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

• unbounded inputs traditionally used to acquire force–distance relationships in AFM, such as ramp functions, in which the cantilever position is displaced linearly with time for a finite period of time. Keywords: atomic force microscopy; force spectroscopy; material properties; viscoelasticity

• force–distance curve, where the cantilever position above the sample follows a ramp function. In the case of intermittent-contact methods (e.g., tapping-mode AFM), the cantilever tip oscillates nearly sinusoidally, but since tip–sample contact is intermittent, the sample does not experience purely

• experiments one observes the deflection of the AFM cantilever as a function of the cantilever base position instead of directly observing stress and strain. From the available observables, one can calculate the tip–sample force and the indentation. In order to account for the AFM probe and sample geometry and

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

• , independent method to detect the variation in Φ. For this we record the frequency shift, Δf, of the resonance frequency of the cantilever oscillating perpendicular to the surface as a function of the bias voltage (see Figure 3b). At the extrema of the parabolic Δf curves, the electrostatic force is minimised

• . Experimental We employ a custom-built ultrahigh-vacuum (below 10−10 mbar) low-temperature (T = 1.4 K) nc-AFM operated in frequency-modulated mode. A stiff qPlus cantilever design [49] (k0 = 1800 N·m−1, f0 = 29077 Hz, Q = 60000) at an oscillation amplitude Aosc = 50 pm enables the nc-AFM functionality. We

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

• have to be subtracted in order to isolate the short-range contributions from the surface feature [2]. If the cantilever is rotated by 90° so that the tip oscillates lateral to the surface, long-range forces with large vertical components do not contribute to the Δf signal [3]. This microscopy technique

• setup) or biaxial AFM with normal force detection is required. Experimentally, there are several methods for performing frequency-modulation lateral force microscopy, what we refer to as LFM in this manuscript. In 2002, Pfeiffer and co-workers excited a silicon cantilever in the first torsional mode [4

• method developed by Giessibl [15], a Laplace transform method developed by Sader and Jarvis [16], and a Fourier method developed by Seeholzer and co-workers [17]. All of these methods require the knowledge of the oscillation amplitude A of the cantilever. Amplitude determination means determining a

Mapping the local dielectric constant of a biological nanostructured system

• Wescley Walison Valeriano,
• Rodrigo Ribeiro Andrade,
• Juan Pablo Vasco,
• Angelo Malachias,
• Bernardo Ruegger Almeida Neves,
• Paulo Sergio Soares Guimarães and
• Wagner Nunes Rodrigues

Beilstein J. Nanotechnol. 2021, 12, 139–150, doi:10.3762/bjnano.12.11

• oscillate, during the second pass, at the resonance frequency of the cantilever, f0. Variations in the local relative permittivity properties of the sample will lead to different tip–sample force gradients, which promote a shift Δf0 in the tip oscillation frequency [21][22] which is, approximately, where dF

• /dz is the tip–sample force gradient and K is the spring constant of the cantilever. The tip–sample-substrate system constitutes a capacitor with the sample (wing) as part of the relative permittivity region, so the force between tip and substrate can be modeled as where C is the system capacitance

• sample and the conductive substrate need to be present within the AFM image. This is a key condition since the conductive substrate establishes a reference level in the analysis. Having both in the imaged region guarantees that the cantilever amplitude and, consequently, the effective radius of the tip

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

• which one prong is fixed onto a substrate and the other prong with an attached tip serves as a self-sensing cantilever [2]. In 1996, F. J. Giessibl et al. first used the qPlus sensor to measure the morphology of a grating and a CD at room temperature [3]. Since then, this technique has been used

• of the cantilever is utilized to detect the forces between tip and sample. The shift Δf induced by the vertical force gradient is tan|φ| times as large as that induced by the lateral force gradient [17]. In other words, in the range from 0 to 90°, if φ > 45°, mainly the vertical force gradient

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

• mode: The AFM probe, a paraboloid-shaped tip with a typical radius 4 nm < R < 40 nm is held at a defined x,y position while it approaches the sample surface by using a Z-piezo positioner. The tip is attached to a cantilever which can be described as an elastic spring following Hooke’s law: with force F

