Enhancing higher-order modal response in multifrequency atomic force microscopy with a coupled cantilever system

• Wendong Sun,
• Jianqiang Qian,
• Yingzi Li,
• Yanan Chen,
• Zhipeng Dou,
• Rui Lin,
• Peng Cheng,
• Xiaodong Gao,
• Quan Yuan and
• Yifan Hu

Beilstein J. Nanotechnol. 2024, 15, 694–703, doi:10.3762/bjnano.15.57

• , Chinese Academy of Sciences, Dalian 116023, P. R. China 10.3762/bjnano.15.57 Abstract Multifrequency atomic force microscopy (AFM) utilizes the multimode operation of cantilevers to achieve rapid high-resolution imaging and extract multiple properties. However, the higher-order modal response of

• traditional rectangular cantilever is weaker in air, which affects the sensitivity of multifrequency AFM detection. To address this issue, we previously proposed a bridge/cantilever coupled system model to enhance the higher-order modal response of the cantilever. This model is simpler and less costly than

• , including increasing the modal frequency of the original cantilever and generating additional resonance peaks, demonstrating the significant potential of the coupled system in various fields of AFM. Keywords: atomic force microscopy; coupled system; higher-order modes; macroscale; multifrequency AFM

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

• the resonant frequency ωc and the linewidth κ of the microwave resonator used to detect cantilever motion. A practical consideration is that our multifrequency measurement apparatus works in the frequency band of 4–8 GHz. This frequency range constrains the possible values of the circuit’s inductance

• of 4–8 GHz of our digital multifrequency lock-in measurement system. Higher frequencies are possible, but the cost of such equipment increases steeply with frequency. Our designs also started with a single thickness of the Si-N plate that forms the cantilever, which is natural as all chips must be

• cryogenic amplifier for low-noise microwave reflection measurement, as shown in Figure 8. Low- and high-frequency signals are synchronously synthesized and measured with a digital multifrequency microwave measurement device (Vivace from Intermodulation Products AB) to measure phase-sensitive

Exploring internal structures and properties of terpolymer fibers via real-space characterizations

• Michael R. Roenbeck and
• Kenneth E. Strawhecker

Beilstein J. Nanotechnol. 2023, 14, 1004–1017, doi:10.3762/bjnano.14.83

• investigated the processing and properties of high-performance terpolymer fibers, much remains to be understood about the internal nano- and microstructures of these fibers, and how these morphologies relate to fiber properties. Here we use a focused ion beam notch technique and multifrequency atomic force

• we present internal structural characterizations of FIB-notched Technora® fibers using multifrequency AFM mapping. We observe a homogeneous microstructure throughout the fiber without any evidence of a fiber skin near the periphery. At the nanoscale, we observe a highly fibrillated structure well

• , overcutting leads to transverse failures near the notches without producing an internal shear plane. Multifrequency atomic force microscopy scanning The exposed internal surfaces of FIB-notched fibers were scanned using a Cypher AFM with an ARC2 controller (Asylum Research). Olympus AC200TS cantilevers (k ≈ 9

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

• . Through such findings we aim to expand the field of multifrequency AFM with innumerable possibilities leading to improved signal-to-noise ratios, all accessible with no additional hardware. Keywords: atomic force microscopy; intermodal coupling; nonlinear mechanics; optomechanics; sideband cooling

• opportunity to bring intermodal coupling techniques, derived from optomechanics, to AFM. It is easily accessible, with no hardware modifications and only requiring multifrequency excitation applied to the cantilever by either a piezoshaker or a modulated laser, found in many AFM setups. The field of

• multifrequency AFM has improved both imaging contrast and the amount of extracted information from AFM experiments by exploiting the nonlinearity of the tip–surface interaction [32][33][34][35][36]. The methods applied excel in both their creativity and engineering prowess. A first example is on-resonance

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

• properties using multifrequency and multimodal AFM operation modes. Research of new quantum materials and devices, however, often requires low temperatures and ultrahigh vacuum (UHV) conditions and, more specifically, AFM instrumentation providing atomic resolution. For this, AFM instrumentation based on a

• tuning fork force sensor became increasingly popular. In comparison to microfabricated cantilevers, the more macroscopic tuning forks, however, lack sensitivity, which limits the measurement bandwidth. Moreover, multimodal and multifrequency techniques, such as those available in cantilever-based AFM

