Direct measurement of tapping force with a cantilever deflection force sensor

An experimental set up dedicated to the measurement of atomic force microscope tapping force was developed. In the set-up, a standard TappingMode™ probe cantilever was used to tap another cantilever equipped with its own low noise and high sensitivity deflection detection system for force measurement. The amplitude and phase change of the tapping lever as well as the deflection of the sensing lever were simultaneously recorded as a function of tip/surface separation. Since the deflection of the sensing cantilever reflects the average force over one interaction cycle, we measured the total average force quantitatively after calibrating the spring constant and deflection sensitivity of the sensing lever. Considerable effort was made to achieve the same force curve in the tapping force measurement as occur during imaging of conventional samples such that the detected tapping force reflects the same interaction of the imaging process.     

Phase imaging quality improvement by modification of AFM probes’ cantilever

Imaging of the surface of materials by atomic force microscopy under tapping and phase imaging mode, with use of modified probes is addressed. In this study, the circularly shaped holes located in varying distance from the probe base, were cut out by focused ion beam. Such modification was a consequence of the results of the previous experiments (probe tip sharpening and cantilever thinning) where significant improvement of image quality in tapping and phase imaging mode has been revealed. The solution proposed herein gives similar results, but is much simpler from the technological point of view. Shorter exposition time of the tip onto gallium ions during FIB processing allows to reduce material degradation. The aim of this modification was to change harmonic oscillators’ properties in the simplest and fastest way, to obtain stronger signal for higher resonant frequencies, which can be advantageous for improving the quality of imaging in PI mode. Probes shaped in that way were used for AFM investigations with Bruker AFM nanoscope 8. As a testing material, titanium roughness standard sample, supplied by Bruker, was used. The results have shown that the modifications performed within these studies influence the oscillation of the probes, which in some cases may result in deterioration of the imaging quality under tapping mode for one or both self‐resonant frequencies. However, phase imaging results obtained using modified probes are of higher quality. The numerical simulations performed by application of finite element method were used to explain the results obtained experimentally. Phenomenon described within this study allows to apply developed modelling methodology for prediction of effects of various modifications on the probes' tip, and as a result, to predict how proposed modifications will affect AFM imaging quality.     

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.     

Investigating ultra-thin lubricant layers using resonant friction force microscopy

The ultrasonic friction mode of an atomic force microscope is a scanning probe technique allowing one to analyze the load and velocity dependence of friction. The technique is based on evaluation of the resonance behavior of an AFM cantilever when in contact with a vibrating sample surface. The effect of load and lateral displacement of the sample surface on the shape of the torsional resonance spectra of the AFM cantilever is evaluated under dry and lubricated sliding conditions. A characteristic flattening of the torsional resonance curve has been observed at large surface displacements, resulting from the onset of sliding friction in the AFM cantilever–sample surface contact. An analytical model describing torsional cantilever vibrations in Hertzian contact with a sample surface is presented, and numerical simulations have been carried out in order to confirm that the flattening of the resonance curve occurs with the onset of the sliding friction in the contact.     

Improving tapping mode atomic force microscopy with piezoelectric cantilevers

This article summarizes improvements to the speed, simplicity and versatility of tapping mode atomic force microscopy (AFM). Improvements are enabled by a piezoelectric microcantilever with a sharp silicon tip and a thin, low-stress zinc oxide (ZnO) film to both actuate and sense deflection. First, we demonstrate self-sensing tapping mode without laser detection. Similar previous work has been limited by unoptimized probe tips, cantilever thicknesses, and stress in the piezoelectric films. Tests indicate self-sensing amplitude resolution is as good or better than optical detection, with double the sensitivity, using the same type of cantilever. Second, we demonstrate self-oscillating tapping mode AFM. The cantilever's integrated piezoelectric film serves as the frequency-determining component of an oscillator circuit. The circuit oscillates the cantilever near its resonant frequency by applying positive feedback to the film. We present images and force-distance curves using both self-sensing and self-oscillating techniques. Finally, high-speed tapping mode imaging in liquid, where electric components of the cantilever require insulation, is demonstrated. Three cantilever coating schemes are tested. The insulated microactuator is used to simultaneously vibrate and actuate the cantilever over topographical features. Preliminary images in water and saline are presented, including one taken at 75.5 μm/s—a threefold improvement in bandwidth versus conventional piezotube actuators.     

Controlling tip–sample interaction forces during a single tap for improved topography and mechanical property imaging of soft materials by AFM

We introduce a method that exploits the “active” nature of the force-sensing integrated readout and active tip (FIRAT), a recently introduced atomic force microscopy (AFM) probe, to control the interaction forces during individual tapping events in tapping mode (TM) AFM. In this method the probe tip is actively retracted if the tip–sample interaction force exceeds a user-specified force threshold during a single tap while the tip is still in contact with the surface. The active tip control (ATC) circuitry designed for this method makes it possible to control the repulsive forces and indentation into soft samples, limiting the repulsive forces during the scan while avoiding instability due to attractive forces. We demonstrate the accurate topographical imaging capability of this method on suitable samples that possess both soft and stiff features.     

