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.     

Novel operation mode for eliminating influence of inclination angle and friction in atomic force microscopy

The accuracy of topography imaging in contact force mode of atomic force microscopy (AFM) depends on the one-to-one corresponding relationship between the cantilever deflection and the tip–sample distance, whereas such a relationship cannot be always achieved in the presence of friction and incline angle of sample surface. Recently, we have developed a novel operation mode in which we keep the van der Waals force as constant instead of the applied normal force, to eliminate the effect of inclination angle and friction on topography imaging in the contact force mode. We have improved our AFM to enable the new operation mode for validation. Comparative experiments have been performed and the results have shown that the effect of friction and inclination angle on topography imaging in contact mode of AFM can be eliminated or at least decreased effectively by working in the new operation mode we present.     

The Roles of Statics and Dynamics in Determining Transitions Between Atomic Friction Regimes

We introduce a model AFM tip/substrate system that includes full atomistic detail as well as system compliance to study the transitions between three regimes of atomic friction: smooth sliding, stick-single slip, and stick-multiple slip. We characterize these atomic friction regimes in terms of static and dynamic effects, and investigate how the slip modes affect the mean friction. Molecular statics calculations show that reduced-order model predictions of possible transitions between slip regimes are generally adequate for a fully atomistic system, even for complex reaction coordinates. However, molecular dynamics simulations demonstrate that, while static features of the system govern possible slip regimes, dynamic effects ultimately determine actual transitions between slip regimes.     

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.     

Observation of proportionality between friction and contact area at the nanometer scale

The nanotribological properties of a hydrogen‐terminated diamond(111)/tungsten‐carbide interface have been studied using ultra‐high vacuum atomic force microscopy. Both friction and local contact conductance were measured as a function of applied load. The contact conductance experiments provide a direct and independent way of determining the contact area between the conductive tungsten‐carbide AFM tip and the doped diamond sample. We demonstrate that the friction force is directly proportional to the real area of contact at the nanometer‐scale. Furthermore, the relation between the contact area and load for this extremely hard heterocontact is found to be in excellent agreement with the Derjaguin–Müller–Toporov continuum mechanics model. This revised version was published online in September 2006 with corrections to the Cover Date.     

Adhesion and Friction Studies of Nano-textured Surfaces Produced by Self-Assembling Au Nanoparticles on Silicon Wafers

This article presents the results of nanoscale friction and adhesion of nanoparticle-textured surfaces (NPTS) using atomic force microscope (AFM). The effects of coverage ratio, texture height, and packing density on the adhesion and friction of the NPTS were investigated. The nano-textured surfaces were produced by self-assembling Au nanoparticles (NPs) with diameters of 20 nm and 50 nm on the silicon (100) surfaces, respectively. Surface morphology of the NPTS was characterized by field emission scanning electron microscopy and AFM. The results show that the NPTS significantly reduced the adhesive force compared to the smooth surface. The adhesion of NPTS is mainly dependent on the coverage ratio of NPs rather than the texture height and higher coverage ratio resulted in smaller adhesive force. The reduced adhesion of textured surfaces was attributed to the reduced real area of contact. The friction of NPTS is mainly dependent on the spacing between asperities. The lowered frictional force was obtained when the spacing between asperities is less than the size of AFM tip, because of the effectively reduced real area of contact between the AFM tip and the NPTS surface.     

Improvement of DNA-visualization in dynamic mode atomic force microscopy in air

Near-contact mode atomic force microscopy (AFM) imaging leads to sharper representations of DNA double strands on mica imaged at ambient conditions compared with noncontact mode AFM. Phase shift was used for feedback control yielding height information using a simple model calculation. No contact between tip and sample occurs. Measured DNA widths were up to four times smaller than measured with the same AFM tip in noncontact mode at ambient condition.     

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.     

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.     

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.     

考虑摩擦力及试样表面倾角的原子力显微镜扫描模式

原子力显微镜(Atomic force microscopes,AFM)接触模式下的测量结果因受样本表面倾角和针尖一样本表面间摩擦力的影响而存在较大的测量误差.为避免针尖-表面间的摩擦力对AFM测量试样表面形貌的影响,并能够准确测量表面倾角,提出了一种新的AFM工作模式--消除倾角和摩擦力影响模式.在这种工作模式中,扫描方向垂直悬臂的长轴方向,通过测量悬臂的竖向和横向偏转而得到针尖所受的竖向和横向力,并计算得到针尖-试样表面间的van der Waals力及试样表面局部倾角,然后结合针尖项点和扫描器的位置及针尖-试样表面间距可以得到试样表面形貌的测量结果.在上述工作模式下,针尖-试样表面间的摩擦力是可控的,能够避免针尖或试样的损伤.仿真结果证明了这种方法的可行性.     