• cantilever-based AFM offers experimental flexibility by permitting multimodal or multifrequency operations with superior force derivative sensitivities and bandwidths. Our instrument has a sub-picometer gap stability and can simultaneously map not only vertical and lateral forces with atomic-scale resolution

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

• governing the performance of single and multifrequency Kelvin probe force microscopy (KPFM) techniques in both air and water. Metrics such as minimum detectable contact potential difference, minimum required AC bias, and signal-to-noise ratio are compared and contrasted both off resonance and utilizing the

• that are most suitable for operation in liquid environments where bias application can lead to unwanted electrochemical reactions. We conclude that open-loop multifrequency KPFM modes operated with the first harmonic of the electrostatic response on the first eigenmode offer the best performance in

• be coupled with the mechanical drive, which may be applied either at a higher eigenmode or off resonance, for example, in the PORT mode [65]. In this paper we refer to any application of two electrical signals with a mechanical drive as HM-KPFM. For OL multifrequency KPFM techniques (DH, Het, ED, HM

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

• has been applied. Additionally, a tilted cantilever has been found to lead to a modification of the tip–sample convolution [12], to enhance the sensitivity of the measurement to the probe side [13], and to influence results of multifrequency AFM and Kelvin probe force microscopy [14]. In the presence

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

• no studies on the static and dynamic behavior of V-shaped cantilevers in multifrequency AFM due to their complex geometry. In this work, the static and dynamic properties of V-shaped cantilevers are studied while investigating their performance in multifrequency AFM (specifically bimodal AFM). By

• ; Introduction Since the invention of atomic force microscopy (AFM), different techniques have been introduced into the field to enhance and improve this nanotechnology equipment. In 2004, multifrequency AFM was introduced as a technique that can capture both topographical and material composition in a single

• , multifrequency AFM has gained the attention of different fields, such as, the measurement of nanoscale chemical and mechanical properties of human dentin [2], the mapping of viscoelastic materials [3], or the characterization of thin molecular films [4]. As different fields have implemented multifrequency AFM in

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

• ]) and band-excitation AFM [9][29], as well as dynamic methods based on multifrequency AFM [4][5] and multi-harmonic AFM [30][31] have also been implemented to measure an effective modulus of elasticity and an effective coefficient of dissipation (or analogous quantities) across the surface. All of these

• case), but would at least be able to begin probing the corresponding types of behavior, say with multifrequency AFM [5][38][44] using a higher (i.e., the 3rd or 4th) eigenmode of a traditional tapping-mode cantilever at a frequency of about 5–10 MHz (or higher with an instrument that has a higher

• , but all equations are coupled through the tip–sample force curve, as is customary in multifrequency AFM simulations [24][38][47][48] or in simulations of AFM imaging in liquid environments [49][50]. The higher eigenfrequencies have the customary rectangular-beam relationship to the fundamental

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

• previous multifrequency AFM experiments [47], falls in the same range as the 30th harmonic). Furthermore, improvements in the reconstruction may be possible due to the fact that the shape of the power spectrum envelope may be known, as is the case for Equation 13 and Equation 18, or could be approximated

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

• multifrequency atomic force microscopy. The compared methods include the lock-in amplifier, coherent demodulator, Kalman filter, Lyapunov filter, and direct-design demodulator. Each method is implemented on a field-programmable gate array (FPGA) with a sampling rate of 1.5 MHz. The metrics for comparison include

• the sensitivity to other frequency components and the magnitude of demodulation artifacts for a range of demodulator bandwidths. Performance differences are demonstrated through higher harmonic atomic force microscopy imaging. Keywords: atomic force microscopy (AFM); multifrequency; demodulation

• the cantilever according to the expression f−3dB = f0/2Q, where f0 is the fundamental resonance frequency. Assuming all other components in the z-axis feedback loop are also working at high speed [3], a low quality factor can demand a fast demodulator [12]. Multifrequency AFM (MF-AFM) is a major field

Microbubbles decorated with dendronized magnetic nanoparticles for biomedical imaging: effective stabilization via fluorous interactions

