gap can be bridged with a qPlus sensor, with a

• fork. The qPlus sensor [8] is based on a quartz tuning fork, in which one prong is attached to a carrier substrate. The large spring constant of the qPlus, k = 1800 Nm−1, allows one to overcome the snap-to-contact-problem in small-amplitude operation [9]. In this mode, the qPlus setup is customized for

• , were previously conducted [11][12], the qPlus sensor has not yet proven its ability to detect weak long-range magnetic dipole interaction. In this article we show that the qPlus sensor is also capable of MFM experiments. We show imaging contrast of several millihertz in the large-amplitude regime