Advanced atomic force microscopy techniques V

• Philipp Rahe,
• Ilko Bald,
• Nadine Hauptmann,
• Regina Hoffmann-Vogel,
• Harry Mönig and
• Michael Reichling

Beilstein J. Nanotechnol. 2025, 16, 54–56, doi:10.3762/bjnano.16.6

• accurate knowledge of the quartz cantilever stiffness, the authors develop a method to quantify the stiffness based on thermal noise measurements and numerical simulation. Calibrated measurements of conductivity and resistivity are the focus of the contribution by Piquemal et al. [3]. A particular

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

• relies both on numerical simulations and experimental results. A thorough analysis of the thermal noise power spectral density of the qPlus fluctuations leads to an estimated stiffness of the first flexural eigenmode of ≃2000 N/m, with a maximum uncertainty of 10%, whereas the static stiffness of the

• ; thermal noise; ultrahigh vacuum; Introduction Since the 2000s, non-contact atomic force microscopy (nc-AFM) has established itself as a scanning probe method for the topographical, chemical, and electrical mapping of the surface of a sample down to the atomic scale [1][2][3]. When used in an ultrahigh

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

• interferometric and beam-deflection detectors of motion are sufficient to resolve the thermal noise force determined by the damping of the cantilever eigenmode in thermal equilibrium with its environment. Operation in high vacuum and at cryogenic temperatures reduces this force noise, improving sensitivity to the

• electromechanical coupling. The coupling of the microwave resonator to a transmission line is also an important design consideration. Our primary goal is high sensitivity to tip–surface forces, given the constraints of the AFM application. If the detector is limited by thermal noise, the sensitivity is given by the

• sidebands in the measured output microwave field SVV(ω). The thermal noise force is detected at these sidebands [8], where is the added noise of the detector, nc is the number of circulating intra-cavity photons in the microwave resonator, g0 is the single-photon electromechanical coupling rate, and α is a

Intermodal coupling spectroscopy of mechanical modes in microcantilevers

• Ioan Ignat,
• Bernhard Schuster,
• Jonas Hafner,
• MinHee Kwon,
• Daniel Platz and
• Ulrich Schmid

Beilstein J. Nanotechnol. 2023, 14, 123–132, doi:10.3762/bjnano.14.13

• , these improvements have yet to find a practical way to AFM. As a solution, we investigate here a mechanism in which individual mechanical eigenmodes of a microcantilever couple to one another, mimicking optomechanical techniques to reduce thermal noise. We have a look at the most commonly used modes in

• , which would activate intermodal coupling between two or more eigenmodes. With this geometric nonlinearity, we can circumvent the use of tip–sample forces and apply techniques from optomechanics. Sideband cooling will reduce thermal noise of the fundamental mode. Parametric amplification relies on

• and mode splitting. Applying the sum, referred to as blue sideband pump, will cause either mode squeezing or parametric amplification [22], provided that the amplitude is optimally chosen. We will focus on the red sideband, as sideband cooling is useful for reducing thermal noise in standard AFM and

Studies of probe tip materials by atomic force microscopy: a review

• Ke Xu and
• Yuzhe Liu

Beilstein J. Nanotechnol. 2022, 13, 1256–1267, doi:10.3762/bjnano.13.104

• the thermal noise method when prepared in the chamber, after which FC is obtained on the substrate to measure the deflection sensitivity, and the position of the loading point is measured by optical microscopy when the sphere is attached. The process of calibrating the kTL into the manifold is shown

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

• al. [59], the measurement noise arises from three different noise sources, that is, thermal noise of the cantilever (thermal noise), noise of the deflection sensor (deflection noise) and noise arising from fluctuations of the oscillator circuitry driving the cantilever oscillation (oscillator noise

• from the measured first mode flexural resonance frequency f1 using: The expressions for the minimally measurable force derivative (Equation 1 and Equation 2) arising from thermal and deflection sensor noise, respectively, reveal that a high quality factor (for a low thermal noise) and a low modal

• cantilever, the deflection noise obtained with typical deflection sensors is negligible such that thermal noise is dominant. Recently, Feng et al. [29] have demonstrated that at room temperature a force derivative of 78 nN/m is detectable in a bandwidth of 1 Hz, which is of particular importance for the