• , spring constant of the cantilever kc, and cantilever deflection δ. In this way, the forces acting on the tip are measured by recording the deflection δ of the cantilever. While decreasing the distance between the tip and the sample, the cantilever deflects toward the sample (attractive forces Fattr, −δ

• depicted in Figure 1. Figure 1(I) zero line: when the tip and the sample are far away from each other. Interacting forces are not detectable and δ is zero which equals the free equilibrium position of the cantilever. Figure 1(II) regime of attractive forces: upon further approach of the sample and the tip

Atomic layer deposited films of Al₂O₃ on fluorine-doped tin oxide electrodes: stability and barrier properties

• Hana Krýsová,
• Michael Neumann-Spallart,
• Hana Tarábková,
• Pavel Janda,
• Ladislav Kavan and
• Josef Krýsa

Beilstein J. Nanotechnol. 2021, 12, 24–34, doi:10.3762/bjnano.12.2

• cantilever (TESPA-V2) with a resonant frequency fres of approx. 300 kHz, a spring constant k of 0.42 N·m−1, and a nominal tip radius of 8 nm (Bruker, USA) was employed. The Gwyddion software (v. 2.53) was utilized for processing AFM image data. Results and Discussion AFM was used to compare the morphology of

Mapping of integrated PIN diodes with a 3D architecture by scanning microwave impedance microscopy and dynamic spectroscopy

• Rosine Coq Germanicus,
• Peter De Wolf,
• Florent Lallemand,
• Catherine Bunel,
• Serge Bardy,
• Hugues Murray and
• Ulrike Lüders

Beilstein J. Nanotechnol. 2020, 11, 1764–1775, doi:10.3762/bjnano.11.159

• capacitor in parallel with a resistance (Figure 1). The incident microwave signal interacts with the sample resulting in a transmitted wave and a reflected wave. Since the probe is shielded, the stray capacitance formed by the cantilever and the sample can be neglected. After a calibration step and

•  9 represents a force curve recorded as function of time for one pixel. In the first step (1) the tip approaches the surface until the force on the cantilever reaches the setpoint force of 50 nN. During the dwell segment, the sMIM tip is maintained in contact (2). During this time, the voltage sweep

Direct observation of the Si(110)-(16×2) surface reconstruction by atomic force microscopy

• Tatsuya Yamamoto,
• Ryo Izumi,
• Kazushi Miki,
• Takahiro Yamasaki,
• Yasuhiro Sugawara and
• Yan Jun Li

Beilstein J. Nanotechnol. 2020, 11, 1750–1756, doi:10.3762/bjnano.11.157

• cantilever was used, which was cleaned by Ar+ sputtering to remove the oxide and contamination on the tip. The deflection of the cantilever was measured by the optical beam deflection method. The topography of the surface was imaged while feedback electronics were used to adjust the tip–sample distance to

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

• analysis, it is concluded that CR measurements are not appropriate for polymer samples. Major drawbacks are the bad resolution for moduli lower than ca. 10 GPa and the lack of a comprehensive physical model accounting for many factors affecting the dynamic response of a cantilever in contact with a sample

• phase image. The resulting contrast is, however, hard to analyze quantitatively. Contact-resonance AFM (CR-AFM) [4][5] is a dynamic contact technique that makes use of the vibrational behavior of the cantilever while the tip is in permanent contact with the sample. Generally, an increase in sample

• stiffness prompts an increase of the contact-resonance frequency (CR frequency). The CR frequency can be obtained from single-point measurements or tracked during scanning with techniques such as dual AC resonance tracking (DART) [6][7]. The vibrational motion of the cantilever is usually described using

Fabrication of nano/microstructures for SERS substrates using an electrochemical method

• Jingran Zhang,
• Tianqi Jia,
• Xiaoping Li,
• Junjie Yang,
• Zhengkai Li,
• Guangfeng Shi,
• Xinming Zhang and
• Zuobin Wang

