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

• highly desirable. Furthermore, we would like the integrated sensor package, that is, transducer and detector, to be easily exchangeable, as AFM tips are frequently damaged when scanning over unknown surface features. Dynamic AFM is typically operated in two alternative modes of scanning feedback, namely

Quantitative dynamic force microscopy with inclined tip oscillation

• Philipp Rahe,
• Daniel Heile,
• Reinhard Olbrich and
• Michael Reichling

Beilstein J. Nanotechnol. 2022, 13, 610–619, doi:10.3762/bjnano.13.53

• . Experimentally, however, the sampling path representing the tip oscillating trajectory is often inclined with respect to the surface normal and the data recording path. Here, we extend the mathematical description of dynamic AFM to include the case of an inclined sampling path. We find that the inclination of

• position Prerequisite to quantitative force microscopy is a precise definition of the involved probe and sample coordinates as well as probe dynamical parameters that are outlined in the following. In dynamic AFM, the force acting between a sharp tip and the surface under investigation is measured as a

• . This point is, however, experimentally not accessible. Instead, precise values for the piezo position zp and the sensor displacement q(t) are experimentally available. To derive a force–distance curve experimentally, the usual procedure is therefore to apply dynamic AFM and to measure the distance

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

• introduced other models to calculate spring constants [22][23]. These methods were improved by Sader to a higher accuracy [11][24]. As a second category of application of V-shaped cantilevers, dynamic AFM is used to characterize soft matter. For example, Korayem et al. have carried out a free-vibration

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

• characterization frequency regardless of the materials properties. In this paper we present a linear viscoelastic analysis of intermittent-contact, nearly resonant dynamic AFM characterization of such materials, considering the possibility of multiple characteristic times. We describe some of the intricacies

• inverting the frequency-dependent viscoelastic behavior of a material from dynamic AFM observables, we suggest that a partial solution is offered by recently developed quasi-static force–distance characterization techniques, which incorporate viscoelastic models with multiple characteristic times and can

• help inform dynamic AFM characterization. Keywords: dynamic atomic force microscopy; Generalized Maxwell model; loss modulus; storage modulus; viscoelasticity; Introduction There have been significant methodology developments since the introduction of atomic force microscopy (AFM) in the mid-1980s [1

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

• contact-mode imaging. To explore its feasibility, we derive the analytical form of the tip–sample current that would be obtained for attractive (noncontact) and repulsive (intermittent-contact) dynamic AFM characterization, and compare it with results obtained from numerical simulations. Although

• plus its higher harmonics, with the an values representing the amplitudes of those harmonics. For instance, a1 corresponds to the fundamental frequency of the cantilever response, which is typically tracked using a lock-in amplifier and modulated during a standard dynamic AFM experiment. As outlined in

• also been measured in dynamic AFM experiments [40][41]. For our cantilever trajectory we will use Equation 9, since a tip–sample force perturbation is present. Since we are still considering a noncontact case, we will use the tunnelling current model from Equation 3. The tip–sample distance is: We

Integration of sharp silicon nitride tips into high-speed SU8 cantilevers in a batch fabrication process

• Nahid Hosseini,
• Matthias Neuenschwander,
• Oliver Peric,
• Santiago H. Andany,
• Jonathan D. Adams and
• Georg E. Fantner

Beilstein J. Nanotechnol. 2019, 10, 2357–2363, doi:10.3762/bjnano.10.226

• pixels 512 × 512, scan rate 1 Hz, free amplitude 123 nm and setpoint at 95% of the free amplitude. With these parameters, we estimated the tip–sample forces using the Virtual Environment for Dynamic AFM (VEDA, nanohub.org/tools/veda) and obtained mean forces of 10 nN. Figure 2a shows an AFM image taken

Nanoscale spatial mapping of mechanical properties through dynamic atomic force microscopy

• Zahra Abooalizadeh,
• Leszek Josef Sudak and
• Philip Egberts

Beilstein J. Nanotechnol. 2019, 10, 1332–1347, doi:10.3762/bjnano.10.132

• , and predictive models of failure. Dynamic atomic force microscopy (AFM) is one technique that is well suited for experimentally measuring the mechanical properties of materials with high spatial resolution [10][11][12]. More specifically, a focus on two dynamic AFM modes, force modulation microscopy

• . Of course the advantages of dynamic AFM come at the expense that the lateral shear force between the tip and sample cannot be eliminated, making the technique inappropriate for weakly bonded samples. On the other hand, more variations of the experimental set up are possible for AFM, such as ultrahigh