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

• forces in KPFM is generally expressed as the minimum detectable CPD [53], and is directly limited by the geometry of the interaction, thermal noise of the cantilever, and the detection noise limits of the AFM [36][54]. Cantilevers have a number of eigenmodes, ωn, where there is a mechanical enhancement

• cantilever. Under small amplitude conditions the tip can be positioned very close to the surface and as such there is an advantage in increasing the spatial resolution. The trade-off here is that the SNR will be small as the mechanical amplitude approaches the thermal noise limits of the cantilever. In

Temperature and chemical effects on the interfacial energy between a Ga–In–Sn eutectic liquid alloy and nanoscopic asperities

• Yujin Han,
• Pierre-Marie Thebault,
• Corentin Audes,
• Xuelin Wang,
• Haiwoong Park,
• Jian-Zhong Jiang and
• Arnaud Caron

Beilstein J. Nanotechnol. 2022, 13, 817–827, doi:10.3762/bjnano.13.72

• force–distance curve with each cantilever on a quartz glass sample (manufactured by Goodfellow, United Kingdom) and extracting its slope in the range of repulsive forces. Subsequently, we determined the bending stiffness Cn of each cantilever by analyzing its thermal noise vibration [18]. After

Gelatin nanoparticles with tunable mechanical properties: effect of crosslinking time and loading

• Agnes-Valencia Weiss,
• Daniel Schorr,
• Julia K. Metz,
• Metin Yildirim,
• Saeed Ahmad Khan and
• Marc Schneider

Beilstein J. Nanotechnol. 2022, 13, 778–787, doi:10.3762/bjnano.13.68

• actual sensitivity and the spring constant of the used cantilever were calibrated on a cleaned silica wafer by the thermal noise method by Hutter et al. [27] using a correction factor of 0.251. The data was acquired using the quantitative imaging mode (QI™) with image sizes of 5 × 5 µm and a resolution

Direct measurement of surface photovoltage by AC bias Kelvin probe force microscopy

• Masato Miyazaki,
• Yasuhiro Sugawara and
• Yan Jun Li

Beilstein J. Nanotechnol. 2022, 13, 712–720, doi:10.3762/bjnano.13.63

• density nFM is described as [74] where ntherm is the thermal noise density, ndetect is the detector noise density, nosc is the oscillator noise density, and nds is the deflection sensor noise density. The frequency noise δf measured with a bandwidth of B at a center of fm is described as When fm ≫ B, δf

Effects of substrate stiffness on the viscoelasticity and migration of prostate cancer cells examined by atomic force microscopy

• Xiaoqiong Tang,
• Yan Zhang,
• Jiangbing Mao,
• Yuhua Wang,
• Zhenghong Zhang,
• Zhengchao Wang and
• Hongqin Yang

Beilstein J. Nanotechnol. 2022, 13, 560–569, doi:10.3762/bjnano.13.47

• Germany) for 2 h to prevent damage to the cells. Before the experiment, the thermal noise method was used to adjust the cantilever spring constant, and then the experiment was carried out in contact mode. The AFM probe (MLCT probe, Bruker, USA) slightly contacted the cell surface and a constant force was

Nonmonotonous temperature dependence of Shapiro steps in YBCO grain boundary junctions

• Leonid S. Revin,
• Dmitriy V. Masterov,
• Alexey E. Parafin,
• Sergey A. Pavlov and
• Andrey L. Pankratov

Beilstein J. Nanotechnol. 2021, 12, 1279–1285, doi:10.3762/bjnano.12.95

• by the resistively–capacitively shunted-junction (RCSJ) model [25][26], especially for measurements obtained at high temperatures. However, taking into account the effect of the YBCO junction resistance thermal noise [16] makes it possible to neutralize this difference and obtain a good agreement

• detection regime is optimal for the junction. This issue is discussed in more details below. The third important parameter is the thermal noise magnitude, kBT, which affects the smearing of the Shapiro steps, and, accordingly, the decrease in the step size in the region of low radiation power. It is not

• important. For low ωmw, the change in the response of the Josephson junction will be small with the temperature [16] since at these frequencies the detection is not optimal. At the same time, at high temperatures, thermal noise will blur the step more than at low temperatures, and with increasing Ic the

A new method for obtaining model-free viscoelastic material properties from atomic force microscopy experiments using discrete integral transform techniques

