Atomic Force Microscope Cantilever Research Articles

Comparison Between Torsional Spring Constants of Rectangular and V-Shaped AFM Cantilevers

The properties of force-sensing micro-cantilevers are of fundamental importance for measurements employing atomic force microscopy (AFM) techniques. Due to the well-known arguments of Sader, it is generally accepted that V-shaped cantilevers are more sensitive to lateral forces than rectangular ones. We present results of numerical (finite element modelling) and experimental comparison between torsional spring constants of rectangular and V-shaped commercial AFM cantilevers. As representative example of such beams, we considered AFM probes available commercially. In particular, we tested scaled-up models of V-shaped cantilevers which had the same geometrical shapes as commercial AFM cantilevers. Both the rectangular and the V-shaped larger scale models were made of the same material; they had the same length, thickness, normal spring constant, as well as the same location and shape of the tip base. In the experiments and the simulations, an external lateral load was applied to the free end of the tip. A good agreement between the experimental work and finite element method (FEM) simulations was observed. The results show that the torsional spring constant of the V-shape cantilevers considered here was greater than that of the equivalent rectangular beams by up to 45%. The discrepancy with the results from Sader should be caused by differences in both the load transfer scheme and the geometrical shapes of the V-shaped beams.

Manipulating the frequency response of small high-frequency atomic force microscope cantilevers

We study small (less than 10 µm-long) high-frequency (greater than 1 MHz) cantilevers specially designed for visualization of biomolecular processes in high-speed atomic force microscopes. The frequency responses of the first three flexural eigenmodes are investigated for the modified geometries. It is found that the Q-factors can be significantly altered in the desired way by reengineering the cantilever geometry without affecting its main operational parameters, such as the spring constant and the resonance frequency of the first flexural eigenmode in an air environment. In addition, higher-order flexural resonances can be moved away from the fundamental resonance with these geometrical modifications. The Q-factors in liquid, on the other hand, do not show a significant difference due to high viscous damping of the medium. Regular cantilevers modified by a focused ion beam are used to demonstrate the validity of the finite element simulation model.

Analysis of Dynamic Behavior of V-Shaped Atomic Force Microscope Cantilever in Contact and Tapping Modes by Considering Various Immersion Surroundings

In atomic force microscope (AFM) as a powerful device for scanning the samples, a cantilever is used to sense the variations of its dynamic characteristics due to the tip–sample interaction. Theoretical models that can accurately simulate the surface-coupled dynamics of the cantilever are necessary for quantifiable and qualitative explanation and understanding of measured results. A good understanding of the dynamics of AFM cantilevers vibrating in liquid is needed for the interpretation of scanning images, selection of AFM operating conditions and evaluation of sample’s mechanical properties. In this paper, the amplitude of frequency response functions (FRF) of vertical and rotational movements for a V-shaped atomic force microscope beam immersed in various surroundings has been surveyed for the first time. For rising the precision of theoretical model, we have considered all needful details for the beam and sample. The amplitude of FRF of vertical and rotational movements and resonant frequency of beam have been surveyed by supposing cantilever thickness, breadth and length, the angle between cantilever and sample surface, tip height and normal and lateral tip–sample interaction force. In this study, carbon tetrachloride (CCL4), methanol, acetone, water and air have been considered as surroundings. The results show that an increase in the tip–sample interaction force considerably raises the amount of resonant frequency. By increasing the liquid viscosity, the amplitude of FRF for vertical and rotational movements and resonant frequency reduce. Moreover, the amplitude of FRF of vertical and rotational movements is reduced by raising the rectangular and tapered parts lengths, but increased by raising the rectangular part breadth and cantilever thickness. The resonant frequency goes down by increasing the rectangular and tapered parts lengths and rectangular part breadth, but increases by rising the cantilever thickness. In this paper, we have tried to model the realistic dynamic behavior of V-shaped AFM beam in contact and tapping modes with the most accuracy. Results show good agreement. Based on the experimental results, the present theoretical model can forestall better the realistic behavior of tapping mode than the contact mode for V-shaped AFM cantilever. Based on the complexity of the V-shaped AFM cantilever, this study has been done for the first time in both of the contact and tapping modes.

