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

• should be higher than the topography feedback bandwidth to prevent crosstalk yet low enough that the mixing products are not too far from ωm to take advantage of gains in the SNR. This limits the accessible bandwidth and, therefore, the scanning speed [10]. (3) Higher eigenmodes – by applying the

• electrical signal to a higher eigenmode, the electrostatic response can be measured simultaneously with topography in a single pass [17][60][61][62]. Higher eigenmodes typically have poorer SNRs than the fundamental eigenmode since kn increases more rapidly than Qn [60][61]. However, these modes still offer

• reactions. Here, we restrict our analysis to the first two eigenmodes of a cantilever, where the SNR is highest, but these calculations could be extended to higher eigenmodes if desired [96]. Performance Characteristics of KPFM Modes In KPFM-based techniques an electrical bias is applied between a

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

• ratios of higher eigenmodes to the fundamental one can be crucial in selecting and designing the optimum cantilever for bimodal AFM imaging. After finding the relationship between parameters of higher eigenmodes and those of the fundamental one, we have studied the effect of the width b on the maximum

• eigenmode is closer to a multiple integer of the fundamental eigenmode frequency, the phase signal of the higher eigenmodes is enhanced [28]. Additionally, a higher eigenmode frequency that is a multiple integer of the first one can help with providing more regular taps on surfaces. This can be useful in

• especially while imaging using higher eigenmodes or multifrequency AFM, as long as the first eigenmode frequency sufficiently high to perform soft matter imaging. Although the commercially used V-shaped cantilevers are not very close in dimensions to the theoretically optimum dimensions, one of them provide

A review of demodulation techniques for multifrequency atomic force microscopy

• David M. Harcombe,
• Michael G. Ruppert and
• Andrew J. Fleming

Beilstein J. Nanotechnol. 2020, 11, 76–91, doi:10.3762/bjnano.11.8

• within dynamic mode AFM. It involves studying multiple frequency components in the cantilever oscillation during tip–sample interactions [13]. Observing higher eigenmodes of the cantilever [14], higher harmonics of the fundamental resonance [15] and intermodulation products [16] have been shown to

• illustrates a cantilever driven at multiple frequencies being amplitude-modulated by a sample topography. In MF-AFM, the cantilever deflection signal contains frequency components originating from the fundamental resonance mode, as well as from higher eigenmodes and/or harmonics. If for simplicity we assume

Imaging of viscoelastic soft matter with small indentation using higher eigenmodes in single-eigenmode amplitude-modulation atomic force microscopy

• Miead Nikfarjam,
• Enrique A. López-Guerra,
• Santiago D. Solares and
• Babak Eslami

Beilstein J. Nanotechnol. 2018, 9, 1116–1122, doi:10.3762/bjnano.9.103

• Abstract In this short paper we explore the use of higher eigenmodes in single-eigenmode amplitude-modulation atomic force microscopy (AFM) for the small-indentation imaging of soft viscoelastic materials. In viscoelastic materials, whose response depends on the deformation rate, the tip–sample forces

• in some cases be reduced by using higher eigenmodes of the cantilever. This effect competes with the lower sensitivity of higher eigenmodes, due to their larger force constant, which for elastic materials leads to greater indentation for similar amplitudes, compared with lower eigenmodes. We offer a

• short theoretical discussion of the key underlying concepts, along with numerical simulations and experiments to illustrate a simple recipe for imaging soft viscoelastic matter with reduced indentation. Keywords: higher eigenmodes; multifrequency AFM; soft matter; viscoelasticity; Introduction Since

Lyapunov estimation for high-speed demodulation in multifrequency atomic force microscopy

• David M. Harcombe,
• Michael G. Ruppert,
• Michael R. P. Ragazzon and
• Andrew J. Fleming

Beilstein J. Nanotechnol. 2018, 9, 490–498, doi:10.3762/bjnano.9.47

• frequency and higher eigenmodes can be seen in the cantilever frequency response. As before, the deflection signal contains additional higher harmonics and intermodulation products due to the non-linear atomic excitation. Note that the DMASP cantilever uses integrated piezoelectric actuation [31], which

High-stress study of bioinspired multifunctional PEDOT:PSS/nanoclay nanocomposites using AFM, SEM and numerical simulation

• Alfredo J. Diaz,
• Hanaul Noh,
• Tobias Meier and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2017, 8, 2069–2082, doi:10.3762/bjnano.8.207

• nanocomposite. As discussed previously, the force applied by the tip to the surface increases with the use of higher eigenmodes and by increasing their free amplitude. Supporting Information File 1, Figure S5 shows the results of a virtual AFM numerical simulation, where the increase in peak forces as the free

Analysis and modification of defective surface aggregates on PCDTBT:PCBM solar cell blends using combined Kelvin probe, conductive and bimodal atomic force microscopy

• Hanaul Noh,
• Alfredo J. Diaz and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2017, 8, 579–589, doi:10.3762/bjnano.8.62

