Atomic force microscopy tip torsion contribution to the measurement of nanomechanical properties

The nanomechanical properties of polymethyl methacrylate and indium phosphide were measured with an atomic force microscope and a nanoindentation system. The elastic moduli measured with the atomic force microscope are in good agreement with the values obtained with the nanoindentation system. The hardness is shown to be affected by the tip radius used in our experiments. The cantilever vertical and lateral movements were independently analyzed during nanoindentation, and the tip torsion can be attributed to a change from elastic to plastic deformation regimes of materials during force microscopy nanoindentation. An analysis of the lateral movement of the laser beam associated with the cantilever torsion was used to determine the material yield stress.     

Quantifying the dielectric constant of thick insulators by electrostatic force microscopy: effects of the microscopic parts of the probe

We present a systematic analysis of the effects that the microscopic parts of electrostatic force microscopy probes (the cone and cantilever) have on the electrostatic interaction between the tip apex and thick insulating substrates (thickness > 100 μm). We discuss how these effects can influence the measurement and quantification of the local dielectric constant of the substrates. We propose and experimentally validate a general methodology that takes into account the influence of the cone and the cantilever, thus enabling us to obtain very accurate values of the dielectric constants of thick insulators.     

Atomic-resolution imaging in liquid by frequency modulation atomic force microscopy using small cantilevers with megahertz-order resonance frequencies

In this study, we have investigated the performance of liquid-environment FM-AFM with various cantilevers having different dimensions from theoretical and experimental aspects. The results show that reduction of the cantilever dimensions provides improvement in the minimum detectable force as long as the tip height is sufficiently long compared with the width of the cantilever. However, we also found two important issues to be overcome to achieve this theoretically expected performance. The stable photothermal excitation of a small cantilever requires much higher pointing stability of the exciting laser beam than that for a long cantilever. We present a way to satisfy this stringent requirement using a temperature controlled laser diode module and a polarization-maintaining optical fiber. Another issue is associated with the tip. While a small carbon tip formed by electron beam deposition (EBD) is desirable for small cantilevers, we found that an EBD tip is not suitable for atomic-scale applications due to the weak tip-sample interaction. Here we show that the tip-sample interaction can be greatly enhanced by coating the tip with Si. With these improvements, we demonstrate atomic-resolution imaging of mica in liquid using a small cantilever with a megahertz-order resonance frequency. In addition, we experimentally demonstrate the improvement in the minimum detectable force obtained by the small cantilever in measurements of oscillatory hydration forces.     

Accurate and precise calibration of AFM cantilever spring constants using laser Doppler vibrometry

Accurate cantilever spring constants are important in atomic force microscopy both in control of sensitive imaging and to provide correct nanomechanical property measurements. Conventional atomic force microscope (AFM) spring constant calibration techniques are usually performed in an AFM. They rely on significant handling and often require touching the cantilever probe tip to a surface to calibrate the optical lever sensitivity of the configuration. This can damage the tip. The thermal calibration technique developed for laser Doppler vibrometry (LDV) can be used to calibrate cantilevers without handling or touching the tip to a surface. Both flexural and torsional spring constants can be measured. Using both Euler-Bernoulli modeling and an SI traceable electrostatic force balance technique as a comparison we demonstrate that the LDV thermal technique is capable of providing rapid calibrations with a combination of ease, accuracy and precision beyond anything previously available.     

偏心轴向荷载作用下薄壁箱梁的约束扭转翘曲应力研究

以薄壁箱梁的约束扭转分析理论为基础,将薄壁箱梁所受偏心轴向荷载作为一种外加双力矩荷载考虑,建立偏心轴向荷载作用下薄壁箱梁约束扭转的双力矩这一广义内力的计算公式。为了便于计算翘曲应力,进一步推导了扭转中心位置及主扇性坐标的实用计算公式。通过对一模型箱梁进行计算,并与按通用有限元软件ANSYS壳单元计算结果进行比较,验证了该文方法和所推导公式的正确性。详细分析箱室高宽比以及悬臂板宽度变化对偏心轴向荷载作用下薄壁箱梁约束扭转翘曲应力的影响。研究结果表明:箱室高宽比及悬臂板宽度对悬臂板端部翘曲应力的影响最大,对腹板与上翼缘、下翼缘交接处翘曲应力的影响相对较小;在偏心轴向分布荷载作用下,悬臂箱梁固定端横截面上控制点处的翘曲应力可达到初等梁应力的12%,不容忽视。     

The plastic hinge position in a circular cantilever when struck normal to its plane by a constant jet at its tip

A rigid/perfectly plastic circular cantilever, when struck normal to its plane by a jet of constant force at its tip, is analysed to determine the relationship between the magnitude of the jet force and the location of the plastic collapse cross-section. Due to the interaction of bending and torsion in circumstances where beam inertia is important, two modes for a generalized plastic hinge may be found to form in the curved beam; the stability of these modes is examined. Some numerical results are given to facilitate understanding related pipe-whip problems.     

Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator

Sensitive transduction of the motion of a microscale cantilever is central to many applications in mass, force, magnetic resonance, and displacement sensing. Reducing cantilever size to nanoscale dimensions can improve the bandwidth and sensitivity of techniques like atomic force microscopy, but current optical transduction methods suffer when the cantilever is small compared to the achievable spot size. Here, we demonstrate sensitive optical transduction in a monolithic cavity-optomechanical system in which a subpicogram silicon cantilever with a sharp probe tip is separated from a microdisk optical resonator by a nanoscale gap. High quality factor (Q ≈ 10(5)) microdisk optical modes transduce the cantilever's megahertz frequency thermally driven vibrations with a displacement sensitivity of ≈4.4 × 10(-16) m/(Hz)(1/2) and bandwidth >1 GHz, and a dynamic range >10(6) is estimated for a 1 s measurement. Optically induced stiffening due to the strong optomechanical interaction is observed, and engineering of probe dynamics through cantilever design and electrostatic actuation is illustrated.     

Multifunctional probe array for nano patterning and imaging

This letter reports the design, fabrication, and testing of a multifunctional scanning probe array for nanoscale imaging and patterning. The probe array consists of multiple cantilever probes, with each probe being able to perform a dedicated function such as scanning probe lithography (e.g., dip pen nanolithography and scanning probe contact printing) or scanning probe microscopy (e.g., atomic force microscopy and lateral force microscopy). The bending states of each probe can be controlled by using an integrated thermal electric actuator so that it is possible to engage any individual probe(s) independently for writing or imaging purposes. The multifunctional probe array is therefore capable of performing a rich variety of operations with minimal chemical crosstalk and high registration accuracy. It will eliminate the need for probe chip exchanges and increase the operational efficiency. The probe tips in a given array may be made of different materials. Further, the tip and cantilever may be made of different materials for a given probe. In this work, we focus on the development of a probe array consisting of dip pen nanolithography probes, scanning probe contact printing probes (of various tip sizes), and scanning probe microscopy probes.     

High spatial resolution Kelvin probe force microscopy with coaxial probes

Kelvin probe force microscopy (KPFM) is a widely used technique to measure the local contact potential difference (CPD) between an AFM probe and the sample surface via the electrostatic force. The spatial resolution of KPFM is intrinsically limited by the long range of the electrostatic interaction, which includes contributions from the macroscopic cantilever and the conical tip. Here, we present coaxial AFM probes in which the cantilever and cone are shielded by a conducting shell, confining the tip-sample electrostatic interaction to a small region near the end of the tip. We have developed a technique to measure the true CPD despite the presence of the shell electrode. We find that the behavior of these probes agrees with an electrostatic model of the force, and we observe a factor of five improvement in spatial resolution relative to unshielded probes. Our discussion centers on KPFM, but the field confinement offered by these probes may improve any variant of electrostatic force microscopy.     

3D finite element analysis of electrostatic deflection of commercial and FIB-modified cantilevers for electric and Kelvin force microscopy: I. Triangular shaped cantilevers with symmetric pyramidal tips

The investigation of the nanoscale distribution of electrostatic forces on material surfaces is of paramount importance for the development of nanotechnology, since these confined forces govern many physical processes on which a large number of technological applications are based. For instance, electric force microscopy (EFM) and micro-electro-mechanical-systems (MEMS) are technologies based on an electrostatic interaction between a cantilever and a specimen. In the present work we report on a 3D finite element analysis of the electrostatic deflection of cantilevers for electric and Kelvin force microscopy. A commercial triangular shaped cantilever with a symmetric pyramidal tip was modelled. In addition, the cantilever was modified by a focused ion beam (FIB) in order to reduce its parasitic electrostatic force, and its behaviour was studied by computation analysis. 3D modelling of the electrostatic deflection was realized by using a multiphysics finite element analysis software and it was applied to the real geometry of the cantilevers and probes obtained by using basic CAD tools. The results of the modelling are in good agreement with experimental data.     