Micromanipulation of Mechanically Compliant Organic Single-Crystal Optical Microwaveguides.

Flexible organic single crystals are evolving as new materials for optical waveguides that can be used for transfer of information in organic optoelectronic microcircuits. Integration in microelectronics of such crystalline waveguides requires downsizing and precise spatial control over their shape and size at the microscale, however that currently is not possible due to difficulties with manipulation of these small, brittle objects that are prone to cracking and disintegration. Here we demonstrate that atomic force microscopy (AFM) can be used to reshape, resize and relocate single-crystal microwaveguides in order to attain spatial control over their light output. Using an AFM cantilever tip, mechanically compliant acicular microcrystals of three N-benzylideneanilines were bent to an arbitrary angle, sliced out from a bundle into individual crystals, cut into shorter crystals of arbitrary length, and moved across and above a solid surface. When excited by using laser light, such bent microcrystals act as active optical microwaveguides that transduce their fluorescence, with the total intensity of transduced light being dependent on the optical path length. This micromanipulation of the crystal waveguides using AFM is non-invasive, and after bending their emissive spectral output remains unaltered. The approach reported here effectively overcomes the difficulties that are commonly encountered with reshaping and positioning of small delicate objects (the "thick fingers" problem), and can be applied to mechanically reconfigure organic optical waveguides in order to attain spatial control over their output in two and three dimensions in optical microcircuits.

Allosterically Linked Binding Sites in Serotonin Transporter Revealed by Single Molecule Force Spectroscopy.

Crystal structures and experiments relying on the tools of molecular pharmacology reported conflicting results on ligand binding sites in neurotransmitter/sodium symporters (NSS). We explored the number and functionality of ligand binding sites of NSS in a physiological setting by designing novel tools for atomic force microscopy (AFM). These allow for directly measuring the interaction forces between the serotonin transporter (SERT) and the antidepressant S-citalopram (S-CIT) on the single molecule level: the AFM cantilever tips were functionalized with S-CIT via a flexible polyethylene glycol (PEG) linker. The tip chemistry was validated by specific force measurements and recognition imaging on CHO cells. Two distinct populations of characteristic binding strengths of S-CIT binding to SERT were revealed in Na+-containing buffer. In contrast, in Li+-containing buffer, SERT showed only low force interactions. Conversely, the vestibular mutant SERT-G402H merely displayed the high force population. These observations provide physical evidence for the existence of two binding sites in SERT. The dissociation rate constant of both binding sites was extracted by varying the dynamics of the force-probing experiments. Competition experiments revealed that the two sites are allosterically coupled and exert reciprocal modulation.

Micromanipulation of Mechanically Compliant Organic Single‐Crystal Optical Microwaveguides

AbstractFlexible organic single crystals are evolving as new materials for optical waveguides that can be used for transfer of information in organic optoelectronic microcircuits. Integration in microelectronics of such crystalline waveguides requires downsizing and precise spatial control over their shape and size at the microscale, however that currently is not possible due to difficulties with manipulation of these small, brittle objects that are prone to cracking and disintegration. Here we demonstrate that atomic force microscopy (AFM) can be used to reshape, resize and relocate single‐crystal microwaveguides in order to attain spatial control over their light output. Using an AFM cantilever tip, mechanically compliant acicular microcrystals of three N‐benzylideneanilines were bent to an arbitrary angle, sliced out from a bundle into individual crystals, cut into shorter crystals of arbitrary length, and moved across and above a solid surface. When excited by using laser light, such bent microcrystals act as active optical microwaveguides that transduce their fluorescence, with the total intensity of transduced light being dependent on the optical path length. This micromanipulation of the crystal waveguides using AFM is non‐invasive, and after bending their emissive spectral output remains unaltered. The approach reported here effectively overcomes the difficulties that are commonly encountered with reshaping and positioning of small delicate objects (the “thick fingers” problem), and can be applied to mechanically reconfigure organic optical waveguides in order to attain spatial control over their output in two and three dimensions in optical microcircuits.