• aggregates, avoiding additional sample modification. Typically, multifrequency AFM uses the first eigenmode of the cantilever to control the tip–sample distance and acquire the topography, and higher eigenmodes to measure additional properties [37][38]. We have also previously shown that the peak forces can

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

• ) also applies to higher eigenmodes; it can be rewritten as where u’ is the normalized deflection of the higher eigenmode in this context. The major distinction between Equation 6 and Equation 21 is the substitution δmax → δ(t) which accounts for the non-zero amplitude of the first eigenmode A1 that

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

• involving a minimum amount of external equipment. For example, the commonly used piezoelectric actuator at the base of the cantilever leads to a highly distorted frequency response with numerous resonances which renders the identification and subsequent analysis of higher eigenmodes exceedingly difficult

• measuring the charge simultaneously at multiple higher eigenmodes. However, the individual resonances are heavily buried in feedthrough originating from the piezoelectric capacitance which yields a dynamic range of less than 1 dB at the resonant modes. In order to recover these modes for subsequent

• common practice for the fundamental mode, it is not feasible for higher eigenmodes, due to their increased dynamic stiffnesses and associated small free-air amplitudes. As such, the sensor sensitivities are calibrated by comparing the sensor outputs for a given drive voltage and comparing it to the

High-frequency multimodal atomic force microscopy

• Adrian P. Nievergelt,
• Jonathan D. Adams,
• Pascal D. Odermatt and
• Georg E. Fantner

Beilstein J. Nanotechnol. 2014, 5, 2459–2467, doi:10.3762/bjnano.5.255

• in water [40]. One issue of note is that higher eigenmodes have an inherently higher dynamic stiffness that can be up to two orders of magnitude larger than the fundamental mode. This can be problematic for softer samples, as the power dissipated into the sample increases linearly with the spring

• constants of higher eigenmodes can be kept at reasonable values without sacrificing imaging bandwidth. However, their application in multifrequency techniques has been restricted due to instrument capability limitations. By using photothermal actuation of small cantilevers along with a current-based

Modeling viscoelasticity through spring–dashpot models in intermittent-contact atomic force microscopy

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

Beilstein J. Nanotechnol. 2014, 5, 2149–2163, doi:10.3762/bjnano.5.224

• cantilevers of different fundamental frequencies or the use of different higher eigenmodes in successive experiments [22]. For this numerical study, we have chosen the first approach and for simplicity we have restricted ourselves to single-eigenmode tapping mode AFM due to the introductory nature of this

Probing viscoelastic surfaces with bimodal tapping-mode atomic force microscopy: Underlying physics and observables for a standard linear solid model

• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 1649–1663, doi:10.3762/bjnano.5.176

• measurements involving different timescales in order to capture the different relaxation times of the sample. In practice this can be accomplished by sequentially studying the same sample with cantilevers of different fundamental frequency or by using different higher eigenmodes in successive experiments. Even

• higher eigenmodes in successive experiments, under constant indentation. The analysis could be repeated at different levels of indentation to give a complete picture of the depth-dependent behavior of the sample. Second, the further development of spectroscopy methods that provide the tip–sample force

Multi-frequency tapping-mode atomic force microscopy beyond three eigenmodes in ambient air

• Santiago D. Solares,
• Sangmin An and
• Christian J. Long

Beilstein J. Nanotechnol. 2014, 5, 1637–1648, doi:10.3762/bjnano.5.175

• , focusing on the case of large amplitude ratios between the fundamental eigenmode and the higher eigenmodes. We discuss the dynamic complexities of the tip response in time and frequency space, as well as the average amplitude and phase response. We also illustrate typical images and spectroscopy curves and

• Figure 1 for an example of non-ideal amplitude vs frequency responses for different eigenmodes), signal processing instrumentation (higher eigenmodes have higher frequencies and require faster electronics as well as tip tracking systems with higher performance), and dynamic complexity [19][20][21][22

• bandwidth and data acquisition limitations prevent us from using the same number of eigenmodes and range of eigenfrequencies in the experiments as in the simulations). We focus on the case of large amplitude ratios between the fundamental eigenmode (used for topographical imaging) and the higher eigenmodes

Trade-offs in sensitivity and sampling depth in bimodal atomic force microscopy and comparison to the trimodal case

• Babak Eslami,
• Daniel Ebeling and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 1144–1151, doi:10.3762/bjnano.5.125

• through changes in the amplitude of the highest driven eigenmode, which has the highest dynamic force constant (the higher stiffness of higher eigenmodes has also been advantageous in subsurface imaging applications in contact resonance AFM [18]). In this paper we show that indentation depth modulation

• cantilever is brought very close to the surface (in these simulations the curves become smoother if one considers a larger number of taps for every cantilever height in the construction of the graphs). As previously reported, the greater indentation capability of higher eigenmodes with respect to the