• Da Shi,
• Justine Wallyn,
• Dinh-Vu Nguyen,
• Francis Perton,
• Delphine Felder-Flesch,
• Sylvie Bégin-Colin,
• Mounir Maaloum and
• Marie Pierre Krafft

Beilstein J. Nanotechnol. 2019, 10, 2103–2115, doi:10.3762/bjnano.10.205

• exploits the sound attenuation undergone by multifrequency ultrasound waves that propagate through the aqueous bubble dispersion. Standard simple-harmonic resonator curves are fitted to measure the attenuation in order to infer the radii of the bubbles. A low-power emitter is used to avoid alteration of

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

• 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

• versatility of the instrument, it has been proposed to use higher cantilever eigenmodes, either by themselves in single-eigenmode imaging [6][7][8][9] or within multifrequency techniques [10]. For example, in the original multifrequency AFM method, introduced by Garcia and coworkers and known as bimodal AFM

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

• 10.3762/bjnano.9.47 Abstract An important issue in the emerging field of multifrequency atomic force microscopy (MF-AFM) is the accurate and fast demodulation of the cantilever-tip deflection signal. As this signal consists of multiple frequency components and noise processes, a lock-in amplifier is

• , enabling both z-axis feedback and phase contrast imaging to be achieved. This article proposes a model-based multifrequency Lyapunov filter implemented on a field-programmable gate array (FPGA) for high-speed MF-AFM demodulation. System descriptions and simulations are verified by experimental results

• ; digital signal processing; field-programmable gate array (FPGA); high-speed; Lyapunov filter; multifrequency; Introduction Atomic force microscopy (AFM) [1] has been integral in the field of nanoscale engineering since its invention in 1986 by Binnig et al. By sensing microcantilever tip–sample

A robust AFM-based method for locally measuring the elasticity of samples

• Alexandre Bubendorf,
• Stefan Walheim,
• Thomas Schimmel and
• Ernst Meyer

Beilstein J. Nanotechnol. 2018, 9, 1–10, doi:10.3762/bjnano.9.1

• dimensions of an ideal beam-shaped cantilever. However, most cantilevers used for measurements are not ideal. Thus, to achieve consistent results, the values of length and tip height have to be corrected. When measurements using the multifrequency AFM [15][16] method of Herruzo et al., which is based on the

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

• ), contact-resonance force microscopy (mechanical properties), and SEM combined with a variety of stress-strain AFM experiments and AFM numerical simulations (internal structure). We further study the nanoclay’s response to the application of pressure with multifrequency AFM and conductive AFM, whereby

• the AFM probe diameter. No pressure-induced changes in conductivity were observed in the clay-free polymer either. Keywords: biomimetics; conductive AFM; conductive nanocomposites; contact-resonance force microscopy; multifrequency AFM; transparent coatings; Introduction Bioinspired material designs

A review of demodulation techniques for amplitude-modulation atomic force microscopy

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

Beilstein J. Nanotechnol. 2017, 8, 1407–1426, doi:10.3762/bjnano.8.142

• frequency components. Specifically for modern multifrequency techniques, where higher harmonic and/or higher eigenmode contributions are present in the oscillation signal, the fidelity of the estimates obtained from some demodulation techniques is not guaranteed. To enable a rigorous comparison, the

• commercial AFM systems. The performance metrics, tracking bandwidth and sensitivity to other frequency components, are especially important in high-speed [15][16][17][18] and multifrequency AFM [19] applications. As the tracking bandwidth directly affects the achievable scan rate, it should be maximized

• . However, this also increases the noise bandwidth. On the other hand, in multifrequency AFM applications, the sensitivity to other frequency components is of greatest concern. These applications may include multiple eigenmode contributions [20][21][22], higher harmonics [23][24][25], and multi-tone near

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

• below 20 GPa). Keywords: atomic force microscopy; metrology; multifrequency; nanomechanics; Introduction When an AFM cantilever oscillating freely and harmonically at a given frequency f and amplitude A1 approaches a solid surface, the oscillation becomes anharmonic due to the non-linear interaction