Melting and Electromigration in Thin Chromium Films

Chromium films with a thickness of 10–40 nm deposited onto silicon substrates by magnetron sputtering are subjected to the action of electric current induced by the tip of an atomic force microscope (AFM) cantilever in air under regular environmental conditions. The melting process at the nanoscale, electric field-induced migration of material, and the chemical reaction of chromium oxidation that occur in melt craters formed around the region affected by the current are investigated using optical and scanning electron microscopies, AFM, and Raman spectroscopy. The flow of melted material induced by electric current is accompanied by the formation and motion of an array of spherical nanoparticles in the melt crater along its periphery. We propose that the formation of nanodrop array at relatively low current densities can be explained by the chromium oxidation reaction and the surface tension of melted material on the silicon substrate.

AFM Cantilever Design for Multimode Q Control: Arbitrary Placement of Higher Order Modes

In the fast growing field of multifrequency atomic force microscopy (AFM), the benefits of using higher order modes have been extensively reported on. However, higher modes of AFM cantilevers are difficult to instrument and Q control is challenging owing to their high-frequency nature. At these high frequencies, the latencies in the computations and analog conversions of digital signal processing platforms become significant and limit the effective bandwidth of digital feedback controller implementations. To address this issue, this article presents a novel cantilever design for which the first five modes are placed within a 200-kHz bandwidth. The proposed cantilever is designed using a structural optimization routine. The close spacing and low mechanical bandwidth of the resulting cantilever allows for the implementation of Q controllers for all five modes using a standard field programmable gate array (FPGA) development board for bimodal AFM and imaging on higher order modes.

Experimental and theoretical studies of frequency response function of dagger‐shaped atomic force microscope cantilever in different immersion environments

In this study, the amplitude of frequency response functions of vertical and rotational displacements and resonant frequency of a dagger-shaped atomic force microscope cantilever have been investigated. To increase the accuracy of theoretical model, all necessary details for cantilever and sample surface have been taken into account. In this paper, carbon tetrachloride (CCL4 ), methanol, acetone, water and air have been considered as the environments. In the most cases, presence and absence of tip-sample interaction force have studied. For a sample cantilever immersed in air, both of the Euler-Bernoulli and Timoshenko beam theories have been compared. The results indicate that the tip-sample interaction force raises the resonant frequency. Increasing the liquid viscosity leads to a decrease in the resonant frequency and the amplitude of frequency response functions of vertical and rotational displacements. Increasing the rectangular and tapered parts lengths, decreases the resonant frequency and amplitude of frequency response functions of vertical and rotational displacements. By increasing the cantilever thickness the resonant frequency and amplitude of frequency response functions of vertical and rotational displacements increases. Theoretical model for air and water has been compared with experimental work. Results show good agreement.

Experimental and theoretical investigations about the nonlinear vibrations of rectangular atomic force microscope cantilevers immersed in different liquids

Nonlinear flexural vibrations of rectangular atomic force microscope cantilever have been investigated by both the theoretical model and experimental works. As for the theoretical model, the Timoshenko beam theory which takes the rotatory inertia and shear deformation effects into consideration has been adopted. To increase the accuracy of the theoretical model, all necessary details for cantilever and sample surface have been taken into account. Differential quadrature method as a simple and fast numerical method has been used for solving the differential equations. During the investigation, the softening behavior was observed for all cases. It was also seen that raising the amplitude of vibrations led to a decrease in the nonlinear resonant frequency to linear resonant frequency ratio. The effects of different parameters such as normal and lateral contact stiffness, cantilever thickness, the angle between cantilever and sample surface and tip height in the presence of air as environment on the softening behavior were also examined. It was also demonstrated that increasing the lateral and normal contact stiffness, but decreasing the Timoshenko beam parameter would lead to an increase in the amplitude of vibrations for the first and second modes. The vibrational behavior of cantilever immersed in different liquids including water, methanol, acetone and carbon tetrachloride has been studied. Results show that increasing the liquid density reduces the nonlinear frequency. Furthermore, experimental works were compared with theoretical model for water and air environments. Results show good agreement.

