Analysis of dynamic cantilever behavior in tapping mode atomic force microscopy

Tapping mode atomic force microscopy (AFM) provides phase images in addition to height and amplitude images. Although the behavior of tapping mode AFM has been investigated using mathematical modeling, comprehensive understanding of the behavior of tapping mode AFM still poses a significant challenge to the AFM community, involving issues such as the correct interpretation of the phase images. In this paper, the cantilever's dynamic behavior in tapping mode AFM is studied through a three dimensional finite element method. The cantilever's dynamic displacement responses are firstly obtained via simulation under different tip‐sample separations, and for different tip‐sample interaction forces, such as elastic force, adhesion force, viscosity force, and the van der Waals force, which correspond to the cantilever's action upon various different representative computer‐generated test samples. Simulated results show that the dynamic cantilever displacement response can be divided into three zones: a free vibration zone, a transition zone, and a contact vibration zone. Phase trajectory, phase shift, transition time, pseudo stable amplitude, and frequency changes are then analyzed from the dynamic displacement responses that are obtained. Finally, experiments are carried out on a real AFM system to support the findings of the simulations. Microsc. Res. Tech. 78:935–946, 2015. © 2015 Wiley Periodicals, Inc.     

Molecular dynamics simulation of the contact process in AFM surface observations

In the present work, several molecular dynamics simulations have been performed to clarify dynamically the contact mechanism between the specimen surface and probe tip in surface observations by an atomic force microscope (SFM) or friction force microscope (FFM). In the simulation, a three‐dimensional model is proposed where the specimen and the probe are assumed to consist of monocrystalline copper and rigid diamond or a carbon atom, respectively. The effect of the cantilever stiffness of the AFM/FFM is also taken into consideration. The surface observation process is simulated on a well‐defined Cu{100} surface. From the simulation results it has been verified that the surface images and the two‐dimensional atomic‐scale stick‐slip phenomenon, just as is the case for real AFM/FFM surface observations, can be detected from the spring force acting on the cantilever. From the evaluation of the behaviour of specimen surface atoms, the importance of the specimen stiffness in deciding the cantilever properties can also be understood. The influence of the probe tip shape on the force images is also evaluated. From the results it can be verified that the behaviour of the specimen surface atoms as well as the solid surface images in AFM/FFM surface observations can be understood using the molecular dynamics simulation of the model presented.     

Study of the tip mass and interaction force effects on the frequency response and mode shapes of the AFM cantilever

The vibrational characteristics of an atomic force microscope (AFM) cantilever beam play a key role in dynamic mode of the atomic force microscope. As the oscillating AFM cantilever tip approaches the sample, the tip–sample interaction force influences the cantilever dynamics. In this paper, we present a detailed theoretical analysis of the frequency response and mode shape behavior of a cantilever beam in the dynamic mode subject to changes in the tip mass and the interaction regime between the AFM cantilever system and the sample. We consider a distributed parameter model for AFM and use Euler–Bernoulli method to derive an expression for AFM characteristics equation contains tip mass and interaction force terms. We study the frequency response of AFM cantilever under variations of interaction force between AFM tip and sample. Also, we investigate the effect of tip mass on the frequency response and also the quality factor and spring constant of each eigenmodes of AFM micro-cantilever. In addition, the mode shape analysis of AFM cantilever under variations of tip mass and interaction force is investigated. This will incorporate the presentation of explicit analytical expressions and numerical analysis. The results show that by considering the tip mass, the resonance frequencies of the cantilever are decreased. Also, the tip mass has a significant effect on the mode shape of the higher eigenmodes of the AFM cantilever. Moreover, tip mass affects the quality factor and spring constant of each modes.     

Unstable amplitude and noisy image induced by tip contamination in dynamic force mode atomic force microscopy

Liquid 1-decanethiol was confined on an atomic force microscope (AFM) tip apex and the effect was investigated by measuring amplitude-distance curves in dynamic force mode. Within the working distance in the dynamic force mode AFM, the thiol showed strong interactions bridging between a gold-coated probe tip and a gold-coated Si substrate, resulting in unstable amplitude and noisy AFM images. We show that under such a situation, the amplitude change is dominated by the extra forces induced by the active material loaded on the tip apex, overwhelming the amplitude change caused by the geometry of the sample surface, thus resulting in noise in the image the tip collects. We also show that such a contaminant may be removed from the apex by pushing the tip into a material soft enough to avoid damage to the tip.     

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.     