• contaminants on the surface when measuring the mechanical properties of atomic-sized defects [15][16][17]. Furthermore, the high quality factor of the AFM cantilever that is achieved under UHV conditions can be very beneficial in dynamic AFM modes, as the Q-factor is inversely proportional to the force

Multimodal noncontact atomic force microscopy and Kelvin probe force microscopy investigations of organolead tribromide perovskite single crystals

• Yann Almadori,
• David Moerman,
• Jaume Llacer Martinez,
• Philippe Leclère and
• Benjamin Grévin

Beilstein J. Nanotechnol. 2018, 9, 1695–1704, doi:10.3762/bjnano.9.161

• -induced SP and lattice changes. Lastly, the tip–sample height measured in dynamic AFM is prone to be affected by variations of the electrostatic forces, which in turn, vary as a function of the illumination state of the photovoltaic sample. Thus, for accurate photostrictive measurements, it is highly

Material property analytical relations for the case of an AFM probe tapping a viscoelastic surface containing multiple characteristic times

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

Beilstein J. Nanotechnol. 2017, 8, 2230–2244, doi:10.3762/bjnano.8.223

• dissipation in the tip–sample interaction [34][40][41]. However, it is well known that varying the dynamic AFM parameters (e.g., excitation frequency, tapping amplitude) can significantly alter the calculated values of dissipated energy when imaging viscoelastic polymers [35]. This clearly represents a

Scaling law to determine peak forces in tapping-mode AFM experiments on finite elastic soft matter systems

• Horacio V. Guzman

Beilstein J. Nanotechnol. 2017, 8, 968–974, doi:10.3762/bjnano.8.98

• posteriori basis. Moreover, those methods could be very time consuming to tune for non-expert enthusiastic AFM experimentalists and their accuracy is under debate within the dynamic AFM community [16][17]. Numerical simulations and analytical scaling laws are well-established methods to estimate the

• ][12][14][30][31]. Moreover, we provide the explicit method to obtain an analytical equation based on the relevant dynamic AFM operational parameters. Here, a parametrical equation to determine the peak interaction force exerted by the AM-AFM on a finite soft material immersed in a liquid environment

• ). One strategy to reduce the order of the cascade function (Equation 5) is to base our modelling on top of one available analytical approach to determine Fts in dynamic AFM [21][42][43]. We have applied the virial–dissipation method [19] to determine an initial equation for the peak force as a function

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

• modes. Simulations and Experimental Details Simulations Simulations have been performed using the Virtual Environment for Dynamic AFM (VEDA) open code, which takes into account the dynamics of oscillating rectangular cantilevers with multiple eigenmodes [16]. The frequencies, stiffness and quality

Generalized Hertz model for bimodal nanomechanical mapping

• Aleksander Labuda,
• Marta Kocuń,
• Waiman Meinhold,
• Deron Walters and
• Roger Proksch

Beilstein J. Nanotechnol. 2016, 7, 970–982, doi:10.3762/bjnano.7.89

• derivation here begins in the context of a Hertzian contact with a paraboloidal tip and is then generalized to any tip shape described by a power-law profile. This theory is then experimentally applied to three variations of bimodal AFM involving different dynamic AFM modes of operation [42][43], namely

• -amplitude dynamic AFM, where the interaction amplitude A1 greatly exceeds δmax. Meanwhile, the second (or higher) eigenmode is deliberately driven at a small amplitude A2, such that the interaction stiffness it experiences is roughly constant throughout one of the higher eigenmode oscillation cycles

• distinction cannot be made in single-mode dynamic AFM imaging. The key to bimodal nanomechanical imaging is that the same stiffness profile is measured simultaneously by two different eigenmodes with different weight functions: and The fact that these weight functions are related by a derivative operation

Noncontact atomic force microscopy III

• Mehmet Z. Baykara and
• Udo D. Schwarz

Beilstein J. Nanotechnol. 2016, 7, 946–947, doi:10.3762/bjnano.7.86

• resonators for NC-AFM operation in air. In addition, the ever increasing importance of simulations for dynamic AFM experiments is underlined via two contributions focusing on three-dimensional viscoelastic modeling as well as “sub-atomic” contrast formation on the prototypical Si(111)-7×7 surface. To

High-bandwidth multimode self-sensing in bimodal atomic force microscopy

• Michael G. Ruppert and
• S. O. Reza Moheimani

Beilstein J. Nanotechnol. 2016, 7, 284–295, doi:10.3762/bjnano.7.26

• higher mode which was already noticed from Figure 6c. On the fifth mode, the strain sensor produces the same output for a much smaller deflection, yielding a much larger sensitivity. Noise analysis The noise performance of cantilever deflection sensors used in dynamic AFM is commonly evaluated with the