Enhanced formation of a confined nano-water meniscus using a 780 nm laser with a quartz tuning fork-atomic force microscope

Demonstrated herein is the optical-field-induced enhancement of the formation of a confined nanowater meniscus using a distance-regulated quartz tuning fork-atomic force microscope (QTF-AFM) with a 780 nm laser. While a pulled optical fiber tip approaches the surface, the laser is suddenly turned on and focuses on the front spot of the tip by the shape of the pulled optical fiber, which plays the role of an objective lens and induces the gathering effect of the water molecules directed to the electromagnetic-field gradient in air. This phenomenon facilitates a new boundary condition to form a long-range confined nano-scale liquid bridge between the tip and the surface. After the pulling of the optical fiber, 20-nm-thick gold was sputtered on the apex (diameter: approximately 100 nm) of the tip to guide and focus the beam on the spot. The critical power of the laser to overcome the barrier for the formation of a new boundary is 100 microW at the distance of 22 nm from the substrate.     

Two-dimensional dopant profiling by electrostatic force microscopy using carbon nanotube modified cantilevers

A two-dimensional (2D) dopant profiling technique is demonstrated in this work. We apply a unique cantilever probe in electrostatic force microscopy (EFM) modified by the attachment of a multiwalled carbon nanotube (MWNT). Furthermore, the tip apex of the MWNT was trimmed to the sharpness of a single-walled carbon nanotube (SWNT). This ultra-sharp MWNT tip helps us to resolve dopant features to within 10?nm in air, which approaches the resolution achieved by ultra-high vacuum scanning tunnelling microscopy (UHV STM). In this study, the CNT-probed EFM is used to profile 2D buried dopant distribution under a nano-scale device structure and shows the feasibility of device characterization for sub-45?nm complementary metal-oxide-semiconductor (CMOS) field-effect transistors.     

Teleoperated 3-D Force Feedback From the Nanoscale With an Atomic Force Microscope

In this study, 3-D experimental teleoperated force feedback during contact with nanoscale surfaces is demonstrated using an atomic force microscope (AFM) on the slave side and a haptic device on the master side. To achieve 3-D force feedback, coupling between one of the horizontal forces and the vertical force is a crucial bottleneck. To solve this coupling issue, a novel force decoupling algorithm is proposed. This algorithm uses local surface slopes, an empirical friction force model, and the haptic device motion angle projected onto the surface to estimate the friction value during experiments. With this estimation, it is possible to decouple the three orthogonal forces acting on the tip of the AFM cantilever. Moreover, using an adaptive observer, parameters of the friction model can be changed online, removing the necessity to calibrate the friction model initially. Finally, a modified passivity-based bilateral control is used to reflect the scaled nanoscale forces to the master side and the operator. The performance of the system is demonstrated on experimental results for flat and non-flat, and hard and soft surfaces.      

The emergence of multifrequency force microscopy

In atomic force microscopy a cantilever with a sharp tip attached to it is scanned over the surface of a sample, and information about the surface is extracted by measuring how the deflection of the cantilever - which is caused by interactions between the tip and the surface - varies with position. In the most common form of atomic force microscopy, dynamic force microscopy, the cantilever is made to vibrate at a specific frequency, and the deflection of the tip is measured at this frequency. But the motion of the cantilever is highly nonlinear, and in conventional dynamic force microscopy, information about the sample that is encoded in the deflection at frequencies other than the excitation frequency is irreversibly lost. Multifrequency force microscopy involves the excitation and/or detection of the deflection at two or more frequencies, and it has the potential to overcome limitations in the spatial resolution and acquisition times of conventional force microscopes. Here we review the development of five different modes of multifrequency force microscopy and examine its application in studies of proteins, the imaging of vibrating nanostructures, measurements of ion diffusion and subsurface imaging in cells.     

Optical fiber sensor for electric field and electric charge using low-coherence, Fabry-Perot interferometry

An optical fiber sensor for electric field and electric charge, based on the deflection of a small cantilever, has been developed. When the sensor head is placed in an electric field, induced charging produces deflection of the cantilever, which is measured using low-coherence, Fabry-Perot interferometry. The sensor has been used to measure the electric field in the vicinity of a Van de Graaff generator, in the range 135-650 V/cm. The measured deflections are in good agreement with the predictions of a simple model equating the electrostatic and mechanical forces acting on the cantilever.     