Complex dynamics of carbon nanotube probe tips

Carbon nanotube (CNT) tips in tapping mode atomic force microscopy (AFM) enable very high-resolution imaging, measurements, and manipulation at the nanoscale. We present recent results based on experimental analysis that yield new insights into the dynamics of CNT probe tips in tapping mode AFM. Experimental measurements are presented of the frequency response and dynamic amplitude-distance data of a high-aspect-ratio multi-walled (MW) CNT tip. Higher harmonics of the microcantilever are measured in frequency ranges corresponding to attractive regime and the repulsive regime where the CNT buckles dynamically. Surface scanning is performed using a MWCNT tip on a SiO(2) grating to verify the imaging instabilities associated with MWCNT buckling when used with normal control schemes in the tapping mode. Lastly, the choice of optimal setpoints for tapping mode control using CNT tip are discussed using the experimental results.     

In-plane contributions to phase contrast in intermittent contact atomic force microscopy

Contrast in the phase response of intermittent-contact atomic force microscopy (IC-AFM) reveals in-plane structural and mechanical properties of polymer monolayers. This result is unexpected, as IC-AFM has previously only been considered as a probe of out-of-plane properties. Until now, AFM measurements of nanoscale in-plane properties have employed contact mode techniques. In-plane property measurements are possible with intermittent contact AFM because there is a small but significant component of tip motion parallel to the sample surface. This in-plane component of tip displacement is virtually universal in AFM, implying that oscillating-tip techniques generally are sensitive to in-plane material properties. We present a simple Hertzian model of intermittent-contact AFM that includes such an in-plane displacement.     

原子力显微镜管式扫描器运动学建模与误差分析

针对样本扫描模式原子力显微镜,对其管式扫描器-样本-探针系统进行了运动学分析,建立了该系统的运动学模型,该模型表明:对于给定原子力显微镜扫描器,样本上与探针接触点的横向和纵向位移取决于探针尖端相对于扫描管轴心的偏置量、所加电压(或名义扫描范围)及样本厚度。据此模型,对由于弯曲运动模式所产生的两种重要误差—交叉耦合误差及扫描范围误差进行了定量分析,分析表明:扫描范围误差主要受样本厚度及名义扫描范围影响,而Z向交叉耦合误差主要受探针偏置量及名义扫描范围影响,实验验证了所建立的运动学模型和误差计算公式的正确性;另外,还提出了相应的减小误差的方法。     

Direct deformation study of AFM probe tips modified by hydrophobic alkylsilane self-assembled monolayers

The in-use wear of atomic force microscopy (AFM) probe tips is crucial for the reliability of AFM measurements. Increase of tip size for several nanometers is difficult to monitor but it can already taint subsequent AFM data. We have developed a method to study the shape evolution of AFM probe tips in nanometer scale. This approach provides direct comparison of probe shape profiles, and thus can help in evaluation of the level of tip damage and quality of acquired AFM data. Consequently, the shape degradation of probes modified by hydrophobic alkylsilane self-assembled monolayers (SAMs) was studied. The tip wear length and wear volume were adopted to quantitatively verify the effectiveness of hydrophobic coatings. When compared with their silicon counterparts, probes modified by SAM materials exhibit superior wear-resistant behavior in tapping mode scans.     

Analysis of simulated scanning of atomic-scale silicon surface by atomic force microscopy

This study constructs a contact-mode atomic force microscopy (AFM) simulation measurement model with constant force mode to simulate and analyze the outline scanning measurement by AFM. The simulation method is that when the probe passes the surface of sample, the action force of the atom of sample received by the atom of the probe can be calculated by using Morse potential. Through calculation, the equivalent force on the cantilever of probe can be acquired. By using the deflection angle equation for the cantilever of probe developed and inferred by this study, the deflection angle of receiving action force can be calculated. On the measurement point, as the deflection angle reaches a fixed deflection angle, the scan height of this simulation model can be acquired. By scanning in the right order, the scan curve of the simulation model can be obtained. By using this simulation measurement model, this study simulates and analyzes the scanning of atomic-scale surface outline. Meanwhile, focusing on the tip radii of different probes, the concept of sensitivity analysis is employed to investigate the effects of the tip radius of probe on the atomic-scale surface outline. As a result, it is found from the simulation on the atomic-scale surface that within the simulation scope of this study, when the tip radius of probe is greater than 12 nm, the effects of single atom on the scan curve of AFM can be better decreased or eliminated.     