Analysis and control of micro-cantilever in dynamic mode AFM

The dynamic behavior of micro-cantilever-sample system in atomic force microscopy (AFM) in tapping operational mode is studied. Micro-cantilever is modeled by single-mode approximation and subjected to sinusoidal force input. The interaction between tip and sample is modeled by Lennard–Jones potential. Using this dynamic model, the phase portrait of the system is obtained for a range of cantilever-sample distance, and the effect of cantilever parameters on predictability of the system is discussed. Then the nonlinear behavior of the cantilever-sample system is controlled by a robust sliding-mode controller. System output is designed to track the sinusoidal stimulation of the cantilever base under sample surface perturbation during scanning process. Results of SMC are simulated in MATLAB and compared to a stability that has been proved by PID controller which shows better controller effort and less cantilever tip position accuracy.     

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.     

Mapping of lateral vibration of the tip in atomic force microscopy at the torsional resonance of the cantilever

Lateral vibration of the tip in atomic force microscopy was mapped at the torsional resonance of the cantilever by attaching a shear piezo element at the base of the cantilever or under the sample. Fixed frequency excitation and self-excitation of torsional motion were implemented. The lateral vibration utilized as measured by an optical lever was in the order of 10 pm to 3 nm, and its frequency approximately 450 kHz for a contact-mode silicon nitride cantilever. The amplitude and phase of the torsional motion of the cantilever was measured by a lock-in-amplifier or a rectifier and plotted in x and y as the sample was raster scanned. The imaging technique gave contrast between graphite terraces, self-assembled monolayer domains, silicon and silicon dioxide, graphite and mica. Changing contrast was observed as silicon islands oxidized in atmosphere, showing that the imaging technique can detect change in lateral tip mobility due to changes occurring near the surface. Torsional self-excitation showed nanometric features of self-assembled monolayer islands due to different lateral dissipation. Dependence of torsional resonance frequency on excitation amplitude, and contrast change due to driving frequency around resonance were observed.     

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.     

Amplitude and frequency modulation torsional resonance mode atomic force microscopy of a mineral surface

Scanning probe imaging in a shear force mode allows for the characterization of in-plane surface properties. In a standard AFM, shear force imaging can be realized by the torsional resonance mode. In order to investigate the imaging conditions on mineral surfaces, a torsional resonance mode atomic force microscope was operated in amplitude (AM) and frequency modulation (FM) feedback. Freshly cleaved chlorite was investigated, which showed brucite-like and talc-like surface areas. In constant amplitude FM mode, a slight variation in energy dissipation was observed between both surfaces. Amplitude and frequency vs. distance curves revealed that the tip was in repulsive contact with the specimen during imaging.     

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.     

Feedback based simultaneous correction of imaging artifacts due to geometrical and mechanical cross-talk and tip-sample stick in atomic force microscopy

This paper presents a feedback scheme that simultaneously corrects, in real time, for the imaging artifacts caused by cantilever and photosensor misalignments as well as misinterpretations in relative lateral position of the tip with respect to the sample due to the tip-sample stick in atomic force microscopy (AFM). The optical beam bounce method, typically used in AFM for imaging, is sensitive to inaccuracies of cantilever geometry and the relative misalignment of the laser source, cantilever, and the laser sensitive diode from the intended design. These inaccuracies, which contribute to the geometrical cross-talk between the normal and the lateral signals, become prominent at the atomic and subnanometer scales, and thereby impede high resolution imaging studies. The feedback scheme accounts for these artifacts and makes imaging insensitive to, in fact, practically independent of these inaccuracies. This scheme counteracts the lateral twisting dynamics of the cantilever, and as a result, it avoids the misinterpretation problem of the relative lateral position of the cantilever tip from the sample and thereby avoids the corresponding imaging artifacts that are typically prominent in contact mode friction force microscopy (FFM). The feedback scheme consists of simultaneously regulating the normal as well as the lateral cantilever deflection signal at their respective set points. This not only removes the imaging artifacts due to geometrical misalignments, mechanical cross-talk, and irregular sliding but also the corresponding compensatory control signal gives a more accurate real time measure of the lateral interaction force between the sample and the cantilever as compared to the lateral deflection signal used in FFM. Experimental results show significant improvement, and in some cases, practical elimination of the artifacts. The design and implementation of a split piezoassembly needed for the lateral actuation for the feedback scheme are also presented.     

Topography imaging with a heated atomic force microscope cantilever in tapping mode

This article describes tapping mode atomic force microscopy (AFM) using a heated AFM cantilever. The electrical and thermal responses of the cantilever were investigated while the cantilever oscillated in free space or was in intermittent contact with a surface. The cantilever oscillates at its mechanical resonant frequency, 70.36 kHz, which is much faster than its thermal time constant of 300 micros, and so the cantilever operates in thermal steady state. The thermal impedance between the cantilever heater and the sample was measured through the cantilever temperature signal. Topographical imaging was performed on silicon calibration gratings of height 20 and 100 nm. The obtained topography sensitivity is as high as 200 microVnm and the resolution is as good as 0.5 nmHz(1/2), depending on the cantilever power. The cantilever heating power ranges 0-7 mW, which corresponds to a temperature range of 25-700 degrees C. The imaging was performed entirely using the cantilever thermal signal and no laser or other optics was required. As in conventional AFM, the tapping mode operation demonstrated here can suppress imaging artifacts and enable imaging of soft samples.     

