Geometric parameters effect of the atomic force microscopy smart piezoelectric cantilever on the different rough surface topography quality by considering the capillary force

Nowadays, the atomic force microscopy (AFM) is widely used in the nanotechnology as a powerful nano‐robot. The surface topography in Nanoscale is by far one of the most important usages of the AFM device. Hence, in this article, the vibration motion of a piezoelectric rectangular cross‐section micro‐cantilever (MC) which oscillates in the moist environment has been examined based on the Timoshenko beam theory. After extracting the MC governing equations according to Hamilton's principle, the finite element method has been used to discretize the motion equations. The surface topography has been simulated for various roughness forms in the tapping and non‐contact modes by considering the effects of the Van der Waals, capillary and contact forces. Also, the experimental results obtained from the glass surface topography have been simulated. The results illustrate that the time delay in higher natural frequencies in the tapping mode is shorter in comparison with the non‐contact mode, especially, for the lower natural frequencies. The sensitivity analysis of the natural frequencies, topography depth and time delay have been simulated. Results indicate that the most effective parameter is the MC length. In the first mode, the first section length has the highest effect on the surface topography time delay, also, in the second vibration mode; the most effective parameter on the time delay is the MC tip length based on the simulation results.     

Dynamic modeling of oblique non-uniform piezoelectric MC in liquid with various percentages of glycerin in the presence of rough surface

One of the most useful applications of an AFM is imaging of biological particles in a liquid medium. The increase of the topography accuracy in a liquid medium requires accurate dynamic modeling of a Microcantilever (MC). This article investigates the accurate dynamic modeling of the non-uniform AFM piezoelectric MC with rectangular geometry in the amplitude mode in liquid medium for rough surfaces. To increase the accuracy of the modeling, the Modified couple stress (MCS) theory in the liquid medium according to the Timoshenko beam model has been used. Moreover, the differential quadrature (DQ) method has been used for solving equations, because in comparison with the other methods it has a high speed in solving equations and is accurate in the number of fewer elements. In addition, the accurate force modeling has been established by considering the shear forces caused by liquid on the sides of the piezoelectric MC by solving the Navier-Stokes equations, and by considering the hydrodynamic force, squeeze force and applied forces between the sample surface and the MC tip. The results illustrate that utilizing higher vibration modes affect the quality of rough surface topography with the step roughness in the liquid medium and increase the quality of surfaces topography in the tapping mode, especially in the second MC vibration mode. Moreover, it should be noted that the sensitivity of the MC vibration amplitude to the piezoelectric MC angle is higher in comparison with other investigated parameters.     

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.     

Non-optical bimorph-based tapping-mode force sensing method for scanning near-field optical microscopy

A non‐optical bimorph‐based tapping‐mode force sensing method for tip–sample distance control in scanning near‐field optical microscopy is developed. Tapping‐mode force sensing is accomplished by use of a suitable piezoelectric bimorph cantilever, attaching an optical fibre tip to the extremity of the cantilever free end and fixing the guiding portion of the fibre to a stationary part near the tip to decouple it from the cantilever. This method is mainly characterized by the use of a bimorph, which carries out simultaneous excitation and detection of mechanical vibration at its resonance frequency owing to piezoelectric and anti‐piezoelectric effects, resulting in simplicity, compactness, ease of implementation and lack of parasitic optical background. In conjugation with a commercially available SPM controller, tapping‐mode images of various samples, such as gratings, human breast adenocarcinoma cells, red blood cells and a close‐packed layer of 220‐nm polystyrene spheres, have been obtained. Furthermore, topographic and near‐field optical images of a layer of polystyrene spheres have also been taken simultaneously. The results suggest that the tapping‐mode set‐up described here is reliable and sensitive, and shows promise for biological applications.     

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.     

Implementation of a short-tip tapping-mode tuning fork near-field scanning optical microscope

We present the implementation of a short‐tip tapping‐mode tuning fork near‐field scanning optical microscope. Tapping frequency dependences of the piezoelectric signal amplitudes for a bare tuning fork fixed on the ceramic plate, a short‐tip tapping‐mode tuning fork scheme and an ordinary tapping‐mode tuning fork configuration with an 80‐cm optical fibre attached are demonstrated and compared. Our experimental results show that this new short‐tip tapping‐mode tuning fork scheme provides a stable and high Q factor at the tapping frequency of the tuning fork and will be very helpful when long optical fibre probes have to be used in an experiment. Both collection and excitation modes of short‐tip tapping‐mode tuning fork near‐field scanning optical microscope are applied to study the near‐field optical properties of a single‐mode telecommunication optical fibre and a green InGaN/GaN multiquantum well light‐emitting diode.     

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.     