Non-optical tip–sample distance control method for scanning near-field optical microscopy using a piezoresistive micro cantilever

A piezoresistive micro cantilever is applied to monitor the displacement of an optical fibre probe and to control tip–sample distance. The piezoresistive cantilever was originally made for a self-sensitive atomic force microscopy (AFM) probe and has dimensions of 400 µm length, 50 µm width and 5 µm thickness with a resistive strain sensor at the bottom of the cantilever. We attach the piezoresistive cantilever tip to the upper side of a vibrating bent optical fibre probe and monitor the resistance change amplitude of the strain sensor caused by the optical fibre displacement. By using this resistance change to control the tip–sample distance, the two-cantilever system successfully provides topographic and near-field optical images of standard samples in a scanning near-field optical microscopy (SNOM)/AFM system. A resonant characteristic of the two-cantilever system is also simulated using a mechanical model, and the results of simulation correspond to the experimental results of resonance characteristics.     

Intermittency in amplitude modulated dynamic atomic force microscopy

From a mathematical point of view, the atomic force microscope (AFM) belongs to a special class of continuous time dynamical systems with intermittent impact collisions. Discontinuities of the velocity result from the collisions of the tip with the surface. Transition to chaos in non-linear systems can occur via the following four routes: bifurcation cascade, crisis, quasi-periodicity, and intermittency. For the AFM period doubling and period-adding cascades are well established. Other routes into chaos, however, also may play an important role. Time series data of a dynamic AFM experiment indicates a chaotic mode that is related to the intermittency route into chaos. The observed intermittency is characterized as a type III intermittency. Understanding the dynamics of the system will help improve the overall system performance by keeping the operation parameters of dynamic AFM in a range, where chaos can be avoided or at least controlled.     

VEDA: a web-based virtual environment for dynamic atomic force microscopy

We describe here the theory and applications of virtual environment dynamic atomic force microscopy (VEDA), a suite of state-of-the-art simulation tools deployed on nanoHUB (www.nanohub.org) for the accurate simulation of tip motion in dynamic atomic force microscopy (dAFM) over organic and inorganic samples. VEDA takes advantage of nanoHUB's cyberinfrastructure to run high-fidelity dAFM tip dynamics computations on local clusters and the teragrid. Consequently, these tools are freely accessible and the dAFM simulations are run using standard web-based browsers without requiring additional software. A wide range of issues in dAFM ranging from optimal probe choice, probe stability, and tip-sample interaction forces, power dissipation, to material property extraction and scanning dynamics over hetereogeneous samples can be addressed.     

A torsional resonance mode AFM for in-plane tip surface interactions

Changing the method of tip/sample interaction leads to contact, tapping and other dynamic imaging modes in atomic force microscopy (AFM) feedback controls. A common characteristic of these feedback controls is that the primary control signals are based on flexural deflection of the cantilever probes, statically or dynamically. We introduce a new AFM mode using the torsional resonance amplitude (or phase) to control the feedback loop and maintain the tip/surface relative position through lateral interaction. The torsional resonance mode (TRmode™) provides complementary information to tapping mode for surface imaging and studies. The nature of tip/surface interaction of the TRmode facilitates phase measurements to resolve the in-plane anisotropy of materials as well as measurements of dynamic friction at nanometer scale. TRmode can image surfaces interleaved with TappingMode™ with the same probe and in the same area. In this way we are able to probe samples dynamically in both vertical and lateral dimensions with high sensitivity to local mechanical and tribological properties. The benefit of TRmode has been proven in studies of water adsorption on HOPG surface steps. TR phase data yields approximately 20 times stronger contrast than tapping phase at step edges, revealing detailed structures that cannot be resolved in tapping mode imaging. The effect of sample rotation relative to the torsional oscillation axis of the cantilever on TR phase contrast has been observed. Tip wear studies of TRmode demonstrated that the interaction forces between tip and sample could be controlled for minimum tip damage by the feedback loop.     