Resonant control of an atomic force microscope micro-cantilever for active Q control

Active Q control may be used to modify the effective quality (Q) factor of an atomic force microscope (AFM) micro-cantilever when operating in tapping mode. The control system uses velocity feedback to obtain an effective cantilever Q factor to achieve optimal scan speed and image resolution for the imaging environment and sample type. Time delay of the cantilever displacement signal is the most common method of cantilever velocity estimation. Spill-over effects from unmodeled dynamics may degrade the closed loop system performance, possibly resulting in system instability, when time delay velocity estimation is used. A resonant controller is proposed in this work as an alternate method of velocity estimation. This new controller has guaranteed closed loop stability, is easy to tune, and may be fitted into existing commercial AFMs with minimal modification. Images of a calibration grating are obtained using this controller to demonstrate its effectiveness.     

Influence of the tip mass on the tip-sample interactions in TM-AFM

This paper focuses on the influences of the tip mass ratio (the ratio of the tip mass to the cantilever mass), on the excitation of higher oscillation eigenmodes and also on the tip-sample interaction forces in tapping mode atomic force microscopy (TM-AFM). A precise model for the cantilever dynamics capable of accurate simulations is essential for the investigation of the tip mass effects on the interaction forces. In the present work, the finite element method (FEM) is used for modeling the AFM cantilever to consider the oscillations of higher eigenmodes oscillations. In addition, molecular dynamics (MD) is used to calculate precise data for the tip-sample force as a function of tip vertical position with respect to the sample. The results demonstrate that in the presence of nonlinear tip-sample interaction forces, the tip mass ratio plays a significant role in the excitations of higher eigenmodes and also in the normal force applied on the surface. Furthermore, it has been shown that the difference between responses of the FEM and point-mass models in different system operational conditions is highly affected by the tip mass ratio.     

Probing material properties of polymeric surface layers with tapping mode AFM: Which cantilever spring constant,tapping amplitude and amplitude set point gives good image contrast and minimal surface damage?

A phase shift between the oscillatory motion and drive motion of an AFM-cantilever used for tapping mode AFM imaging can be related to adhesive and elastic properties of surface layers. In this study it was studied how optimal contrast between hard and soft surface layers can be achieved while minimizing the surface damage. This was investigated by performing classical force-distance measurements while driving the cantilever as in tapping mode imaging. The amplitude and phase response as a function of the average tip-surface separation was recorded. Five different cantilevers with a wide range of spring constants and four different tapping amplitudes were investigated and compared. Based on these experiments it is concluded that too stiff cantilever, high free tapping amplitude and low amplitude set point value often lead to surface damage, while too low spring constant and low free tapping amplitude result in poor phase image contrast. Intermediate values where little surface damage and significant image contrast are obtained were identified. In all cases it was observed that the best image contrast was obtained when the amplitude set point was chosen such that the amplitude during imaging was reduced to approximately 50% of the free amplitude.     

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.     

Origin of phase shift in atomic force microscopic investigation of the surface morphology of NR/NBR blend film

Atomic force microscopy (AFM) was used to study the morphology and surface properties of NR/NBR blend. Blends at 1/3, 1/1 and 3/1 weight ratios were prepared in benzene and formed film by casting. AFM phase images of these blends in tapping mode displayed islands in the sea morphology or matrix-dispersed structures. For blend 1/3, NR formed dispersed phase while in blends 1/1 and 3/1 phase inversion was observed. NR showed higher phase shift angle in AFM phase imaging for all blends. This circumstance was governed by adhesion energy hysteresis between the device tip and the rubber surface rather than surface stiffness of the materials, as proved by force distance measurements in the AFM contact mode.     

使用自激振荡法提高原子力光子扫描隧道组合显微镜的扫描速度

介绍了采用频率偏移控制样品/探针间距的原子力光子扫描隧道组合显微镜(AF/PSTM)。制备了尖端直径100nm,锥角为60～90°的锐利大锥角探针用于轻敲自激振荡模式的AF/PSTM,该探针固定在压电陶瓷片上置于一个正反馈回路中激励探针振荡。使用锁相器解调自激振荡探针的频率,调整Z方向压电陶瓷的运动使得锁相器检测到的值维持恒定来跟踪样品的起伏。对外加激励模式和自激振荡模式进行了对比。理论分析表明,自激振荡方法减小了探针响应时间;测试试验显示,采用自激振荡模式AF/PSTM的带宽为50Hz,比外加振荡模式快一个数量级。采用改进后的仪器对光栅样品以1Hz的速度进行了扫描,扫描结果显示,采用自激振荡的方式得到的形貌和光学图像比外加激励模式更清晰,不仅响应时间更快,通过提高Q值还可以提高分辨率而不会增加系统进入稳态的时间。