Wear of a single asperity using Lateral Force Microscopy

This report describes an observation of alternating transitions between linear (Amontons) and non-linear friction-load behavior during Lateral Force Microscope experiments using a silicon tip sliding on a quartz surface. Initially, a transition from linear to non-linear behavior was attributed to nanoscale ‘running-in’ of the tip to form a single contact junction at the interface. Once this had occurred, a non-linear relationship between friction and applied load was observed during a number of loading and unloading cycles. For higher compressive loads, a further transition to a more linear friction-load behavior was attributed to nanoscale wear in the contact zone. Notably, when applied load was reduced below this ‘high-load’ transition point, the same non-linear friction-load behavior was again observed, but with a larger (friction per load) magnitude than seen previously. This cycle was repeated five times in these experiments, and each time, switching between non-linear and linear friction-load behavior occurred, along with a progressive increase in friction (per load) each time load was reduced below the transition point. The progressive increase in friction is attributed to an increased area of contact, caused by nanoscale wear at higher applied loads. An increase in tip size was confirmed by tip profiling before and after experiment. By progressively wearing the asperity at higher loads, the (interfacial or true) contact area, A, between the surfaces could be progressively increased, and as a result, a progressive increase in interfacial sliding friction, F _f , was obtained at lower loads (according to F _f = τA).     

Selection of Piezoelectric Cells for Piezoelectric Transducers

A simple technique has been suggested for selecting piezoelectric cells (PC) for piezoelectric transducers used in ultrasonic testing instruments. The technique enables one to evaluate rapidly and efficiently various PC parameters in a wide frequency range. PCs are characterized by two parameters: the antiresonance frequency f _a and voltage U _a at the antiresonance frequency generated in PC. Experimental measurements of f _a and U _a are given for various PCs fabricated by Russian and foreign firms.     

FEM analysis of the vibrational motion of oblique piezoelectric microcantilever in the vicinity of a sample surface in liquid

This article examines an oblique Microcantilever (MC) with an extended piezoelectric layer in liquid. The study of hydrodynamic force in MC which has been floated in viscous fluid is considered as paramount importance. To model the Vibrational motion, the Hamilton's principle has been used. For this purpose, the Vibrational motion equation has been modeled by considering the continuous beam based on the Euler–Bernoulli beam theory in liquid. Furthermore, using the Galerkin method and the Newmark algorithm, the differential equations of the MC has been solved. In this modeling, the inter-atomic forces between the MC tip and the sample surface have been considered in addition to the hydrodynamic and squeeze forces. The simulation results illustrate a reduction in the sensitivity of the vibrational motion under the effect of the squeeze force during the angularization of the MC. Moreover, the results illustrate that by reducing the MC distance from the sample surface, the Vibration amplitude decreases due to the increase in the fluid squeeze force. At the end, it has been shown that the time delay in sample surface topography in liquid substantially decreases in comparison with the air.     

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.     

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.     

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.     

Error analysis and regression mode of the V‐grooved sample in the atomic force microscope simulation measurement mode by the molecular mechanics

Based on the molecular mechanics, this study uses the two‐body potential energy function to construct a trapezoidal cantilever nano‐scale simulation measurement model of contact mode atomic force microscopy (AFM) under the constant force mode to simulate the measurement the nano‐scale V‐grooved standard sample. We investigate the error of offset distance of the cross‐section profile when using the probes with different trapezoidal cantilever probe tip radii (9.5, 8.5, and 7.5 Å) to scan the peak of the V‐grooved standard sample being reduced to one‐tenth (1/10) of its size, and use the offset error to inversely find out the regression equation. We analyze how the tip apex as well as the profile of the tip edge oblique angle and the oblique edge angle affects the offset distance. Furthermore, a probe with a larger radius of 9.5 nm is used to simulate and measure the offset error of scan curve, and acquire the regression equation. By the conversion proportion coefficient of size (ω), and revising the size‐reduced regression equation during the small size scale, a revised regression equation of a larger size scale can be acquired. The error is then reduced, further enhancing the accuracy of the AFM scanning and measurement. SCANNING 31: 147–159, 2009. © 2009 Wiley Periodicals, Inc.     

Modeling and simulation of the probe tip based nanochannel scratching

This paper presents the theoretical modeling and numerical simulation of the probe tip based nanochannel scratching. According to the scratching depth, the probe tip is modeled as a spherical capped conical tip or a spherical capped regular three side pyramid tip to calculate the normal force needed for the nanochannel scratching. In order to further investigate the impact of scratching speed, scratching depth and scratching direction on the scratching process, the scratching simulation is implemented in LS-DYNA software, and a mesh-less method called smooth particle hydrodynamics (SPH) is used for the sample construction. Based on the theoretical and simulated analyses, the increase of the scratching speed, the scratching depth and the face angle will result in an increase in the normal force. At the same scratching depth, the normal forces of the spherical capped regular three side pyramid tip model are different in different scratching directions, which are in agreement with the theoretical calculations in the d₃ and d₄ directions. Moreover, the errors between the theoretical and simulated normal forces increase as the face angle increases.     