一维矩形光栅AFM图像盲探针表面重建模拟研究

探针结构参数的合理选取将直接决定扫描图像及其盲探针修正图像的失真程度。基于此,以一维矩形模拟光栅为典型案例,对该模拟光栅的原子力显微镜(AFM)扫描成像过程与盲探针修正过程进行了仿真,阐明了探针结构参数对扫描成像过程与盲探针修正过程的影响规律。通过建立线宽变化度与半高宽相结合的图像重建误差评价指标,确定了针对该模拟光栅的AFM探针建议结构参数,并取得了良好的光栅图像重建效果。研究表明,应用线宽变化度结合半高宽来综合评价光栅的AFM测量和图像重建过程,有利于提升实际光栅AFM图像盲探针重建的准确度。     

Fabrication of various tip-size AFM probes for evaluating single-molecular retraction force between actin and anti-actin

The authors fabricated a probe tip with various sizes and examined the size dependency of the probe tip on the distribution of retraction forces between actin and anti-actin. Probe tips of various sizes were fabricated by two-photon polymerization methods on a micro cantilever of an atomic force microscope (AFM). The authors succeeded in fabricating a spherical tip having a smooth surface and the tip size varied between φ 0.8 and 5.5 μm. Anti-actin was immobilized on the fabricated probe tips and force curves were measured against an actin-immobilized mica substrate by AFM to analyze the retraction forces. The histograms of retraction forces showed that the single-molecular retraction force between actin and anti-actin was ca. 350–400 pN. It was observed that the average retraction forces for each tip size correlated with the square of the tip radius.     

Tip radius effect of AFM probe on K4Nb6O17·3H2O nanosheets groove machining accuracy

This paper presents a technique for groove machining of potassium niobate nanosheets using an atomic force microscope (AFM). Groove machining operations are performed using super sharp silicon (SSS) probes. The tip radius of these probes is less than 5 nm and is one-third that of a conventional silicon (Si) probe. The results obtained using these probes are compared with those obtained using a Si probe, in order to examine the tip radius effects of the AFM probe on groove machining accuracy, i.e., coarseness of the machined groove. These results show that the degree of coarseness of the machined groove for varying machining loads with the SSS probe was much worse than that with the Si probe. Thus, groove machining with the SSS probe was more difficult to control with varying machining loads. We propose a groove fabrication model that considers the stochastic energy and difference in tip radius of the AFM probe. Using our groove fabrication model, changes in the coarseness of the machined groove for varying machining loads can be predicted.     

Computational models of a nano probe tip for static behaviors

It is difficult to predict the measurement bias arising from the compliance of the atomic force microscope (AFM) probe. The issue becomes particularly important in this situation where nanometer uncertainties are sought for measurements with dimensional probes composed of flexible carbon nanotubes mounted on AFM cantilevers. We have developed a finite element model for simulating the mechanical behavior of AFM cantilevers with carbon nanotubes attached. Spring constants of both the nanotube and cantilever in two directions are calculated using the finite element method with known Young's moduli of both silicon and multiwall nanotube as input data. Compliance of the nanotube-attached AFM probe tip may be calculated from the set of spring constants. This paper presents static models that together provide a basis to estimate uncertainties in linewidth measurement using nanotubes. In particular, the interaction between a multiwall nanotube tip and a silicon sample is modeled using the Lennard-Jones theory. Snap-in and snap-out of the probe tip in a scanning mode are calculated by integrating the compliance of the probe and the sample-tip interacting force model. Cantilever and probe tip deflections and points of contact are derived for both horizontal scanning of a plateau and vertically scanning of a wall. The finite element method and the Lennard-Jones model provide a means to analyze the interaction of the probe and sample and measurement uncertainty, including actual deflection and the gap between the probe tip and the measured sample surface.     

Lateral Displacement of an AFM Tip Observed by In-Situ TEM/AFM Combined Microscopy: The Effect of the Friction in AFM

When the lateral displacement of an AFM tip due to friction is comparable to or larger than the scan size, for example during atomic-scale friction measurement, the interpretation of the friction image is different from the situation where the scan size is much larger than the lateral displacement of the tip and the image is a simple direct mapping of the friction value. This is because, due to the lateral displacement of the tip, the tip is not at the position where the scan indicates, as can be clearly observed by an in-situ TEM/AFM combined microscopy and atomic-scale friction analysis. This lateral displacement of the tip at the nanometer scale affects the shape of the force-distance curve. We discuss the effect of the tip lateral displacement in AFM data and its normal load dependence.     

Nanotribology: tip–sample wear under adhesive contact

In this report, the irreversible variation of mass of the probe tip of an atomic force microscope (AFM) is considered from theoretical and numerical points of view through statistical methods. The tip–sample interaction due to the intermittent-contact operating mode of an AFM is modelled as a double-well potential where the wear mechanism, which reveals itself as mass sticking to the probe tip, is described as a transition between the two potential wells. We evaluate the interaction of a silicon nitride AFM/FFM tip with gold in order to compare the results with those obtained from previous experimental and numerical studies.