• that mode and the fact that the cantilever is actively driven at resonance. However, the authors believe that the procedure is closer to the actual dynamic AFM application (using lock-in demodulation of actively driven cantilevers) and therefore the values reported are a realistic representation of

Kelvin probe force microscopy for local characterisation of active nanoelectronic devices

• Tino Wagner,
• Hannes Beyer,
• Patrick Reissner,
• Philipp Mensch,
• Heike Riel,
• Bernd Gotsmann and
• Andreas Stemmer

Beilstein J. Nanotechnol. 2015, 6, 2193–2206, doi:10.3762/bjnano.6.225

• dynamic AFM modes. Precise knowledge of their frequency dependence in low and high Q environments is not only neccessary for accurate open-loop KFM techniques, but also offers a direct approach to noise performance and optimisation of frequency modulated KFM [19]. For example, ωm should ideally be chosen

Optimization of phase contrast in bimodal amplitude modulation AFM

• Mehrnoosh Damircheli,
• Amir F. Payam and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2015, 6, 1072–1081, doi:10.3762/bjnano.6.108

• phase contrast improves by decreasing the energy of second mode relative to those of the first and third modes. Keywords: bimodal AFM; dynamic AFM; tapping mode; Introduction The atomic force microscope is a versatile and powerful tool for imaging, compositional mapping and modification of surfaces

Capillary and van der Waals interactions on CaF₂ crystals from amplitude modulation AFM force reconstruction profiles under ambient conditions

• Annalisa Calò,
• Oriol Vidal Robles,
• Sergio Santos and
• Albert Verdaguer

Beilstein J. Nanotechnol. 2015, 6, 809–819, doi:10.3762/bjnano.6.84

• and interaction forces can be determined through analytical descriptions [28] or numerical methods [29] from minute changes in the amplitude [30] or in the frequency [6][7] of the oscillation when the tip–sample separation distance is changed. Furthermore, the advantage of performing dynamic AFM

• in dynamic AFM and interpreted as the result of dynamic capillary interactions. In the experiments reported on graphite additional spectroscopic IR measurements were performed [9][10] to exclude that the observed change in force profiles could depend on chemical contamination or aging of the sample

• equation [31], and the ΔΦ vs distance evolution [27]. Our results indicate that standard expressions for capillary forces based on a constant chemical potential can also be a valuable tool to predict the experimental phenomena observed in dynamic AFM [14]. Results Figure 1a and Figure 1b show AFM images of

Influence of spurious resonances on the interaction force in dynamic AFM

• Luca Costa and
• Mario S. Rodrigues

Beilstein J. Nanotechnol. 2015, 6, 420–427, doi:10.3762/bjnano.6.42

• peaks. Conclusion We have introduced a methodology to directly derive the conservative and dissipative interactions between the AFM probe and the sample in dynamic AFM experiments when small oscillation amplitudes of the tip are used, and for different tip excitation and detection schemes. We considered

Dynamic force microscopy simulator (dForce): A tool for planning and understanding tapping and bimodal AFM experiments

• Horacio V. Guzman,
• Pablo D. Garcia and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2015, 6, 369–379, doi:10.3762/bjnano.6.36

• experiments. The simulator presents the cantilever–tip dynamics for two dynamic AFM methods, tapping mode AFM and bimodal AFM. It can be applied for a wide variety of experimental situations in air or liquid. The code provides all the variables and parameters relevant in those modes, for example, the

• simulations. Finally, the accuracy of dForce has been tested against numerical simulations performed during the last 18 years. Keywords: bimodal AFM; dynamic AFM; nanomechanics; numerical simulations; tapping mode AFM; Introduction Numerical simulations have played a pivotal role to advance the

• spatial resolution and contrast of different dynamic AFM methods has also been studied by simulations [28][30][31]. Finally, the emergence of multifrequency AFM [32] in particular bimodal [33][34], trimodal [35], intermodulation [36] or torsional harmonics [37] has been supported by simulations [38]. In

Frequency, amplitude, and phase measurements in contact resonance atomic force microscopies

• Gheorghe Stan and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 278–288, doi:10.3762/bjnano.5.30

• is provided. Keywords: contact-resonance AFM; dynamic AFM; frequency modulation; phase-locked loop; viscoelasticity; Introduction A number of atomic force microscopy (AFM) variants have emerged since the introduction of the original technique in 1986 [1]. Besides topographical acquisition and