• calibrated by using amplitude–distance curves and the amplitude of higher eigenmodes was estimated by using their respective optical sensitivity factors (see Table 1 in [2]). The experimental sample consisted of the proton exchange membrane Nafion® 115, purchased from Ion Power, Inc. (New Castle, DE, USA

Challenges and complexities of multifrequency atomic force microscopy in liquid environments

• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 298–307, doi:10.3762/bjnano.5.33

• context of multifrequency atomic force microscopy (AFM). The focus is primarily on (i) the amplitude and phase relaxation of driven higher eigenmodes between successive tip–sample impacts, (ii) the momentary excitation of non-driven higher eigenmodes and (iii) base excitation artifacts. The results and

• discussion are mostly applicable to the cases where higher eigenmodes are driven in open loop and frequency modulation within bimodal schemes, but some concepts are also applicable to other types of multifrequency operations and to single-eigenmode amplitude and frequency modulation methods. Keywords

• of higher eigenmodes and multiple-impact regimes [21][26], mass loading and fluid-borne cantilever excitation [19][23][24], discrepancies between the photodetector signal and the actual tip position for base-excited cantilever systems [24][28] and non-ideal spectroscopy curves (for example, curved

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

• topographical measurement, while one or more higher eigenmodes are driven simultaneously in order to also map compositional (viscoelastic) contrast. Since the higher eigenmodes are not directly affected by the topographical acquisition controls, they can be tuned independently to map Vts and Pts with high

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

• to inconsistencies [37]. This issue becomes more prominent when dealing with third or higher eigenmodes [27][38], for which the theory is now emerging [31]. The introduction of exact harmonic external drives keeps the fundamental frequency intact and the analytical expressions are simplified by

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

• studies have related the phase contrast, when measuring in liquid in which low Q-factors are found, to two origins: the excitation of higher eigenmodes and the energy dissipation on the sample surface [8][9]. In this work we show that for surface associated manipulation of nanoparticles in liquid, the

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

• lead to the momentary excitation of higher eigenmodes, in particular the second eigenmode [7]. To account for those effects we also describe the microcantilever–tip system by using an extended Euler–Bernoulli equation [39]. This model considers the cantilever as a continuous and uniform rectangular

Multiple regimes of operation in bimodal AFM: understanding the energy of cantilever eigenmodes

• Daniel Kiracofe,
• Arvind Raman and
• Dalia Yablon

Beilstein J. Nanotechnol. 2013, 4, 385–393, doi:10.3762/bjnano.4.45

• . Bimodal AFM traditionally uses the first two eigenmodes of the AFM cantilever. In this work, the authors explore the use of higher eigenmodes in bimodal AFM (e.g., exciting the first and fourth eigenmodes). It is found that such operation leads to interesting contrast reversals compared to traditional

• bimodal AFM operation (or even multiple higher eigenmodes simultaneously [9]). In this work, we wish to examine the choice of specific higher order eigenmodes for bimodal operation in order to understand if they provide any practical advantages in terms of material discrimination and identification. There

• natural frequency, piezo resonances are generally only an issue in liquid [14]. However, on our instrument, piezo resonances can distort the higher eigenmode tuning curves significantly, especially for third and higher eigenmodes. Therefore, a thermally driven spectrum was obtained when the cantilever was

Optimal geometry for a quartz multipurpose SPM sensor

• Julian Stirling

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

• of moving the dynamic spring constant closer to the static constant [20], removing the ≈3% error. (Note that this is not true in higher eigenmodes for cantilever geometries as the inertia shifts the position of the antinodes [1]. In this system, however, the antinodes are pinned due to the symmetry

Determining cantilever stiffness from thermal noise

• Jannis Lübbe,
• Matthias Temmen,
• Philipp Rahe,
• Angelika Kühnle and
• Michael Reichling

Beilstein J. Nanotechnol. 2013, 4, 227–233, doi:10.3762/bjnano.4.23

• excited near their fundamental eigenfrequency f0, higher eigenmodes [7] have been investigated in the context of noise analysis [8], and it has been debated whether the thermal noise limitations in NC-AFM measurements could be reduced by operating cantilevers at higher eigenmodes [9]. It has further been

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

• higher eigenmodes [36][37]. The present theory does not extend to soft microcantilevers in liquids. However, from prior work, we can expect that the primary difference for soft microcantilevers is that the dissipation reflects the energy lost to higher harmonics [38][39]. Performance metrics for high

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

• ] have shown that the dimensions of conical tips also have large effects on the dynamics of higher eigenmodes, suggesting that careful consideration of tip geometry is necessary for sensors operated in the second eigenmode or above. In this paper we go further, providing a detailed analytical solution

• amplitude of deflection, az. The ratio of dynamic spring constants kn to the cantilever static spring constant kstat for n = 1,2,3,4, plotted for a range of tip lengths and diameters. The sudden increases in the higher eigenmodes result from nodes positioned at the end of the tip resulting in infinite