A novel compliant mechanism based system to calibrate spring constant of AFM cantilevers

Calibrating spring constant of atomic force microscope (AFM) cantilevers is necessary for the measurement of micro/nano newton forces, which are commonly-used in the characterization of micro/nano functional surfaces and materials, cell manipulation, and many more applications. This paper presents a novel compliant mechanism based system to calibrate the spring constant of AFM cantilevers. The calibration system is mainly composed of a compliant suspension mechanism and an electromagnetic force actuator, where two kinds of compliant structures of “L” shape flexures and “Archimedes” planar flexures are assembled in parallel to achieve compact devices, respectively. The characteristics of the suspension mechanism are investigated by analytical model and finite element analysis (FEA). Furthermore, a prototype of the calibration system is established and experimental tests are carried out to verify the performance. An electromagnetic force actuator is employed to provide calibration force. Meanwhile, a capacitance sensor is utilized to monitor the displacement of the suspension mechanism. The calibration results of AFM cantilevers reveal that the compliant mechanism based calibration system has a good performance and it can calibrate the spring constant of AFM cantilevers accurately and effectively.

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

In this work, a high-resolution atomic force acoustic microscopy imaging technique is developed in order to obtain the local indentation modulus at the nanoscale level. The technique uses a model that gives a qualitative relationship between a set of contact resonance frequencies and the indentation modulus. It is based on white-noise excitation of the tip–sample interaction and uses system theory for the extraction of the resonance modes. During conventional scanning, for each pixel, the tip–sample interaction is excited with a white-noise signal. Then, a fast Fourier transform is applied to the deflection signal that comes from the photodiodes of the atomic force microscopy (AFM) equipment. This approach allows for the measurement of several vibrational modes in a single step with high 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 properties of a material. S-AFAM is implemented and compared with a conventional technique (resonance tracking-atomic force acoustic microscopy, RT-AFAM). A sample of a graphite film on a glass substrate is analyzed. S-AFAM can be implemented in any AFM system due to its reduced instrumentation requirements compared to conventional techniques.

(Invited) In-Situ Microscopy and Spectroscopy Probing of Li Dendrite Nucleation and Growth

Lithium (Li) metal has very low standard electrochemical redox potential and very high theoretical specific capacity, making it an ultimate anode material for rechargeable batteries. However, its application has been impeded by the formation of Li whiskers, which not only considerably consumes electrolyte and active Li, but also may lead to short-circuit of the battery. Tackling of these obstacles is limited by the elusive understanding on the intrinsic formation mechanisms of the Li whiskers and their growth behavior under the constraints from the separator. Here, by coupling an atomic force microscopy cantilever into a solid open-cell setup in environmental transmission electron microscopy, we directly captured the nucleation and growth behavior of Li whiskers under elastic constraint that mimics the effect of a separator. We show that Li deposition is initiated by a sluggish nucleation of a single crystalline Li particle with no preferential growth directions. Dramatically, we discovered that carbonate species in the initial solid electrolyte interphase that is very adjacent to the developing Li metal plays a decisive role in the subsequent formation of Li with a whisker morphology. Characteristically, the growing Li whisker, depending on both intrinsic and extrinsic conditions, can yield, buckle, kink, or stop (axial) growth under elastic constraint from the separator. These findings reveal the intrinsic cause and give a clear process on the formation and behavior of dendritic Li under stress, providing the much-needed insights for solving the Li whisker formation from the root cause rather than as currently containing it, and therefore potentially leading to the safe operation of Li metal anode in batteries.