Characterization of Probe Dynamic Behaviors in Critical Dimension Atomic Force Microscopy

This paper describes a detailed computational model of the interaction between an atomic force microscope probe tip and a sample surface. The model provides analyses of dynamic behaviors of the tip to estimate the probe deflections due to surface intermittent contact and the resulting dimensional biases and uncertainties. Probe tip and cantilever beam responses to intermittent contact between the probe tip and sample surface are computed using the finite element method. Intermittent contacts with a wall and a horizontal surface are computed and modeled, respectively. Using a 75 nm Critical Dimension (CD) tip as an example, the responses of the probe to interaction forces between the sample surface and the probe tip are shown in both time and frequency domains. In particular, interaction forces between the tip and both a vertical wall and a horizontal surface of a silicon sample are modeled using Lennard-Jones theory. The Snap-in and Snap-out of the probe tip in surface scanning are calculated and shown in the time domain. Based on the given tip-sample interaction force model, the calculation includes the compliance of the probe and dynamic forces generated by an excitation. Cantilever and probe tip deflections versus interaction forces in the time domain can be derived for both vertical contact with a plateau and horizontal contact with a side wall. Dynamic analysis using the finite element method and Lennard-Jones model provide a unique means to analyze the interaction of the probe and sample, including calculation of the deflection and the gap between the probe tip and the measured sample surface.     

Mechanical manifestations of rare atomic jumps in dynamic force microscopy

The resonance frequency and the excitation amplitude of a silicon cantilever have been measured as a function of distance to a cleaved KBr(001) surface with a low-temperature scanning force microscope (SFM) in ultrahigh vacuum. We identify two regimes of tip-sample distances. Above a site-dependent critical tip-sample distance reproducible data with low noise and no interaction-induced energy dissipation are measured. In this regime reproducible SFM images can be recorded. At closer tip-sample distances, above two distinct atomic sites, the frequency values jump between two limiting curves on a timescale of tens of milliseconds. Furthermore, additional energy dissipation occurs wherever jumps are observed. We attribute both phenomena to rarely occurring changes in the tip apex configuration which are affected by short-range interactions with the sample. Their respective magnitudes are related to each other. A specific candidate two-level system is also proposed.     

Cantilever tip-surface contact as a catastrophe machine

The contact of a cantilever tip with a sample surface in a scanning-probe microscopy is considered for the first time as a catastrophe machine. Using an approach of the catastrophe theory, behavior of the tip-surface system is analyzed depending on the internal parameters (stiffness and coordinates of the cantilever holder). The tip jumps and the adhesion force variations in the course of the vertical and lateral cantilever motions are calculated. Projections of the equilibrium surface are constructed and the regimes are established that eliminate the “jumps to contact” and “ microslips.” A new method for the surface vacancy diagnostics and a new algorithm for the controlled tip approach to the surface are proposed.     

Nanomachining by rubbing at ultrasonic frequency under controlled shear force

This study proposes a new method of proximal-probe machining that uses a rubbing process by introducing concentrated-mass (CM) cantilevers. At the second resonance of the CM cantilever vibration, the tip site of the cantilever becomes a node of the standing deflection wave because of the sufficient inertia of the attached concentrated mass. The tip makes a cyclic motion that is tangential to the sample surface, not vertical to it, as in a tapping motion. This lateral tip motion that is selectively excited by CM cantilevers was effective for the material modification of a sample due to the friction between the tip and the sample. Imaging and nanomachining under controlled shear force were demonstrated by means of the modified cantilever and a normal atomic force microscope. We were able to write a micron-sized letter "Z" having a line width of 30-100 nm on a resin surface.     

Probing near-surface nanoscale mechanical properties of low modulus materials using a quartz crystal resonator atomic force microscope

We describe the development of a technique for making indentations on the top 5-20 nm of the surfaces of relatively low modulus materials using a high spatial and force sensitivity atomic force microscope (AFM) whose optical cantilever has been replaced by a quartz crystal resonator (QCR). Unlike conventional optical-cantilever-based AFMs, the accuracy of this technique is not compromised by the compliance of the loading system due to the high stiffness of the QCR. To obtain material modulus values from the indentation results, we find the commonly used Oliver-Pharr model to be unsuitable because of our use of a sharp tip and relatively deep indentation. Instead, we develop a new analysis that may be more appropriate for the geometry we use as well as the non-linear constitutive behavior exhibited by the materials we examined. We calculated values for the moduli of several different materials, which we find to be consistent with the range of published data.