Study on the nano machining process with a vibrating AFM tip on the polymer surface

The polymer has been proved to be nano machined by a vibrating tip in tapping mode of Atomic Force Microscope (AFM). The force between the tip and the surface is an important factor which determines success of the machining process. Controlling this force with high accuracy is the foundation of nanomachining in AFM tapping mode. To achieve a deeper understanding on this process, the tip is modeled as a driving oscillator with damping. Factors affecting the nano machining process are studied. The Hertz elastic contact theory is used to calculate the maximum contact pressure applied by the tip which is employed as a criterion to judge the deformation state of the sample. The simulation results show that: The driven amplitude can be used as a main parameter of controlling the machined depth. Sharper tips and harder cantilevers should be used for successful nanomachining with the vibrating tip. Under the same conditions, a larger tip radius will not only result in the machining error, but also lead to failure of the nanomachining process. The higher driving frequency will lead to a larger tapping force. However it cannot be used as a parameter to control the machined depth because of its narrow variation range. But it is a main error source for the nanomachining process in AFM tapping mode. Moreover, a larger Young's modulus polymer sample will induce a smaller machined depth, a larger maximum contact pressure and a bigger tapping force.     

How to measure energy dissipation in dynamic mode atomic force microscopy

When studying a mechanical system like an atomic force microscope (AFM) in dynamic mode it is intuitive and instructive to analyse the forces involved in tip–sample interaction. A different but complementary approach is based on analysing the energy that is dissipated when the tip periodically interacts with the sample surface. This method does not require solving the differential equation of motion for the oscillating cantilever, but is based entirely on the analysis of the energy flow in and out of the dynamic system. Therefore the problem of finding a realistic model to describe the tip–sample interaction in terms of non-linear force–distance dependencies and damping effects is omitted. Instead, it is possible to determine the energy dissipated by the tip–sample interaction directly by measuring such quantities as oscillation amplitude, frequency, phase shift and drive amplitude. The method proved to be important when interpreting phase data obtained in tapping mode, but is also applicable to a variety of scanning probe microscopes operating in different dynamic modes. Additional electronics were designed to allow a direct mapping of local energy dissipation while scanning a sample surface. By applying this technique to the cross-section of a polymer blend a material specific contrast was observed.     

Contact dynamics of tapping mode atomic force microscopy

A comprehensive model on the dynamics of a tilted tapping mode atomic force microscopy (AFM) is presented, which includes the multimodal analysis, mode coupling mechanisms, adhesion, contact and friction forces induced by the tilting angle. A displacement criterion of contact/impact is proposed to eliminate the assumptions of the previous models such as infinite stiffness of sample or zero impact velocity, which makes the model presented here suitable for more general AFM application scenario, especially for the soft sample case. The AFM tip mass, tip–sample damping, contact forces and intermittent contact can all induce the higher modes participation into the system motion. One degree of freedom or one mode study on the AFM contact dynamics of tapping mode is shown to be inaccurate. The Hertz and Derjaguin–Muller–Toporov models are used for the comparison study of the non-adhesive and adhesive contacts. The intermittent contact and the contact forces are the two major sources of the system nonlinearity. The rich dynamic responses of the system and its sensitivity to the initial conditions are demonstrated by presenting various subharmonic and nonperiodic motions.     

扫描探针声显微镜轻敲模式中相位像的反差机理

根据扫描探针声显微镜(SPAM)轻敲工作模式中探针作周期振动的特点,以及在探针与试样相接触过程中激振力和悬臂探针自由振动的阻尼力很小的假设下,解析求解了探针与试样的碰撞运动方程,得到了最大压痕深度和碰撞时间与探针半径、等效杨氏模量以及界面吸附能等之间的关系式,较直观地说明了SPAM中轻敲模式的相位像反差机理:信号的相位与试样微区的性质、探针振幅、设置点以及试样形貌等有关。并定量预计了纳米金刚石像中的相位差值72.59°,与实验测量平均值73.2°±8.2°一致。同时,合理地解释了实验得到的光学薄膜试样相位像的反差。这些表明SPAM轻敲模式的相位成像是一种纳米分辨率测量材料表面物理性质的成像技术。      