• Berkin Uluutku,
• Enrique A. López-Guerra and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2021, 12, 1063–1077, doi:10.3762/bjnano.12.79

• material and its relationship to the modified harmonic components should also be investigated further. One final area of future work concerns the effect of electronic or thermal noise on the quality of the viscoelastic analysis. Generally speaking, analyses in the complex domain can handle noise more

Bulk chemical composition contrast from attractive forces in AFM force spectroscopy

• Dorothee Silbernagl,
• Media Ghasem Zadeh Khorasani,
• Natalia Cano Murillo,
• Anna Maria Elert and
• Heinz Sturm

Beilstein J. Nanotechnol. 2021, 12, 58–71, doi:10.3762/bjnano.12.5

• recorded with a frequency of 1 Hz. The spring constant of the cantilever was determined by a noninvasive thermal noise method. In the case of FDC experiments, the tip radius was estimated by fitting the reference measurements of glass and by applying the Hertz theory, as described in Supporting Information

Application of contact-resonance AFM methods to polymer samples

• Sebastian Friedrich and
• Brunero Cappella

Beilstein J. Nanotechnol. 2020, 11, 1714–1727, doi:10.3762/bjnano.11.154

• curves on an uncompliant substrate, such as a silicon wafer. The spring constant could then be determined from the thermal noise spectrum [42]. Tip radii have been obtained through scanning a TGT1 test grating (NT-MDT Spectrum Instruments, Moscow, Russia) consisting of an array of sharp tips. The

Thermophoretic tweezers for single nanoparticle manipulation

• Jošt Stergar and
• Natan Osterman

Beilstein J. Nanotechnol. 2020, 11, 1126–1133, doi:10.3762/bjnano.11.97

• heating. While it is also possible to trap atoms and molecules in vacuum using electromagnetic traps, thermal noise is a governing factor when particles are under biological conditions, namely at room temperature in an aqueous medium. Laser tweezers [1][2][3], invented long ago and recognized with the

Microwave photon detection by an Al Josephson junction

• Leonid S. Revin,
• Andrey L. Pankratov,
• Anna V. Gordeeva,
• Anton A. Yablokov,
• Igor V. Rakut,
• Victor O. Zbrozhek and
• Leonid S. Kuzmin

Beilstein J. Nanotechnol. 2020, 11, 960–965, doi:10.3762/bjnano.11.80

• layered high-temperature superconductors [27]. The significance of this effect depends on the ratio of thermal fluctuations kBT, the damping parameter α and the Josephson energy EJ. Here we will consider a small tunnel junction with the thermal noise intensity of γ = kBT/EJ ≥ 2 × 10−2 and α > 0.1, and

• excitation caused by a rapid decrease in the barrier, and remained constant until the appearance of a gap voltage due to thermal noise or quantum tunneling. The lifetime measurements were repeated at least 200 times for each value of the bias current. For a high-frequency experiment, a microwave signal was

Extracting viscoelastic material parameters using an atomic force microscope and static force spectroscopy

• Cameron H. Parvini,
• M. A. S. R. Saadi and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2020, 11, 922–937, doi:10.3762/bjnano.11.77

• velocities were selected in a logarithmic distribution: 10, 100, and 1000 nm/s. The probe utilized was an OLYMPUS AC 240TS-R3, featuring a tip radius of roughly 10 nm. Before measurement, the tip was calibrated using the thermal noise method [29] in which a hard silicon sample was used after sonicating using

Measurement of electrostatic tip–sample interactions by time-domain Kelvin probe force microscopy

• Christian Ritz,
• Tino Wagner and
• Andreas Stemmer

Beilstein J. Nanotechnol. 2020, 11, 911–921, doi:10.3762/bjnano.11.76

• measurement noise is assumed to be Gaussian white noise and is defined by . This is the case for measurements where thermal noise is the dominating noise source, i.e., when the modulation frequency is below the crossover of thermal white noise and (with increasing frequency) detection noise [29]. The power

• spectral density (PSD) of the thermal noise can be calculated as For detection-noise-limited measurements, an additional state has to be introduced to keep track of the dynamics of the apparent noise. The approximation in Equation 17 contains the system output matrix . It depends on the current tip–sample

• transition noise matrix of the detection system QD is the zero matrix with the PSD of the thermal noise Rth at its top-left position. The covariance matrix QK contains the assumed PSD of the sample properties. The values of QK are design parameters and determine how much change may be expected between two