Beilstein J. Nanotechnol. 2020, 11, 1568–1576, doi:10.3762/bjnano.11.139

• three-dimensional topographies of the nanopores. Imaging was performed in contact mode and an elastic constant of 0.2 N/m was selected for the silicon cantilever. The scanning area was 50 × 50 μm2. In addition, a scanning electron microscopy (SEM) system (Zeiss, Germany) was employed to characterize the

Design of V-shaped cantilevers for enhanced multifrequency AFM measurements

• Mehrnoosh Damircheli and
• Babak Eslami

Beilstein J. Nanotechnol. 2020, 11, 1525–1541, doi:10.3762/bjnano.11.135

• dimensions, the optimum V-shaped cantilever that can provide the maximum phase contrast in bimodal AFM between gold (Au) and polystyrene (PS) is found. Based on this study, it is found that as the length of the cantilever increases the 2nd eigenmode phase contrast decreases. However, the base width exhibits

• the opposite relationship. It is also found that the leg width does not have a monotone relationship similar to length and base width. The phase contrast increases for the range of 14 to 32 µm but decreases afterwards. The thickness of a V-shaped cantilever does not play a major role in defining the

• dynamics of the cantilever compared to other parameters. This work shows that in order to maximize the phase contrast, the ratio of second to first eigenmode frequencies should be minimized and be close to a whole number. Additionally, since V-shaped cantilevers are mostly used for soft matter imaging

On the frequency dependence of viscoelastic material characterization with intermittent-contact dynamic atomic force microscopy: avoiding mischaracterization across large frequency ranges

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

Beilstein J. Nanotechnol. 2020, 11, 1409–1418, doi:10.3762/bjnano.11.125

• response of the cantilever with respect to the excitation, within amplitude-modulation AFM (AM-AFM)), which generally yields high-contrast images for dissipative materials [22]. Dynamic contact-mode techniques such as contact-resonance AFM [11][12][13][28], dual-amplitude resonance tracking AFM (DART [10

• -static force spectroscopy (i.e., using force–distance curves acquired at frequencies much lower than the resonance frequency of the cantilever). Specifically, we have introduced a methodology based on the Generalized Voigt (Kelvin) or Maxwell viscoelastic model (Figure 1), including an arbitrary number

• performed with different types of cantilevers (short high-frequency cantilevers as well as traditional cantilevers) and with different methods, involving wide frequency ranges and different cantilever eigenmodes. In general, this is routinely done without considering the types of viscoelastic behavior

An atomic force microscope integrated with a helium ion microscope for correlative nanoscale characterization

• Santiago H. Andany,
• Gregor Hlawacek,
• Stefan Hummel,
• Charlène Brillard,
• Mustafa Kangül and
• Georg E. Fantner

Beilstein J. Nanotechnol. 2020, 11, 1272–1279, doi:10.3762/bjnano.11.111

• correlative imaging on electrically insulating samples. In this first attempt, the readout of cantilever deflection was achieved using the electron beam itself. Shortly after, better performing combined setups were described utilizing more conventional self-sensing [5] and optical [6] techniques for the

• readout of cantilever deflection. Since then, more advanced and versatile combined instruments have been proposed for a broad spectrum of applications in nanoscale characterization and nanoscale fabrication inside SEM and focused ion beam (FIB) setups [7][8][9][10][11]. Given the extent of the interest

• depicted in Figure 1. The prototype tip-scanning AFM scan head is designed explicitly for correlative analysis inside electron and ion-beam microscopes. Unlike sample scanning solutions [9][16], where the sample is raster-scanned relative to a stationary cantilever, a tip-scanning configuration [10][17

Ultrasensitive detection of cadmium ions using a microcantilever-based piezoresistive sensor for groundwater

• Dinesh Rotake,
• Anand Darji and
• Nitin Kale

Beilstein J. Nanotechnol. 2020, 11, 1242–1253, doi:10.3762/bjnano.11.108

• . [28], but it is not suitable for other high-temperature sputtering processes. Microcantilevers based on SiO2 have been manufactured by Tang et al. [29] to enhance the sensitivity of cantilever sensors. Many authors use optical setups for microcantilevers. However, an optical output has several