• dynamic AFM modes. Within the force modulation method [2], the tip and the sample are brought into contact at a prescribed tip–sample force setpoint (cantilever deflection setpoint, as in contact mode imaging) and the sample is excited with a sinusoidal oscillation in the vertical direction (atomic force

Unlocking higher harmonics in atomic force microscopy with gentle interactions

• Sergio Santos,
• Victor Barcons,
• Josep Font and
• Albert Verdaguer

Beilstein J. Nanotechnol. 2014, 5, 268–277, doi:10.3762/bjnano.5.29

• tip–sample system and imply that higher harmonics can be translated into conservative and dissipative [7] nanoscale and atomic properties [8]. Furthermore, conventional dynamic AFM can already reach molecular [9][10], sub-molecular [11] and atomic [12][13] resolution in some systems. Thus, the

•  2 for n > 1. This is the standard operational mode in dynamic AFM, in which a single external drive is employed. In this case we have PR = 0 throughout (Table 3). Case 2: Higher harmonic external drives are allowed. In particular, A0n = 1 pm in Equation 2 for n > 1. This is the proposed mode of

• frequency of the second flexural mode [17][25][26]. In standard monomodal dynamic AFM, in which a single external drive is employed, the higher harmonics are excited by the tip–sample interaction according to Equation 9. That is, energy needs to flow into the higher harmonic frequencies in order to increase

Exploring the retention properties of CaF₂ nanoparticles as possible additives for dental care application with tapping-mode atomic force microscope in liquid

• Matthias Wasem,
• Joachim Köser,
• Sylvia Hess,
• Enrico Gnecco and
• Ernst Meyer

Beilstein J. Nanotechnol. 2014, 5, 36–43, doi:10.3762/bjnano.5.4

• nanoparticles on silicon substrates with dynamic AFM [16]. Darwich et al. investigated the retention of colloidal gold nanoparticles depending on particle–substrate affinity and humidity with tapping mode AFM [17]. In all these studies the major difficulty arises to quantify the dynamic processes during

Peak forces and lateral resolution in amplitude modulation force microscopy in liquid

• Horacio V. Guzman and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2013, 4, 852–859, doi:10.3762/bjnano.4.96

• –sample interaction force is a major issue in dynamic AFM because the force gives access to the materials properties of the sample; nonetheless the force is not a direct observable. Therefore, several methods have been proposed to reconstruct the force in dynamic AFM [12][13][14][15][16][17][18]. However

Dynamic nanoindentation by instrumented nanoindentation and force microscopy: a comparative review

• Sidney R. Cohen and
• Estelle Kalfon-Cohen

Beilstein J. Nanotechnol. 2013, 4, 815–833, doi:10.3762/bjnano.4.93

• should always recall that the simplified or even complex mechanical models are describing a substantially more complex molecular system. Dynamic AFM probe nanoindentation Boasting the advantage of wider bandwidth, smaller inertia of the system, better lateral resolution and more sensitive force detection

• dynamic AFM operation the displacement may be applied to the base of the cantilever or to the base of the sample, in which case the cantilever spring acts in series with the tip–surface compliance [20][73]. A very different response is obtained when the modulation is applied at the tip–sample contact [98

• ]. Burnham et al., in an analysis of the mechanics of dynamic AFM contact, described the various modes, in which the AFM can be used to study energy dissipation [63]. They split the possible operation modes into three categories: force modulation, sample modulation and tip modulation. They found that a

High-resolution nanomechanical analysis of suspended electrospun silk fibers with the torsional harmonic atomic force microscope

• Mark Cronin-Golomb and
• Ozgur Sahin

Beilstein J. Nanotechnol. 2013, 4, 243–248, doi:10.3762/bjnano.4.25

• -resolution compositional mapping of heterogeneous samples [1]. Recent developments in dynamic AFM methods offer the possibility of relating the measured vibration signals to the particular physical properties of the samples, such as elastic modulus, viscosity, adhesion, and chemical affinity [2][3][4][5][6

• ][7][8][9][10][11][12][13][14][15][16]. These developments are accomplished by employing multiple excitation and detection frequencies during dynamic AFM imaging [17][18][19][20][21][22][23][24][25][26]. A critical element of these mechanical measurements is the physical model being used to relate the

• the surface topography and local mechanical response with high spatial resolution [20][31]. This mode uses a T-shaped cantilever with an offset tip. When used in dynamic AFM, the cantilever vibrates up and down, similar to conventional cantilevers. In addition to the vertical motion, tip–sample