Tip-sample Interaction Force Research Articles

True 3D-AFM sensor for nanometrology

A new three dimensional (3D) atomic force microscopic (AFM) probe, referred to as the 3D-Nanoprobe, is introduced. The 3D-Nanoprobe is realized by introducing flexure hinge structures to the cantilever of a conventional critical dimension AFM (CD-AFM) probe. It has quasi-isotropic stiffness in 3D directions and is thus more powerful for detecting 3D tip-sample interaction forces in AFM measurements. In addition, the stiffness of the 3D-Nanoprobe is balanced to the bending stiffness of slender CD-AFM tips, offering improved 3D sensitivity. In this paper, a design example of a 3D-Nanoprobe based on a CD-AFM probe with a tip nominal diameter of 70 nm is presented. The design parameters are optimized via analytic modelling and the finite element analysis (FEA) method. The simulation results indicate that the designed 3D-Nanoprobe has much better performance than that of the original CD-AFM probe, for instance, its stiffness’ anisotropy ratio (including the tip contribution) has been improved from 8:8:1 (x, y, z) to 0.9:0.9:1 (x, y, z). The probing sensitivity is improved by a factor of more than 106, 128 and 1.6 in x-, y- and z-direction, respectively. Moreover, the designed 3D-Nanoprobe has the first bending mode eigenfrequency of 84.4 kHz and the first torsional mode eigenfrequency of 346 kHz. The 3D-Nanoprobe has been manufactured by applying a focused ion beam (FIB) tool. Finally, to detect the full 3D interaction forces by the 3D-Nanoprobe, a new AFM-head prototype which consists of two independently adjustable dual optical levers have been developed.

Simultaneous atomic-resolution flexural and torsional imaging in liquid by frequency modulation atomic force microscopy

Liquid-environment frequency modulation atomic force microscopy (FM-AFM) is a powerful nanotool that can investigate phenomena occurring at solid–liquid interfaces in atomic-scale. To extend its function, we have developed FM-AFM system for simultaneous detection of vertical and lateral tip-sample interaction forces in liquid. Owing to tip-sample distance regulation by using a vertical force as a z-feedback signal, we succeeded in detecting a lateral force stably without full contact of a tip to a sample surface. This enabled simultaneous atomic-resolution flexural and torsional imaging in liquid. We demonstrated that the torsional images, which show different contrast pattern with that of the conventional topographic (flexural) images, emphasize specific structures of the topmost surface such as protruding atoms.

Real-Time Estimation of the Tip-Sample Interactions in Tapping Mode Atomic Force Microscopy With a Regularized Kalman Filter

The real-time and accurate measurement of tip-sample interaction forces in Tapping Mode Atomic Force Microscopy (TM-AFM) is a remaining challenge. This obstruction fundamentally stems from the causality of the physical systems. Since i) the input of the dynamic systems propagates to the output with some delay, and ii) , multiple different inputs can generate the same output, there exist no measurement or estimation technique that can estimate the force input of the systems in real-time without phase and amplitude distortion. However, an approximate and delayed estimation can still be possible. This article presents a general-purpose algorithm which aims to estimate an approximation of the force input of TM-AFM with minimum delay and error. For this reason, first, the input estimation problem is converted to an ill-posed state observation problem. Then, a Tikhonov-like regularization technique is applied to eliminate the ill-conditioning and estimate the force input using a linear Kalman filter. The proposed input observer is remarkably robust, real-time in the order of the sampling frequency, and applicable for any Linear Time Invariant (LTI) system with a (semi-) periodic process. Simulation and experimental results show that using the proposed algorithm with a wide-band AFM probe; one can determine the tip-sample forces with only a few percent error and a delay in the order of sampling time. Unlike the existing force estimation techniques for AFM, this algorithm does not require any prior knowledge of the force-distance relationship which can be very beneficial for the closed-loop control of AFM.

Amplitude Dependence of Resonance Frequency and its Consequences for Scanning Probe Microscopy.