• cantilever sensors. Moreover, the proposed piezoresistive device has capabilities to directly capture the surface stress make this a better option for HMI applications. Microfluidic Platform with Piezosensor In the proposed method, the benefits of three different technologies are combined, namely thin film

• the fabricated MEMS-based sensor is capable of selective Cd(II) detection using SAMs of cysteamine with cross-linked ᴅʟ-glyceraldehyde (Cys-DL-GC). To characterize the SAM on the microcantilever device only a few analytical techniques are available because of the fragile nature of the cantilever

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

• materials. AFM static force spectroscopy (SFS) is one approach commonly used in pursuit of this goal. It is capable of acquiring rich temporal insight into the behavior of a sample. During AFM-SFS experiments the cantilever base approaches samples with a nearly constant velocity, which is manipulated to

• cantilever, and the time-derivative of the Z-Sensor data should be equal to the experimental approach velocity. To perform the fit procedure, only the deflection and Z-Sensor datasets are necessary. Figure 2a illustrates the shape of a common result as read from a force–distance curve output file. Because

• using the cantilever stiffness (kc), the minimum deflection offsets (z0, d0), the deflection (d(t)), and the following relations: where kc in Equation 14 is the AFM cantilever stiffness. This data is not used directly in the fit, but can be useful for showing the indentation and force during the

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

• conventional frequency-modulated (FM-) KFM, the contributions at ωm and 2ωm are detected via lock-in techniques, either at the Δf output of a phase-locked loop (PLL) [12] or by detecting the sidebands of the cantilever oscillation [13]. In closed-loop FM-KFM, a feedback loop is employed to nullify the

• response of the cantilever at the modulation frequency ωm (not visible in Figure 1 since Udc ≈ Ulcpd) and at 2ωm [13][26][27]. A feedback loop is used to adjust Udc in order to nullify the component at ωm. If this is achieved, the resulting Δfmean, which is used for the topography control, is independent

• PLL is used, its transfer function, which is known for a given cantilever and given PI gains, can be approximated by the transfer function of a low-pass filter. Using the relationship shown in Equation 10 and the transfer function of the detection system, the sample properties, the expected error

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

Hexagonal boron nitride: a review of the emerging material platform for single-photon sources and the spin–photon interface

• Stefania Castelletto,
• Faraz A. Inam,
• Shin-ichiro Sato and
• Alberto Boretti

Beilstein J. Nanotechnol. 2020, 11, 740–769, doi:10.3762/bjnano.11.61

Quantitative determination of the interaction potential between two surfaces using frequency-modulated atomic force microscopy

• Nicholas Chan,
• Carrie Lin,
• Tevis Jacobs,
• Robert W. Carpick and
• Philip Egberts

Beilstein J. Nanotechnol. 2020, 11, 729–739, doi:10.3762/bjnano.11.60

• laterally relative to the sample. A piezoactuator acting in the z-direction brings the probe closer or further from the sample. Due to non-linear tip–sample interaction forces, the resonance frequency of the oscillating cantilever will shift. This shift can be used as a feedback signal to measure the sample

• topography, among other parameters. In order to determine the interaction force behavior as a function of the separation distance, we measured the frequency shift of the oscillating cantilever as a function of the separation distance (Δf–d curves) between a silicon AFM probe and a diamond sample. An

• analytical relationship between the resonance frequency shift and the tip–sample interaction force in FM-AFM was first derived by Giessibl [42] and is seen in the following equation: In Equation 1, Δf represents the change in the primary flexural resonance frequency of the cantilever near the surface, fres

Stochastic excitation for high-resolution atomic force acoustic microscopy imaging: a system theory approach

• Edgar Cruz Valeriano,
• José Juan Gervacio Arciniega,
• Christian Iván Enriquez Flores,
• Susana Meraz Dávila,
• Joel Moreno Palmerin,
• Martín Adelaido Hernández Landaverde,
• Yuri Lizbeth Chipatecua Godoy,
• Aime Margarita Gutiérrez Peralta,
• Rafael Ramírez Bon and
• José Martín Yañez Limón