Investigation of growth dynamics of carbon nanotubes

• Marianna V. Kharlamova

Beilstein J. Nanotechnol. 2017, 8, 826–856, doi:10.3762/bjnano.8.85

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

• force microscopy; multifrequency AFM; organic photovoltaics; polymer solar cells; surface defects; Introduction Polymer solar cells (PSCs) [1] have been widely studied due to the abundance of their constituents, their mechanical flexibility and light weight, as well as the possibility of low-cost roll

• blend–electrode interface. In addition, we use bimodal AFM, a multifrequency AFM technique [18], to modify and remove the surface molecular layers. The series of AFM analyses and modification performed can be useful to better understand the nature of PSC surface defects. A detailed description of the

• 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

Multimodal cantilevers with novel piezoelectric layer topology for sensitivity enhancement

• Steven Ian Moore,
• Michael G. Ruppert and
• Yuen Kuan Yong

Beilstein J. Nanotechnol. 2017, 8, 358–371, doi:10.3762/bjnano.8.38

• characteristics compared to the optical beam deflection method. The possibility of down scaling, parallelization of cantilever arrays and the absence of optical interference associated imaging artifacts have led to an increased research interest in these methods. However, for multifrequency AFM, the optimization

• multifrequency AFM and has the potential to provide higher resolution imaging on higher order modes. Keywords: atomic force microscopy; multifrequency AFM; multimodal AFM; piezoelectric cantilever, self-sensing; Introduction The invention of the atomic force microscope (AFM) [1] provided for the observation of

• with multiple frequencies has led to vast improvements in the nanomechanical characterization of the sample beyond it’s topography [16]. For these multifrequency AFM (MF-AFM) methods, higher order modes provide enhanced imaging properties such as higher modal stiffnesses and faster response times. It

Advanced atomic force microscopy techniques III

• Thilo Glatzel and
• Thomas Schimmel

Beilstein J. Nanotechnol. 2016, 7, 1052–1054, doi:10.3762/bjnano.7.98

• developed an advanced microscope capable of obtaining nanoscale topography as well as mechanical properties by multifrequency AFM at high speed. They combined recent progress in increased imaging speed and photothermal actuation in a unique and versatile AFM head using ultrasmall cantilevers [18]. Single

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

• experimental data and extract a shape and size of the tip interacting with a polystyrene surface. Keywords: bimodal atomic force microscopy; bimodal spectroscopy; contact mechanics; multifrequency; nanomechanical mapping; nanomechanics; Introduction Over the decades since its invention [1] the atomic force

• include bimodal [28][29][30][31][32][33], trimodal [34] or more generally multimodal/multifrequency [35] techniques, and have demonstrated quantitative mapping without compromising on the high speeds that define parametric imaging techniques. Currently, state-of-the-art bimodal methodologies are mostly

Nanoscale effects in the characterization of viscoelastic materials with atomic force microscopy: coupling of a quasi-three-dimensional standard linear solid model with in-plane surface interactions

• Santiago D. Solares

Beilstein J. Nanotechnol. 2016, 7, 554–571, doi:10.3762/bjnano.7.49

• -solid viscoelastic elements. The enhanced model introduces in-plane surface elastic forces that can be approximately related to a two-dimensional (2D) Young’s modulus. Relevant cases are discussed for single- and multifrequency intermittent-contact AFM imaging, with focus on the calculated surface

• AFM simulation. A multifrequency AFM simulation tool based on the above sample model is provided as supporting information. Keywords: atomic force microscopy; modeling; polymers; simulation; spectroscopy; standard linear solid; surface elasticity; surface energy; viscoelasticity; Introduction The

• measurements (this includes both single- and multifrequency techniques) because, (i) the tip–sample interaction in that mode of imaging is not continuous and therefore the stress response of the material is not able to reach a steady state during the measurement, and (ii) the complex modulus depends on the

Efficiency improvement in the cantilever photothermal excitation method using a photothermal conversion layer

• Natsumi Inada,
• Hitoshi Asakawa,
• Taiki Kobayashi and
• Takeshi Fukuma

Beilstein J. Nanotechnol. 2016, 7, 409–417, doi:10.3762/bjnano.7.36

• multifrequency AFM [10][11][12] have been developed based on dynamic-mode AFM. In dynamic-mode AFM, a stiff cantilever is mechanically oscillated at a frequency near its resonance frequency. The vibrational characteristics, such as frequency, amplitude and phase are monitored to detect interaction forces between