Dynamic analysis of tapping mode atomic force microscope (AFM) for critical dimension measurement

Transient dynamics of tapping mode atomic force microscope (AFM) for critical dimension measurement are analyzed. A simplified nonlinear model of AFM is presented to describe the forced vibration of the micro cantilever-tip system with consideration of both contact and non-contact transient behavior for critical dimension measurement. The governing motion equations of the AFM cantilever system are derived from the developed model. Based on the established dynamic model, motion state of the AFM cantilever system is calculated utilizing the method of averaging with the form of slow flow equations. Further analytical solutions are obtained to reveal the effects of critical parameters on the system dynamic performance. In addition, features of dynamic response of tapping mode AFM in critical dimension measurement are studied, where the effects of equivalent contact stiffness, quality factor and resonance frequency of cantilever on the system dynamic behavior are investigated. Contact behavior between the tip and sample is also analyzed and the frequency drift in contact phase is further explored. Influence of the interaction between the tip and sample on the subsequent non-contact phase is studied with regard to different parameters. The dependence of the minimum amplitude of tip displacement and maximum phase difference on the equivalent contact stiffness, quality factor and resonance frequency are investigated. This study brings further insights into the dynamic characteristics of tapping mode AFM for critical dimension measurement, and thus provides guidelines for the high fidelity tapping mode AFM scanning.

Investigation of the interface in nanodielectrics using electrostatic force microscopy

The improved electrical properties of nanodielectrics compared to micro-filled and unfilled polymers are credited largely to the interfacial region surrounding the nanoparticles embedded in the polymer matrix. However, the interface is yet to be investigated extensively. In the present work, an experimental method using electrostatic force microscopy (EFM) has been proposed to probe the interface in nanocomposites. The EFM in the direct current (DC) mode maps the gradient of the electrostatic force to a phase shift in the oscillation of the AFM cantilever. Barium titanate (BaTiO 3 ) nanoparticles are used as fillers in epoxy resin in this work. A 3-D electrostatic model based on the finite element method (FEM) is developed to compute the expected phase shift based on the material properties of the polymer and its nanofillers. A match between experimental and computational EFM data yields an estimate for the dielectric constant and thickness of the proposed interface around each particle. Further, particle size distribution of the nanoparticles obtained using characterization techniques like transmission electron microscopy (TEM) and atomic force microscopy (AFM) are found to support the estimates obtained through the EFM model.

Covalent Attachment of Single Molecules for AFM-based Force Spectroscopy.

Atomic force microscopy (AFM)-based single molecule force spectroscopy is an ideal tool for investigating the interactions between a single polymer and surfaces. For a true single molecule experiment, covalent attachment of the probe molecule is essential because only then can hundreds of force-extension traces with one and the same single molecule be obtained. Many traces are in turn necessary to prove that a single molecule alone is probed. Additionally, passivation is crucial for preventing unwanted interactions between the single probe molecule and the AFM cantilever tip as well as between the AFM cantilever tip and the underlying surface. The functionalization protocol presented here is reliable and can easily be applied to a variety of polymers. Characteristic single molecule events (i.e., stretches and plateaus) are detected in the force-extension traces. From these events, physical parameters such as stretching force, desorption force and desorption length can be obtained. This is particularly important for the precise investigation of stimuli-responsive systems at the single molecule level. As exemplary systems poly(ethylene glycol) (PEG), poly(N-isopropylacrylamide) (PNiPAM) and polystyrene (PS) are stretched and desorbed from SiOx (for PEG and PNiPAM) and from hydrophobic self-assembled monolayer surfaces (for PS) in aqueous environment.