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.     

The effect of surface roughness on the vibration behavior of AFM piezoelectric MC in the vicinity of sample surface in air environment based on MCS theory

Recent developments in the field of piezoelectric materials have led to the increasing use of piezoelectric materials in a variety of Atomic Force Microscopy (AFM). Utilizing piezoelectric layer as a sensor and actuator not only reduces the size of microscope but also enhances the quality of surface topography in Micro and Nano scales. In the current study, the effect of surface roughnesson the vibration behavior of AFM piezoelectric micro cantilever (MC) has been investigated in Micro and Nano scales according to the types of the surface roughness. Furthermore, the micro cantilever modelling has been schemed based on the Modified Couple Stress (MCS) theoryin order to model the vibration amplitude of AFM piezoelectric MC that precisely indicates the measured surface roughness. Besides, according to the various modelling of surface roughness, the effect of roughness radius on the minimum and maximum amplitude of Piezoelectric MC has been studied based on the geometry of roughness in air environment. In this environment, the effect of environmental forces including van der Waals, Capillary and contact forces on the vibration amplitude of MC forms the basis of surface topography which has, also, been studied in this article. Moreover, the present study intends to investigate the effect of surface roughness on the vibrating amplitude of MC in both the Tapping and Non-Contact Modes.     

Weighting Factor in Calculation of Comprehensive Quality Index and Optimization of PVC Membrane Composition for Ion Selective Electrode

Abstract

The comprehensive quality index (CQI) method which is used in evaluating the response performance of an ion‐selective electrode has been presented recently. Under this strategy, a set of weighting factors (f _s , f _LR , f _LD , f _t ,) involving a numerical calculation of CQI is the key parameter, not only influencing the magnitude of CQI value, but also inducing a different conclusion on the optimization of composition for poly(vinyl chloride) (PVC)‐based sensing membranes, which was formulated with an electroactive substance, PVC, and plasticizer. In the present work, two techniques, multivariate regression and extremum analysis of a multiple function are used to study the optimization of the weighting factor. The best set of weighting factors obtained is as follows: f _s =0.38, f _LR =0.30, f _LD =0.20, f _t ,=0.10.     

Study of ductile mode cutting in grooving of tungsten carbide with and without ultrasonic vibration assistance

In this study, ductile mode chip formation in conventional cutting and ultrasonic vibration assisted cutting of tungsten carbide workpiece material has been investigated through experimental grooving tests using CBN tools on a CNC lathe. The experimental results show that as the depth of cut was increased there was a transition from ductile mode to brittle mode chip formation in grooving both with and without ultrasonic vibration assistance. However, the critical value of the depth of cut for ductile mode cutting with ultrasonic vibration assistance was much larger than that without ultrasonic vibration assistance. The ratio of the volume of removed material to the volume of the machined groove, f _ab , was used to identify the ductile mode and brittle mode of chip formation in the grooving tests, in which f _ab <1 indicates ductile mode chip formation and f _ab >1 indicates brittle mode chip formation. For the same radius of tool cutting edge, the value of f _ab at the ductile-brittle transition region either with or without ultrasonic vibration was less than 1. However, the f _ab value with ultrasonic vibration assistance was close to 1. The experimental results demonstrate that ultrasonic vibration assisted cutting can be used to improve the ductile mode cutting performance of tungsten carbide work material.Nomenclature A amplitude - A ₁ , A ₂ cross-section areas of the ridge - A _V cross-section area of the groove - A _W the value of A _V subtracted by A ₁+A ₂ - f vibration frequency - f _ab ratio of work material removal - t time - v nominal cutting speed - v _u vibration velocity - v _t true cutting speed in ultrasonic cutting - angular frequency     

Nonlinear dynamic perspectives on dynamic force microscopy

Dynamic force microscopy (DFM) utilizes the dynamic response of a resonating probe tip as it approaches and retracts from a sample to measure the topography and material properties of a nanostructure. We present recent results based on nonlinear dynamical systems theory, computational continuation techniques and detailed experiments that yield new perspectives and insights into DFM.A dynamic model including van der Waals and Derjaguin-Müller-Toporov contact forces demonstrates that periodic solutions can be represented as a catastrophe surface with respect to the approach distance and excitation frequency. Turning points on the surface lead to hysteretic amplitude jumps as the tip nears/retracts from the sample. New light is cast upon sudden global changes that occur in the interaction potential at certain gap widths that cause the tip to "stick" to, or tap irregularly the sample. Experiments are performed using a tapping mode tip on a graphite sample to verify the predictions.