Coupled lateral bending-torsional vibration sensitivity of atomic force microscope cantilever

We study the influence of the contact stiffness and the ration between cantilever and tip lengths on the resonance frequencies and sensitivities of lateral cantilever modes. We derive expressions to determine both the effective resonance frequency and the mode sensitivity of an atomic force microscope (AFM) rectangular cantilever. Once the contact stiffness is given, the resonance frequency and the sensitivity of the vibration modes can be obtained from the expression. The results show that each mode has a different resonant frequency to variations in contact stiffness and each frequency increased until it eventually reached a constant value at very high contact stiffness. The low-order vibration modes are more sensitive to vibration than the high-order mode when the contact stiffness is low. However, the situation is reversed when the lateral contact stiffness became higher. Furthermore, increasing the ratio of tip length to cantilever length increases the vibration frequency and the sensitivity of AFM cantilever.     

Velocity dependent friction laws in contact mode atomic force microscopy

Friction forces in the tip–sample contact govern the dynamics of contact mode atomic force microscopy. In ambient conditions typical contact radii between tip and sample are in the order of a few nanometers. In order to account for the large interaction area the dynamics of contact mode atomic force microscope (AFM) is investigated under the assumption of a multi-asperity contact interface between tip and sample. Thus, the kinetic friction force between tip and sample is the product of the real contact area between both solids and the interfacial shear strength. The velocity strengthening of the lateral force is modeled assuming a logarithmic relationship between shear-strength and velocity. Numerical simulations of the system dynamics with this empirical model show the existence of two different regimes in contact mode AFM: steady sliding and stick–slip where the tip undergoes periodically stiction and kinetic friction. The state of the system depends on the scan velocity as well as on the velocity dependence of the interfacial friction force between tip and sample. Already small viscous damping contributions in the tip–sample contact are sufficient to suppress stick–slip oscillations.     

Quantitative elastic modulus measurement by magnetic force modulation microscopy

It is experimentally demonstrated that magnetic force modulation microscopy (MFMM) is a technique allowing quantitative elastic modulus measurements. A model of the cantilever–tip–sample interaction taking into account the lateral contact stiffness (i.e., the friction effects at the level of the tip–sample contact), the position of the magnetic force applied to the cantilever with respect to the tip position, as well as the inclination of the cantilever arm with respect to the sample surface is presented. The model shows that MFMM is much less sensitive to lateral force than the other modulation techniques and thus, in contrast to the latter, that the contrast of the stiffness images can be interpreted as a true elasticity contrast and not as a mixture of friction and elasticity. Thanks to the study of the normal contact stiffness versus normal load that allows the characterization of contact between tip and sample, it is possible to perform quantitative elastic modulus measurements with a dynamic modulation method.     

Carbon nanotubes: a promising standard for quantitative evaluation of AFM tip apex geometry

The direct contact between tip and sample in atomic force microscopy (AFM) leads to demand for a quantitative knowledge of the AFM tip apex geometry in high-resolution AFM imaging and many other types of AFM applications like force measurements and surface roughness measurements. Given, the AFM tip apex may change continuously during measurements due to wear or during storage due to oxidation, it is very desirable to develop an easy and quick way for quantitative evaluation of AFM tip radius when necessary. In this study, we present an efficient method based on Zenhausern model (Scanning 14 (1992) 212) by measuring single-wall carbon nanotubes deposited on a flat substrate to reach this goal. Experimental results show the method can be used for routine quantitative evaluation of AFM tip apex geometry for tips with effective radii down to the nanometer scale.     

Effect of contact stiffness on wedge calibration of lateral force in atomic force microscopy

Quantitative friction measurement of nanomaterials in atomic force microscope requires accurate calibration method for lateral force. The effect of contact stiffness on lateral force calibration of atomic force microscope is discussed in detail and an improved calibration method is presented. The calibration factor derived from the original method increased with the applied normal load, which indicates that separate calibration should be required for every given applied normal load to keep the accuracy of friction measurement. We improve the original method by introducing the contact factor, which is derived from the contact stiffness between the tip and the sample, to the calculation of calibration factors. The improved method makes the calculation of calibration factors under different applied normal loads possible without repeating the calibration procedure. Comparative experiments on a silicon wafer have been done by both the two methods to validate the method in this article.     

Fabrication of sharp tungsten-coated tip for atomic force microscopy by ion-beam sputter deposition

Tungsten (W) is significantly suitable as a tip material for atomic force microscopy (AFM) because its high mechanical stiffness enables the stable detection of tip-sample interaction forces. We have developed W sputter-coating equipment to compensate the drawbacks of conventional Si cantilever tips used in AFM measurements. By employing an ion gun commonly used for sputter cleaning of a cantilever tip, the equipment is capable of depositing conductive W films in the preparation chamber of a general ultrahigh vacuum (UHV)-AFM system without the need for an additional chamber or transfer system. This enables W coating of a cantilever tip immediately after sputter cleaning of the tip apex and just before the use in AFM observations. The W film consists of grain structures, which prevent tip dulling and provide sharpness (<3 nm in radius of curvature at the apex) comparable to that of the original Si tip apex. We demonstrate that in non-contact (NC)-AFM measurement, a W-coated Si tip can clearly resolve the atomic structures of a Ge(001) surface without any artifacts, indicating that, as a force sensor, the fabricated W-coated Si tip is superior to a bare Si tip.     