Beilstein J. Nanotechnol. 2020, 11, 703–716, doi:10.3762/bjnano.11.58

• frequency resolution, with less computational cost and at a faster speed than other similar techniques. This technique is referred to as stochastic atomic force acoustic microscopy (S-AFAM), and the frequency shifts of the free resonance frequencies of an AFM cantilever are used to determine the mechanical

• nanotechnology [3] because it offers a non-destructive alternative for measuring mechanical properties at the nanoscale using the small size of the cantilever tip with a radius of 5–50 nm. There are two kinds of conventional AFM methods for the measurement of mechanical properties [4][5], i.e., the measurement

• of force–displacement curves or of contact resonance frequencies. The techniques based on force–displacement curves are ideal when the stiffness of the cantilever and the sample are similar. The techniques based on contact resonance frequencies are appropriate when the stiffness of the sample

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

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

• approaches. Conductivity, in particular, is mapped using the contact-mode method. However, this modality can be destructive to delicate samples, since it involves continuously dragging the cantilever tip on the surface during the raster scan, while a constant tip–sample force is applied. In this paper we

• discuss a possible approach to develop an intermittent-contact conductive AFM mode based on Fourier analysis, whereby the measured current response consists of higher harmonics of the cantilever oscillation frequency. Such an approach may enable the characterization of soft samples with less damage than

• cantilever oscillation, can be a less destructive technique [16][19][20], and this could be advantageous also for performing current measurements on such samples. Additionally, scanning tunnelling microscopy (STM) applications may also benefit from current measurements during which the tip oscillates above

Atomic-resolution imaging of rutile TiO₂(110)-(1 × 2) reconstructed surface by non-contact atomic force microscopy

• Daiki Katsube,
• Shoki Ojima,
• Eiichi Inami and
• Masayuki Abe

Beilstein J. Nanotechnol. 2020, 11, 443–449, doi:10.3762/bjnano.11.35

• performed using Pt-coated Si cantilevers (Budget Sensors, ElectriTAP190G). All cantilevers were cleaned by Ar+ sputtering (0.6 keV, Ar partial pressure of 1.0 × 10−5 Pa, ion current of 0.05 µA, 5 min) before scanning. STM imaging was performed in constant-current mode without cantilever oscillation. NC-AFM

• feedback control was applied in frequency-modulation mode [30] with constant amplitude oscillation. The cantilever deflection was detected using an optical interferometer [31]. Since the electrostatic force due to the contact potential difference (CPD) between the tip and sample prevents high-resolution NC

• 10 pA, respectively. (a) STM and (b) NC-AFM images of a rutile TiO2(110)-(1 × 2) reconstructed surface. (c, d) Height profiles along black (STM) and blue (NC-AFM) lines in the images. The STM and NC-AFM images were obtained using a Pt-coated Si cantilever with a resonance frequency of f0 = 154.1 kHz

Implementation of data-cube pump–probe KPFM on organic solar cells

• Benjamin Grévin,
• Olivier Bardagot and
• Renaud Demadrille

Beilstein J. Nanotechnol. 2020, 11, 323–337, doi:10.3762/bjnano.11.24

• –acceptor blends with sub-ms time resolution [1]. Subsequent works have shown that sub-μs time resolution can be achieved by acquiring the full information on the cantilever oscillation, leading to the development of fast trEFM [2] and general-mode KPFM [3]. Contrary to feedback-free electrostatic methods

• ][14] and nanocrystal-based [15] solar cells. However, there are some disadvantages to using this technique. First, at specific frequencies, the excitation signal used to generate charge carriers can interfere [16] with the cantilever oscillation or the ac voltage applied for the detection of the CPD

• be taken into account, which renders the interpretation of IM-KPFM data even more difficult. Upon illumination, the capacitive junction formed by the cantilever tip and the conducting substrate onto which the organic layer is deposited is indeed reduced due to photogenerated carriers [19]. As a first