Atomic friction studies on well-defined surfaces

Atomic friction studies have been performed by means of a friction force microscope (FFM) in ultrahigh vacuum, where well-defined surfaces can be prepared. A home-built FFM allows us to study lateral forces as low as 0.05 nN using rectangular silicon cantilevers. Furthermore, comparison with dissipation measurements performed in non-contact mode are possible. Recent experimental results are presented and discussed in the framework of a one-dimensional Tomlinson model which includes thermal activation. Atomic-scale stick–slip processes on a metallic surface could be repeatedly measured on Cu(111), while the Cu(100) surface was distorted by the tip during the scanning process. A logarithmic velocity dependence of atomic friction has been measured on Cu(111) and NaCl(100) for low scanning velocities. The dissipation found in stick–slip measurements is compared to the power loss detected in dynamic non-contact measurement.     

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.     

Contact mechanics and tip shape in AFM-based nanomechanical measurements

Stiffness-load curves obtained in quantitative atomic force acoustic microscopy (AFAM) measurements depend on both the elastic properties of the sample and the geometry of the atomic force microscope (AFM) tip. The geometry of silicon AFM tips changes when used in contact mode, affecting measurement accuracy. To study the influence of tip geometry, we subjected ten AFM tips to the same series of AFAM measurements. Changes in tip shape were observed in the scanning electron microscope (SEM) between individual AFAM tests. Because all of the AFAM measurements were performed on the same sample, variations in AFAM stiffness-load curves were attributed to differences in tip geometry. Contact-mechanics models that assumed simple tip geometries were used to analyze the AFAM data, but the calculated values for tip dimensions did not agree with those provided by SEM images. Therefore, we used a power-law approach that allows for a nonspherical tip geometry. We found that after several AFAM measurements, the geometry of the tips at the very end is intermediate between those of a flat punch and a hemisphere. These results indicate that the nanoscale tip-sample contact cannot easily be described in terms of simple, ideal geometries.     

Atomic Friction Modulation on the Reconstructed Au(111) Surface

Friction between a nanoscale tip and a reconstructed Au(111) surface is investigated both by atomic force microscopy (AFM) and molecular statics calculations. Lateral force AFM images exhibit atomic lattice stick–slip behavior with a superstructure corresponding to the herringbone reconstruction pattern. However, the superstructure contrast is not primarily due to variations in the local frictional dissipation (which corresponds to the local width of the friction loop). Rather, the contrast occurs primarily because the local centerline position of the friction loop is periodically shifted from its usual value of zero. Qualitatively, similar behavior is reproduced in atomistic simulations of an AFM tip sliding on the reconstructed Au(111) substrate. In both simulations and experiments, this centerline modulation effect is not observed on unreconstructed surfaces. Similarly, using a topographically flat surface as a hypothetical control system, the simulations show that the centerline modulation is not caused by variations in the reconstructed surface’s topography. Rather, we attribute it to the long-range variation of the local average value of the tip-sample interaction potential that arises from the surface reconstruction. In other words, surface atoms located at unfavorable sites, i.e., in the transition between face-centered-cubic (FCC) and hexagonal-close-packed (HCP) regions, have a higher surface free energy. This leads to a varying conservative force which locally shifts the centerline position of the friction force. This demonstrates that stick–slip behavior in AFM can serve as a rather sensitive probe of the local energetics of surface atoms, with an attainable lateral spatial resolution of a few nanometers.     

Macro- and Nanotribological Properties of Graphite Tribofilms: Influence of the Sliding Interface

Macrotribological studies of microcrystalline graphite powder reveal a drastic decrease in the friction coefficient when the experiments are carried out in the presence of low-viscosity liquids. The friction reduction is attributed to the simultaneous presence of particles and liquid in the sliding contact, but the mechanisms involved remain unclear. In order to contribute to the understanding of liquid action in friction reduction mechanisms, nanoscale investigations of the tribofilms have been performed using lateral force microscopy. Attention is devoted to the nanostructure of the film surfaces and their nanofriction behavior using an atomic force microscope. The influence of the tip/sample interfaces on friction properties is investigated by using AFM tips constituted of different compounds (silicon, gold/chromium alloy, silicon nitride or carbon-covered AFM tip) and by performing the nanofriction tests in air or liquid environments. The results indicate that the friction reduction observed at macroscale is attributed neither to the lowering of the shear strength of the carbon/carbon interface in the presence of liquid nor to the nanostructure of the film surface. Collective liquid/particles effects inside the contact during sliding are probably involved.     