Adhesion Mechanics between Nanoscale Silicon Oxide Tips and Few-Layer Graphene

Finite element method (FEM) simulations of the adhesive contact between a nanoscale tip and a silicon oxide substrate covered with graphene were performed, modelling experimental atomic force microscopy pull-off measurements. Simulations showed a slight increase in the pull-off force as layer number increased. This small enhancement was within reported experimental error, agreeing with the experimental findings of layer-independent adhesion forces. Pull-off forces did not vary with the elastic strain in the system for a given number of layers, but were influenced by the greater adhesive stresses for tip–graphene interaction compared with tip–substrate interactions. FEM simulations were also performed on suspended graphene and showed that the adhesive forces increased slightly beyond one layer of graphene, but then varied little from two to four layers of graphene. The results indicate that while there is some local delamination of the graphene sheets from the substrate, the adhesive stresses between the graphene layers in multilayer graphene effectively prevent out-of-plane mechanical deformation of the graphene layers that could result from tip–graphene interactions. Thus, the increased pull-off forces observed beyond one monolayer results from a change in the amount of material between the tip and substrate, or in this case the number of graphene layers, thus increasing the van der Waals force between tip and graphene.     

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.     

Experimental observation of contact mode cantilever dynamics with nanosecond resolution

We report the use of a laser Doppler vibrometer to measure the motion of an atomic force microscope contact mode cantilever during continuous line scans of a mica surface. With a sufficiently high density of measurement points the dynamics of the entire cantilever beam, from the apex to the base, can be reconstructed. We demonstrate nanosecond resolution of both rectangular and triangular cantilevers. This technique permits visualization and quantitative measurements of both the normal and lateral tip sample interactions for the first and higher order eigenmodes. The ability to derive quantitative lateral force measurements is of interest to the field of microtribology/nanotribology while the comprehensive understanding of the cantilever's dynamics also aids new cantilever designs and simulations.     

Multiple Slips in Atomic-Scale Friction: An Indicator for the Lateral Contact Damping

The occurrence of multiple jumps in 2D atomic-scale friction measurements is used to quantify the viscous damping accompanying the stick–slip motion of a sharp tip in contact with a NaCl(001) surface. Multiple slips are observed without apparent wear for normal forces between 13 and 91 nN. For scans parallel to [100] directions, the tip jumps between minima of the substrate corrugation potential in a zigzag fashion. An algorithm is applied to determine histograms of lateral force jumps which characterize multiple slips. The same algorithm is used to classify multiple slips occurring in calculated lateral force maps. Comparisons between simulations and experiments indicate that the nanometer-sized contact is underdamped at intermediate loads (13–26 nN) and becomes slightly overdamped at higher loads. The proposed procedure is a novel way to estimate the lateral contact damping which plays an important role in the interpretation of measurements of the velocity and temperature dependence of friction, of slip duration, and of the reduction of friction by applied perpendicular or parallel oscillations.     

Lateral force microscopy of multiwalled carbon nanotubes

Carbon nanotubes are usually imaged with the atomic force microscope (AFM) in non-contact mode. However, in many applications, such as mechanical manipulation or elasticity measurements, contact mode is used. The forces affecting the nanotube are then considerable and not fully understood. In this work lateral forces were measured during contact mode imaging with an AFM across a carbon nanotube. We found that, qualitatively, both magnitude and sign of the lateral forces to the AFM tip were independent of scan direction and can be concluded to arise from the tip slipping on the round edges of the nanotube. The dependence on the normal force applied to the tip and on the ratio between nanotube diameter and tip radius was studied. We show that for small values of this ratio, the lateral force signal can be explained with a simple geometrical model.     

Stick–slip motion in the atomic force microscope

Measurements of atomic friction in the atomic force microscope frequently show periodic variations at the lattice spacing of the surface being scanned, which have the saw‐tooth wave form characteristic of “stick–slip” motion. Simple models of this behaviour have been proposed, in which the “dynamic element” of the system is provided by the elastic stiffness and inertia of the cantilever which supports the tip of the microscope, in its lateral, i.e., torsional mode of vibration. These models have been successful in predicting the observed motion, but only by assuming that the cantilever is heavily damped. However, the source of this damping in a highly elastic cantilever is not explained. To resolve the paradox, it is shown in this note that it is necessary to introduce the elastic stiffness of the contact into the model. The relationship between the contact stiffness, the cantilever stiffness and the amplitude of the periodic friction force is derived in order for stick–slip motion at lattice spacing to be achieved. This revised version was published online in July 2006 with corrections to the Cover Date.     