Examination of the relationship between viscoelastic properties and the invasion of ovarian cancer cells by atomic force microscopy

• Mengdan Chen,
• Jinshu Zeng,
• Weiwei Ruan,
• Zhenghong Zhang,
• Yuhua Wang,
• Shusen Xie,
• Zhengchao Wang and
• Hongqin Yang

Beilstein J. Nanotechnol. 2020, 11, 568–582, doi:10.3762/bjnano.11.45

• . Force–distance curve-based AFM measurements were carried out to calculate the optical photodiode deflection sensitivity and the cantilever spring constant was verified by the thermal noise method before experiments. MLCT cantilevers (Bruker, USA) made of silicon nitride with approximate spring constant

Subsurface imaging of flexible circuits via contact resonance atomic force microscopy

• Wenting Wang,
• Chengfu Ma,
• Yuhang Chen,
• Lei Zheng,
• Huarong Liu and
• Jiaru Chu

Beilstein J. Nanotechnol. 2019, 10, 1636–1647, doi:10.3762/bjnano.10.159

• the second eigenmodes, respectively. The cantilever stiffness and the free resonance frequency were calibrated by utilizing the thermal noise method while others were provided by the respective manufacturers. Multilayer contact model The axisymmetric indentation of a tip contacting with a multilayered

Review of time-resolved non-contact electrostatic force microscopy techniques with applications to ionic transport measurements

• Aaron Mascaro,
• Yoichi Miyahara,
• Tyler Enright,
• Omur E. Dagdeviren and
• Peter Grütter

Beilstein J. Nanotechnol. 2019, 10, 617–633, doi:10.3762/bjnano.10.62

• by the detection electronics, but instead is theoretically limited only by the thermal noise of the cantilever [18]. This principle can be easily extended to ionic systems (such as those discussed previously) by simply replacing the pulsed light source with a pulsed voltage. In this case, the

Effective sensor properties and sensitivity considerations of a dynamic co-resonantly coupled cantilever sensor

• Julia Körner

Beilstein J. Nanotechnol. 2018, 9, 2546–2560, doi:10.3762/bjnano.9.237

• which becomes possible with the derived analytic expressions. Besides the description of effective sensor properties, it was studied how the thermal noise and, consequently, minimal detectable frequency shift for the co-resonantly coupled sensor represented by a coupled harmonic oscillator could be

• presented. These allow to estimate the potential performance and limitation of the system (e.g., sensitivity for a given task) before fabricating it and give new insights into the behaviour of co-resonantly coupled oscillating systems. Additionally, the treatment of thermal noise within the coupled system

• will be outlined. Sensitivity of a Cantilever Sensor The sensitivity of a cantilever sensor is given by its minimal detectable frequency shift with respect to an external interaction. It is influenced by various noise contributions which are due to the cantilever itself (e.g., thermal noise, thermal

A simple extension of the commonly used fitting equation for oscillatory structural forces in case of silica nanoparticle suspensions

• Sebastian Schön and
• Regine von Klitzing

Beilstein J. Nanotechnol. 2018, 9, 1095–1107, doi:10.3762/bjnano.9.101

• ) serving as colloidal probe. The spring constant of the cantilever was determined via the thermal noise method [62]. The surface of the colloidal probe and the silicon wafer form the two confining walls for the experiment. As the colloidal probe is orders of magnitude larger than their distance, the forces

• multiple factors. On one hand, identifying the factual A depends on the correct determination of the spring constant. As mentioned above this was done via the thermal noise method and already introduces an error of about 10%. On the other hand, it is highly sensitive to the correct transformation of the

Beyond Moore’s technologies: operation principles of a superconductor alternative

• Igor I. Soloviev,
• Nikolay V. Klenov,
• Sergey V. Bakurskiy,
• Mikhail Yu. Kupriyanov,
• Alexander L. Gudkov and
• Anatoli S. Sidorenko

Beilstein J. Nanotechnol. 2017, 8, 2689–2710, doi:10.3762/bjnano.8.269

• of Josephson junctions on a chip. There is no need for large-scale circuit partitioning. (iv) The bias current plays the role of the clock signal. There is no need for an SFQ clock distribution network. (v) The clock signal is not affected by thermal noise. Logical unity (or zero) is represented by a