With recent advances in scanning probe microscopy (SPM), it is now routine to determine the atomic structure of surfaces and molecules while quantifying the local tip-sample interaction potentials. Such quantitative experiments using noncontact frequency modulation atomic force microscopy is based on the accurate measurement of the resonance frequency shift due to the tip-sample interaction. Here, we experimentally show that the resonance frequency of oscillating probes used for SPM experiments change systematically as a function of oscillation amplitude under typical operating conditions. This change in resonance frequency is not due to tip-sample interactions, but rather due to the cantilever strain or geometric effects and thus the resonance frequency is a function of the oscillation amplitude. Our numerical calculations demonstrate that the amplitude dependence of the resonance frequency is an additional yet overlooked systematic error source that can result in nonnegligible errors in measured interaction potentials and forces. Our experimental results and complementary numerical calculations reveal that the frequency shift due to this amplitude dependence needs to be corrected even for experiments with active oscillation amplitude control to be able to quantify the tip-sample interaction potentials and forces with milli-electron volt and pico-Newton resolutions.

Adaptive Control of Atomic Force Microscope for Surface-Profile Estimation

This paper describes a methodology for designing an adaptive tracking controller of an atomic force microscope to estimate a surface profile of a sample. A microbeam of the atomic force microscope is modeled as an Euler-Bernoulli beam with single mode considered. A tip-sample interaction force used here is a piecewise function described by the attractive van der Waals force and the repulsive Derjaguin-Muller-Toporov force which can represent the indentation made by a tip of the microbeam into the sample surface. The adaptive-tracking controllers for both regions are designed based on adaptive control Lyapunov functions. With the driving and measured signals, the controlled acceleration is generated and superimposed onto the harmonic excitation and the estimated surface profile is obtained. If the tip of the microbeam taps harder on the sample surface, the more estimation error is obtained. To reduce the estimated surface-profile error, the regression model needs more higher-order terms to approximate the repulsive Derjaguin-Muller-Toporov force.

Measurement of Radial Elasticity and Original Height of DNA Duplex Using Tapping-Mode Atomic Force Microscopy.

Atomic force microscopy (AFM) can characterize nanomaterial elasticity. However, some one-dimensional nanomaterials, such as DNA, are too small to locate with an AFM tip because of thermal drift and the nonlinearity of piezoelectric actuators. In this study, we propose a novel approach to address the shortcomings of AFM and obtain the radial Young’s modulus of a DNA duplex. The elastic properties are evaluated by combining physical calculations and measured experimental results. The initial elasticity of the DNA is first assumed; based on tapping-mode scanning images and tip–sample interaction force simulations, the calculated elastic modulus is extracted. By minimizing the error between the assumed and experimental values, the extracted elasticity is assigned as the actual modulus for the material. Furthermore, tapping-mode image scanning avoids the necessity of locating the probe exactly on the target sample. In addition to elasticity measurements, the deformation caused by the tapping force from the AFM tip is compensated and the original height of the DNA is calculated. The results show that the radial compressive Young’s modulus of DNA is 125–150 MPa under a tapping force of 0.5–1.3 nN; its original height is 1.9 nm. This approach can be applied to the measurement of other nanomaterials.

Tip wear and tip breakage in high-speed atomic force microscopes

Tip abrasion is a critical issue particularly for high-speed atomic force microscopy (AFM). In this paper, a quantitative investigation on the tip abrasion of diamond-like-carbon (DLC) coated tips in a high-speed metrological large range AFM device has been detailed. Wear tests are conducted on four different surfaces made of silicon, niobium, aluminum and steel. During the tests, different scanning speeds up to 1 mm/s and different vertical load forces up to approximately 33.2 nN are applied. Various tip characterization techniques such as scanning electron microscopy (SEM) and AFM tip characterizers have been jointly applied to measure the tip form change precisely. The experimental results show that tip form changes abruptly rather than progressively, particularly when structures with steep sidewalls were measured. This result indicates the increased tip breakage risk in high-speed AFM measurements. To understand the mechanism of tip breakage, tip-sample interaction is modelled, simulated and experimentally verified. The results indicate that the tip-sample interaction force increases dramatically in measurement scenarios of steep surfaces.