Hydrodynamic damping of a magnetically oscillated cantilever close to a surface

We studied the frequency response of a magnetically driven atomic force microscope (AFM) cantilever close to a sample surface in liquids. Amplitude–frequency (tuning) curves showed pronounced differences in dependence on the tip–sample separation (from 1 to 50 μm), with significant shifts of the resonance peak. A model was developed in which the cantilever was described in a full shape manner and the hydrodynamic forces acting on the cantilever were approximately calculated. The slight inclination of the cantilever to the surface (15°) leads to a force profile along the cantilever. Therefore, the mathematical problem can be strictly solved only numerically. For an approximate analytical solution, the hydrodynamic force profile was approximated by a constant force along the cantilever for large separations and by a point force acting on the tip of the cantilever for small separations. The theoretical results calculated within this model agreed well with the experimental data and allowed to determine the cantilever mass in liquid M^*, the joint mass at the tip end m_t^*, and the coefficient of viscous interaction of the cantilever with free liquid, γ_∞.     

Prediction of atomic force microscope probe dynamics through the receptance coupling method

The increased growth in the use of tip-based sensing, manipulations, and fabrication of devices in atomic force microscopy (AFM) necessitates the accurate prediction of the dynamic behavior of the AFM probe. The chip holder, to which the micro-sensing device is attached, and the rest of the AFM system can affect the overall dynamics of the probe. In order to consider these boundary effects, we propose a novel receptance coupling method to mathematically combine the dynamics of the AFM setup and probe, based on the equilibrium and compatibility conditions at the joint. Once the frequency response functions of displacement over force at the tool tip are obtained, the dynamic interaction forces between the tip and the sample in nanoscale can be determined by measuring the probe tip displacement.     

Microscopic stick–slip in friction force microscopy

Friction force measurements were performed on 2-hydroxy stearic acid (2-HSA) and 12-hydroxy stearic acid (12-HSA) coated silica surfaces in air using an atomic force microscope. The 2-HSA displayed viscoelastic behaviour with a yield point as the static–dynamic friction transition. Steady sliding motion was replaced by microscopic stick–slip at lower velocities and higher loads. Stick–slip motion was successfully described and fitted to a phenomenological model ascribed to interfacial material melting and freezing in periodic cycles. The stick–slip periodicity is of the same order as the contact diameter. The 12-HSA did not experience a yield point and exhibited steady sliding over the entire load and velocity regime. We attribute these observations to the difference in molecular configuration, shear strength and adsorption density of the stearic acid layers. This revised version was published online in August 2006 with corrections to the Cover Date.     

Observations of Stick-Slip Friction in Velcro®

Friction, and in particular stick-slip friction, occurs on every length scale, from the movement of atomic force microscope tips at the nanoscale to the movement of tectonic plates of the Earth’s crust. Even with this ubiquity, there still appears to be outstanding fundamental questions, especially on the way that frictional motion varies generally with the mechanical parameters of a system. In this study, the frictional dynamics of the hook-and-loop system of Velcro^® in shear is explored by varying the typical parameters of driving velocity, applied load, and apparent contact area. It is demonstrated that in Velcro^® both the maximum static frictional force and the average kinetic frictional force vary linearly with apparent contact area (hook number), and moreover, in the kinetic regime, stick-slip dynamics are evident. Surprisingly, the average kinetic friction force is independent of velocity over nearly two-and-a-half orders of magnitude (~2 × 10^?4 to ~6 × 10^?2 m/s). The frictional force varies as a power law on the applied load with an exponent of 0.28 and 0.24 for the maximum static and kinetic frictional forces, respectively. Furthermore, the evolution of stick-slip friction to more smooth sliding, as controlled by contact area, is demonstrated by both a decrease in the spread of the kinetic friction and the spread of the fluctuations of the average kinetic friction when normalized to the average kinetic friction; these decreases follow power-law behaviors with respect to the increasing contact area with exponents of approximately ?0.3 and ?0.8, respectively. Lastly, we note that the coefficients of friction μ _s and μ _k are not constant with applied load but rather decrease monotonically with power-law behavior with an exponent of nearly ?0.8. Phenomenologically, this system exhibits interesting physics whereby in some instances it follows classical Amontons–Coulomb (AC) behavior and in others lies in stark contrast and hopefully will assist in the understanding of the friction behavior in dry surfaces.