Force modulation with a scanning force microscope: an analysis

A magnetic force modulation microscope (FMM) has been employed to measure the dynamic behavior of a contact between a scanning force microscope (SFM) tip and a surface. Our experimental results show the inefficiency of the classical models (two Kelvin-Voigt elements in parallel). A new model which takes into account the normal and tangential stiffness of the contact, and also the geometrical and mechanical properties of the cantilever which hold the tip, is proposed. This model shows that the natural frequency is sensitive to the normal stiffness, only if the ratio of the normal contact stiffness to the cantilever stiffness is between 0.2 and 200. Above this domain, the natural frequency is sensitive to sliding (Mindlin theory).     

Dual resonance excitation system for the contact mode of atomic force microscopy

We propose an improved system that enables simultaneous excitation and measurements of at least two resonance frequency spectra of a vibrating atomic force microscopy (AFM) cantilever. With the dual resonance excitation system it is not only possible to excite the cantilever vibrations in different frequency ranges but also to control the excitation amplitude for the individual modes. This system can be used to excite the resonance frequencies of a cantilever that is either free of the tip-sample interactions or engaged in contact with the sample surface. The atomic force acoustic microscopy and principally similar methods utilize resonance frequencies of the AFM cantilever vibrating while in contact with the sample surface to determine its local elastic modulus. As such calculation demands values of at least two resonance frequencies, two or three subsequent measurements of the contact resonance spectra are necessary. Our approach shortens the measurement time by a factor of two and limits the influence of the AFM tip wear on the values of the tip-sample contact stiffness. In addition, it allows for in situ observation of processes transpiring within the AFM tip or the sample during non-elastic interaction, such as tip fracture.     

A versatile multipurpose scanning probe microscope

A combined scanning probe microscope has been developed that allows simultaneous operation as a non‐contact/tapping mode atomic force microscope, a scattering near‐field optical microscope, and a scanning tunnelling microscope on conductive samples. The instrument is based on a commercial optical microscope. It operates with etched tungsten tips and exploits a tuning fork detection system for tip/sample distance control. The system has been tested on a p‐doped silicon substrate with aluminium depositions, being able to discriminate the two materials by the electrical and optical images with a lateral resolution of 130 nm.     

Correlation Between Mechanical Properties and Nanofriction of [Ti–Cr/Ti–Cr–N] n and [Ti–Al/Ti–Al–N] n Multilayers

In this work, thin films deposited by pulsed DC magnetron sputtering of [Ti–Al/Ti–Al–N] _n and [Ti–Cr/Ti–Cr–N] _n multilayers of nanometric periods were analyzed by AFM in contact mode to measure values of lateral and normal forces. From these measurements, the coefficient of friction (COF) of these materials in contact with the AFM tip was calculated. Measurements were made with three types of silicon tips, diamond-coated, Pt–Cr-coated, and bare silicon. Significant differences between the tip materials in contact with the samples, which affected the COF, were observed. The effect of the environmental layer of water covering the surface sample and the tip appears as the most important factor affecting the tribology behavior of the tip-sample contact. For diamond-coated and bare silicon tips there is an additional adherence force increasing the normal load. But for tips platinum–chromium-coated there is a repulsive force due to this water layer, which behaves as a lubricant layer before a threshold load.     

考虑基体变形的混合润滑结合面接触特性

为研究混合润滑状态下粗糙表面基体变形对结合面接触特性的影响,建立了考虑基体变形的结合面接触刚度模型。首先,通过单微凸体-基体系统模型分别求解微凸体和基体的接触刚度,利用不动点迭代法获得微凸体真实变形量;其次,基于分形理论建立结合面固体接触刚度模型,通过固体接触刚度获得液体介质的接触刚度。根据仿真结果分析了基体变形、粗糙表面形貌以及润滑介质对结合面接触特性的影响规律。结果表明:当真实接触面积一定时,通过新模型计算的法向载荷小于忽略基体变形的模型;在接触前期,结合面的接触刚度主要由液体介质接触刚度主导,随着真实接触面积的增加,液体接触刚度占总刚度的比率越来越小,最后转变为固体的接触刚度主导结合面的接触刚度。该模型为研究混合润滑状态下结合面的接触特性提供了理论基础。     

A new calibration method of the lateral contact stiffness and lateral force using modulated lateral force microscopy

We describe a new calibration method for lateral contact stiffness using modulated lateral force microscopy, a technique that offers some advantages with respect to the more classical friction force microscopy currently used for characterizing the friction properties of materials. The calibration method is based on the study of the lateral contact stiffness versus applied load and on the use of elasticity contact theories to determine by fit the calibration coefficient, allowing the scaling of experimental data. The method is tested by measuring the friction coefficient and shear strength of silicon and mica samples, respectively, and compared with results from the literature. This revised version was published online in August 2006 with corrections to the Cover Date.     

Evidence of commensurate contact and rolling motion: AFM manipulation studies of carbon nanotubes on HOPG

We report on experiments in which multiwall carbon nanotubes (CNTs) are manipulated with AFM on a graphite (HOPG) substrate. We find certain discrete orientations in which the lateral force of manipulation dramatically increases as we rotate the CNT in the plane of the HOPG surface with the AFM tip. The three-fold symmetry of these discrete orientations indicates commensurate contact of the hexagonal graphene surfaces of the HOPG and CNT. As the CNT moves into commensurate contact, we observe the motion change from sliding/rotating in-plane to stick–roll motion.     

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.