Dynamical modeling of manipulation process in Trolling-Mode AFM

Dynamical lumped modeling of Trolling-mode AFM in manipulation of bio-samples is presented. The combination of high accuracy and compatibility with physiological conditions makes AFM a unique tool for studying biological materials in liquid medium. However, AFM microcantilever suffers from severe sensitivity degradation and noise intensification while operating in liquid; the large hydrodynamic drag between the cantilever and the surrounding liquid overwhelms the tip-sample interaction forces that are important in controlling the process. Therefore, an appropriate nanoneedle should be long enough to keep the cantilever out of liquid medium and short enough to be able to transmit the required force to push nanoparticle. Nonetheless, a long nanoneedle may deflect under the pushing force; therefore, its bending deflection should be accounted for in governing equations. Moreover, analytical and finite element stress analysis of nanoneedle and cantilever is performed to assure about their selected material and geometry. JKR theory is utilized to model contact mechanics between the needle/surface and the particle. Drag and meniscus forces are used to model the liquid media. Governing equations are solved using ODE45 and the system behavior is simulated. Critical conditions of sliding including critical time and force are obtained and changes of pushing force, needle deflection and indentation depths are illustrated. Also, effects of velocity variations are observed. Then, different heights for nanoneedle are tested and an appropriate one is selected for our purpose (to keep the needle out of liquid and transmit the force appropriately). The simulation is repeated for various biological particles and their behaviors are studied. At the end, the present simulation is validated through comparing the results with a previous work. This comparison shows that the simulation is reliable for the intended purpose.

Finite element modeling and analysis of an atomic force microscope cantilever beam coupled to a piezoceramic base actuator

Characterization and analysis of sample surfaces with nanometer order topologies is essential to study properties such as roughness, resistance, molecular arrangements, failure, among others. Therefore, in recent decades, atomic force microscope (AFM) has become an essential tool, since it has the ability to get 3D nanometer order images of surfaces from some predefined kind of interaction. In order to understand the dynamics and improve the operation of base-cantilever-tip-sample AFM systems, several mathematical models were proposed in the literature. However, it seems that there is still a need of representative and parametric models able to capture material and geometric properties of the cantilever beam and piezoceramic base actuator. Hence, this work focuses on the development and analysis of a parametric model capable of properly representing the dynamics of an AFM cantilever beam when subjected to realistic operation conditions, using a finite element model for the cantilever beam and accounting for translational and rotational inertia of the probe tip and for the piezoceramic actuator that excites and controls the beam motion. All material and geometrical properties for the system (cantilever beam, probe tip and piezoceramic actuator) can be parametrized. Experimental SEM images and frequency responses of a real AFM cantilever beam are used to verify the model and also to define its parameters with very satisfactory results. A dynamic analysis of the cantilever beam when subjected to tip-sample nonlinear interaction forces is performed to develop a proper reduced-order model. The interaction forces were modeled using Lennard Jones potentials. Then, an analysis of the dynamic response of the cantilever beam for varying tip-sample initial distances is performed. Besides the appearance of the expected nonlinear behavior due to the tip-sample interaction forces, it is observed that the closer the sample is to the beam tip, the smaller is the tip displacement amplitude. Based on this observation, an analysis is performed to assess the correlation between the tip displacement and the surface topology of a diamond sample with satisfactory results.