A Nanomechanical Genosensor Using Functionalized Cantilevers to Detect the Cancer Biomarkers miRNA-203 and miRNA-205

We report a nanomechanical genosensor based on an atomic force microscope (AFM) cantilever functionalized with complementary strands of miRNA-203 and miRNA-205, which are potential biomarkers of metastasis in head and neck squamous cell carcinomas (HNSCC), especially in cervical lymph nodes. Hybridization with the corresponding complementary strand led to cantilever deflections that increased almost linearly with the concentration of either miRNA-203 or miRNA-205 in the fluid cell where AFM experiments were made. The detection limit was ca. 95 nM and 97 nM for miRNA-203 or miRNA-205, respectively, with higher deflections observed for miRNA-205 due to the larger number of interaction groups during hybridization. Selectivity was proven by measuring negligible cantilever deflections for non-specific miRNA sequences. The cantilever functionalization process during genosensor design was confirmed by fluorescence microscopy and AFM imaging. The use of a single genosensor platform for detecting different miRNA molecules is advantageous for diagnosis and prognosis of cases where multiple biomarkers may be relevant, as in the case of HNSCC metastasis.

Fundamental Characteristics of Neuron Adhesion Revealed by Forced Peeling and Time-Dependent Healing

A current bottleneck in the advance of neurophysics is the lack of reliable methods to quantitatively measure the interactions between neural cells and their microenvironment. Here, we present an experimental technique to probe the fundamental characteristics of neuron adhesion through repeated peeling of well-developed neurite branches on a substrate with an atomic force microscopy cantilever. At the same time, a total internal reflection fluorescence microscope is also used to monitor the activities of neural cell adhesion molecules (NCAMs) during detaching. It was found that NCAMs aggregate into clusters at the neurite-substrate interface, resulting in strong local attachment with an adhesion energy of ∼0.1 mJ/m2 and sudden force jumps in the recorded force-displacement curve. Furthermore, by introducing a healing period between two forced peelings, we showed that stable neurite-substrate attachment can be re-established in 2–5 min. These findings are rationalized by a stochastic model, accounting for the breakage and rebinding of NCAM-based molecular bonds along the interface, and provide new insights into the mechanics of neuron adhesion as well as many related biological processes including axon outgrowth and nerve regeneration.

Opto-nanomechanical test instrument in mechanical characterization of DLC coated MEMS devices

Nanomechanical test instruments can precisely measure force and displacement and produce repeatable load-unload curves that can be used in characterizing mechanical behaviour at the nanoscale. In this study, a newly developed translucent nanomechanical test instrument was used in deriving reproducible stiffness values for ultra nano crystalline diamond (UNCD)-made atomic force microscope (AFM) cantilevers that are used for mechanical properties characterization of DLC films. The instrument which is calibrated according to the ISO-14577 standard is integrated with nano/micropositioners and multi-view optical microscopes to facilitate precise manipulation of those AFM cantilevers that were dozens of micrometers in size. Experimental results on UNCD-made AFM cantilever stiffness measurements are provided and compared with theoretical and batch production values.

Single-Molecule Manipulation in Zero-Mode Waveguides.

The mechanobiology of receptor-ligand interactions and force-induced enzymatic turnover can be revealed by simultaneous measurements of force response and fluorescence. Investigations at physiologically relevant high labeled substrate concentrations require total internal reflection fluorescence microscopy or zero mode waveguides (ZMWs), which are difficult to combine with atomic force microscopy (AFM). A fully automatized workflow is established to manipulate single molecules inside ZMWs autonomously with noninvasive cantilever tip localization. A protein model system comprising a receptor-ligand pair of streptavidin blocked with a biotin-tagged ligand is introduced. The ligand is pulled out of streptavidin by an AFM cantilever leaving the receptor vacant for reoccupation by freely diffusing fluorescently labeled biotin, which can be detected in single-molecule fluorescence concurrently to study rebinding rates. This work illustrates the potential of the seamless fusion of these two powerful single-molecule techniques.