Effect of Inhibitor Modifications on Initial Localized Dealloying of Metallic Alloy Surfaces

Despite a substantial number of reports on corrosion testing is available, only a few projects aim to understand the basic processes driving materials degradation. A special type of corrosion, localized dealloying, takes place on metallic alloy surfaces modified with self-assembled monolayers (SAMs) of organic inhibitors[1-2]. Corrosion initiation at the nanoscale can be addressed by controlling the spatial distribution and molecular organization of inhibitor-molecule SAMs at nano and micro length scales. We use micro-contact printing on model ultra-flat gold surfaces and obtain well-defined complex organic layers following a multi-step approach [3]. This approach was applied on locally atomically flat Cu3Au (100) surfaces to study initial localized dealloying which results in the initiation of localized dealloying being strongly dependent on the nanoscale surface morphology (Figure 1) [4]. In addition, different organic inhibitors containing -SH (thiol end) films were subsequently applied on polycrystalline Cu and CuZn alloys to analyse inhibitor film stabilities. Force Spectroscopy of Atomic Force Microscopy (FS-AFM) provides a stability status of such inhibitor layers by analysing AFM tip sample force interaction on inhibitor-modified metallic surfaces.

Force and time-dependent self-assembly, disruption and recovery of supramolecular peptide amphiphile nanofibers

Biological feedback mechanisms exert precise control over the initiation and termination of molecular self-assembly in response to environmental stimuli, while minimizing the formation and propagation of defects through self-repair processes. Peptide amphiphile (PA) molecules can self-assemble at physiological conditions to form supramolecular nanostructures that structurally and functionally resemble the nanofibrous proteins of the extracellular matrix, and their ability to reconfigure themselves in response to external stimuli is crucial for the design of intelligent biomaterials systems. Here, we investigated real-time self-assembly, deformation, and recovery of PA nanofibers in aqueous solution by using a force-stabilizing double-pass scanning atomic force microscopy imaging method to disrupt the self-assembled peptide nanofibers in a force-dependent manner. We demonstrate that nanofiber damage occurs at tip-sample interaction forces exceeding 1 nN, and the damaged fibers subsequently recover when the tip pressure is reduced. Nanofiber ends occasionally fail to reconnect following breakage and continue to grow as two individual nanofibers. Energy minimization calculations of nanofibers with increasing cross-sectional ellipticity (corresponding to varying levels of tip-induced fiber deformation) support our observations, with high-ellipticity nanofibers exhibiting lower stability compared to their non-deformed counterparts. Consequently, tip-mediated mechanical forces can provide an effective means of altering nanofiber integrity and visualizing the self-recovery of PA assemblies.

Electrostatically actuated encased cantilevers.

Background: Encased cantilevers are novel force sensors that overcome major limitations of liquid scanning probe microscopy. By trapping air inside an encasement around the cantilever, they provide low damping and maintain high resonance frequencies for exquisitely low tip–sample interaction forces even when immersed in a viscous fluid. Quantitative measurements of stiffness, energy dissipation and tip–sample interactions using dynamic force sensors remain challenging due to spurious resonances of the system.Results: We demonstrate for the first time electrostatic actuation with a built-in electrode. Solely actuating the cantilever results in a frequency response free of spurious peaks. We analyze static, harmonic, and sub-harmonic actuation modes. Sub-harmonic mode results in stable amplitudes unaffected by potential offsets or fluctuations of the electrical surface potential. We present a simple plate capacitor model to describe the electrostatic actuation. The predicted deflection and amplitudes match experimental results within a few percent. Consequently, target amplitudes can be set by the drive voltage without requiring calibration of optical lever sensitivity. Furthermore, the excitation bandwidth outperforms most other excitation methods.Conclusion: Compatible with any instrument using optical beam deflection detection electrostatic actuation in encased cantilevers combines ultra-low force noise with clean and stable excitation well-suited for quantitative measurements in liquid, compatible with air, or vacuum environments.

Direct visualization of single virus restoration after damage in real time.

We use the nano-dissection capabilities of atomic force microscopy to induce structural alterations on individual virus capsids in liquid milieu. We fracture the protein shells either with single nanoindentations or by increasing the tip-sample interaction force in amplitude modulation dynamic mode. The normal behavior is that these cracks persist in time. However, in very rare occasions they self-recuperate to retrieve apparently unaltered virus particles. In this work, we show the topographical evolution of three of these exceptional events occurring in T7 bacteriophage capsids. Our data show that single nanoindentation produces a local recoverable fracture that corresponds to the deepening of a capsomer. In contrast, imaging in dynamic mode induced cracks that separate the virus morphological subunits. In both cases, the breakage patterns follow intratrimeric loci.

Multi-frequency Atomic Force Microscopy based on enhanced internal resonance of an inner-paddled cantilever

In this work, we study the performance of a new cantilever design during multi-frequency tapping mode Atomic Force Microscopy (AFM). The system consists of a base cantilever with an inner paddle which, under harmonic excitation, vibrates like a system of linearly coupled oscillators engaging simultaneously a lower, in-phase and a higher, out-of-phase resonant mode. The cantilever is designed so that the 2nd mode frequency (i.e., the out-of-phase eigenfrequency) coincides with an integer multiple of the fundamental mode frequency, providing the necessary conditions for realization of internal resonance. During tapping mode, the nonlinear tip-sample force activates the internal resonance and thereby amplifies the out-of-phase resonant mode. We study energy transfer from the lower to the higher mode for different cantilever designs in order to optimize the internal resonance and the amplification of the high-frequency component of the measured response. Numerical and experimental examination of the inner-paddled cantilever performance confirms that a 1:2 internal resonance is optimal. AFM scans of cyanobacteria are taken, and the higher mode observables (amplitude and phase) along with the phase of the lower mode reveal differences in branch selection caused by variations in the stiffness that are not detected by the topographical data. In a computational simulation of an AFM scan across a flat sample with stratified stiffness, we show that the amplitude of the higher mode is significantly more sensitive to variations in Young’s modulus than the phase of the lower mode. Further, unlike for a conventional cantilever, we show that the phase of the lower mode indeed depends on the sample’s Young’s modulus in the absence of a dissipative component in the tip-sample interaction force.

Review: Tip-based vibrational spectroscopy for nanoscale analysis of emerging energy materials

Vibrational spectroscopy is one of the key instrumentations that provide non-invasive investigation of structural and chemical composition for both organic and inorganic materials. However, diffraction of light fundamentally limits the spatial resolution of far-field vibrational spectroscopy to roughly half the wavelength. In this article, we thoroughly review the integration of atomic force microscopy (AFM) with vibrational spectroscopy to enable the nanoscale characterization of emerging energy materials, which has not been possible with far-field optical techniques. The discussed methods utilize the AFM tip as a nanoscopic tool to extract spatially resolved electronic or molecular vibrational resonance spectra of a sample illuminated by a visible or infrared (IR) light source. The absorption of light by electrons or individual functional groups within molecules leads to changes in the sample’s thermal response, optical scattering, and atomic force interactions, all of which can be readily probed by an AFM tip. For example, photothermal induced resonance (PTIR) spectroscopy methods measure a sample’s local thermal expansion or temperature rise. Therefore, they use the AFM tip as a thermal detector to directly relate absorbed IR light to the thermal response of a sample. Optical scattering methods based on scanning near-field optical microscopy (SNOM) correlate the spectrum of scattered near-field light with molecular vibrational modes. More recently, photo-induced force microscopy (PiFM) has been developed to measure the change of the optical force gradient due to the light absorption by molecular vibrational resonances using AFM’s superb sensitivity in detecting tip-sample force interactions. Such recent efforts successfully breech the diffraction limit of light to provide nanoscale spatial resolution of vibrational spectroscopy, which will become a critical technique for characterizing novel energy materials.

Material discrimination and mixture ratio estimation in nanocomposites via harmonic atomic force microscopy.

Harmonic atomic force microscopy (AFM) was employed to discriminate between different materials and to estimate the mixture ratio of the constituent components in nanocomposites. The major influencing factors, namely amplitude feedback set-point, drive frequency and laser spot position along the cantilever beam, were systematically investigated. Employing different set-points induces alternation of tip–sample interaction forces and thus different harmonic responses. The numerical simulations of the cantilever dynamics were well-correlated with the experimental observations. Owing to the deviation of the drive frequency from the fundamental resonance, harmonic amplitude contrast reversal may occur. It was also found that the laser spot position affects the harmonic signal strengths as expected. Based on these investigations, harmonic AFM was employed to identify material components and estimate the mixture ratio in multicomponent materials. The composite samples are composed of different kinds of nanoparticles with almost the same shape and size. Higher harmonic imaging offers better information on the distribution and mixture of different nanoparticles as compared to other techniques, including topography and conventional tapping phase. Therefore, harmonic AFM has potential applications in various fields of nanoscience and nanotechnology.

Electroviscous Dissipation in Aqueous Electrolyte Films with Overlapping Electric Double Layers.

We use dynamic atomic force microscopy (AFM) to investigate the forces involved in squeezing out thin films of aqueous electrolyte between an AFM tip and silica substrates at variable pH and salt concentration. From amplitude and phase of the AFM signal we determine both conservative and dissipative components of the tip sample interaction forces. The measured dissipation is enhanced by up to a factor of 5 at tip–sample separations of ≈ one Debye length compared to the expectations based on classical hydrodynamic Reynolds damping with bulk viscosity. Calculating the surface charge density from the conservative forces using Derjaguin–Landau–Verwey–Overbeek (DLVO) theory in combination with a charge regulation boundary condition we find that the viscosity enhancement correlates with increasing surface charge density. We compare the observed viscosity enhancement with two competing continuum theory models: (i) electroviscous dissipation due to the electrophoretic flow driven by the streaming current that is generated upon squeezing out the counterions in the diffuse part of the electric double layer, and (ii) visco-electric enhancement of the local water viscosity caused by the strong electric fields within the electric double layer. While the visco-electric model correctly captures the qualitative trends observed in the experiments, a quantitative description of the data presumably requires more sophisticated simulations that include microscopic aspects of the distribution and mobility of ions in the Stern layer.

A combined averaging and frequency mixing approach for force identification in weakly nonlinear high-Q oscillators: Atomic force microscope

We present a polynomial force reconstruction of the tip-sample interaction force in Atomic Force Microscopy. The method uses analytical expressions for the slow-time amplitude and phase evolution, ...

Imaging contrast and tip-sample interaction of non-contact amplitude modulation atomic force microscopy with Q-control

Active quality factor (Q) exhibits many promising properties in dynamic atomic force microscopy. Energy dissipation and image contrasts are investigated in the non-contact amplitude modulation atomic force microscopy (AM-AFM) with an active Q-control circuit in the ambient air environment. Dissipated power and virial were calculated to compare the highly nonlinear interaction of tip-sample and image contrasts with different Q gain values. Greater free amplitudes and lower effective Q values show better contrasts for the same setpoint ratio. Active quality factor also can be employed to change tip-sample interaction force in non-contact regime. It is meaningful that non-destructive and better contrast images can be realized in non-contact AM-AFM by applying an active Q-control to the dynamic system.

High-speed dynamic-mode atomic force microscopy imaging of polymers: an adaptive multiloop-mode approach.

Adaptive multiloop-mode (AMLM) imaging to substantially increase (over an order of magnitude) the speed of tapping-mode (TM) imaging is tested and evaluated through imaging three largely different heterogeneous polymer samples in experiments. It has been demonstrated that AMLM imaging, through the combination of a suite of advanced control techniques, is promising to achieve high-speed dynamic-mode atomic force microscopy imaging. The performance, usability, and robustness of the AMLM in various imaging applications, however, is yet to be assessed. In this work, three benchmark polymer samples, including a PS–LDPE sample, an SBS sample, and a Celgard sample, differing in feature size and stiffness of two orders of magnitude, are imaged using the AMLM technique at high-speeds of 25 Hz and 20 Hz, respectively. The comparison of the images obtained to those obtained by using TM imaging at scan rates of 1 Hz and 2 Hz showed that the quality of the 25 Hz and 20 Hz AMLM imaging is at the same level of that of the 1 Hz TM imaging, while the tip–sample interaction force is substantially smaller than that of the 2 Hz TM imaging.