Ultrasonic radiation in dynamic force microscopy

In dynamic force microscopy the cantilever of an atomic force microscope is vibrated at ultrasonic frequencies in the range of several 10 kHz up to several MHz while scanning a sample surface. The amplitude and phase of the cantilever vibration as well as the shift of the cantilever resonance frequencies provide information about local sample surface properties. In several operation modes of dynamic force microscopy, for example force modulation microscopy, tapping mode or atomic force acoustic microscopy, the sensor tip is in contact with the sample at least during a fraction of its vibration cycle. The periodic indentation of the tip with the sample surface generates ultrasonic waves. In this paper, the ultrasonic radiation of a vibrating cantilever into a sample and its contribution to the damping of the cantilever vibration are calculated. The theoretical results are compared to experiments.     

Downwards to metrology in nanoscale: determination of the AFM tip shape with well-known sharp-edged calibration structures

More and more AFMs and AFM profilers will be used to quantify micro- and nanostructures. For a correct characterization and evaluation of the measured structural details, in the nanoscale range, knowledge of the current shape of the AFM tip is needed. Often, the interaction between the AFM tip and the sample leads to a change in the tip shape. Our concept for the determination of tip shapes is based on the measurement of a well-known sharp-edged silicon structure. Each calibration sample contains a selected structure serving as a calibrated width standard, and has a certified pitch. Consequently, the shape of AFM tips can be determined with an accuracy of 10 nm. Received: 2 September 2002 / Accepted: 2 September 2002 / Published online: 5 March 2003 RID="*" ID="*"Corresponding author. Fax: +49-3641/206-199, E-mail: huebner@ipht-jena.de     

Hydrophobic optical elements for near-field optical analysis (NOA) in liquid environment--a preliminary study.

Near-field Scanning Optical Microscopy (NSOM) in liquid environment is expected to allow time resolved morphological mappings on cellular surfaces on the nanoscale level. Near-field Optical Analysis (NOA) via NSOM exploits the energy transfer from the tip of an optical element (tip diameter > or = 20nm), oscillating within the range of the characteristic length of the energy transfer ( approximately 10nm) in the near-field of the surface to be analysed. In NOA, a molecular assembly is monitored by visible light with a resolution far below the wavelength of visible light. Actually, NOA is successfully applied in mapping local optical contrasts, for instance in photonic crystals with dielectric periodicities on the nanoscale. NSOM could in principle be performed in two different modes: tapping mode, with tip-oscillations perpendicular, or shear force mode, with tip-oscillations parallel to the substrate. Both basic modes have specific advantages and disadvantages. In biological systems (e.g. in cell cultures), where scanning in liquids is prevalent, elongated optical elements non-invasively operated in the shear force modus could have some specific advantages when compared to contact modus systems. While tapping mode NSOM provides satisfactory nanoscale images even on solid surfaces covered with millimetres of liquids, the performance of shear force mode NSOM is presently largely confined to operations on dry samples. This is due to the inability of conventional shear force mode NSOM systems to provide sharp topographic images of sample surfaces substantially covered with liquids. By equipping a conventional NSOM system with hydrophobic optical elements, shear force mode based topographic images could be obtained on biological samples in dry as well as in aqueous environment, and with resolutions on the nanoscale level.     

Theoretical Study on the Capillary Force between an Atomic Force Microscope Tip and a Nanoparticle

Considering that capillary force is one of the most important forces between nanoparticles and atomic force microscope （AFM） tips in ambient atmosphere, we develop an analytic approach on the capillary force between an AFM tip and a nanoparticle. The results show that the capillary forces are considerably affected by the geometry of the AFM tip, the humidity of the environment, the vertical distance between the AFM tip and the nanoparticle, as well as the contact angles of the meniscus with an AFM tip and a nanoparticle. It is found that the sharper the AFM tip, the smaller the capillary force. The analyses and results are expected to be helpful for the quantitative imaging and manipulating of nanoparticles by AFMs.     

试样激励下轻敲模式原子力声显微镜的非线性动力学特性

利用Euler-Bernoulli梁理论和DMT针尖-样品作用力模型建立了试样激励下轻敲模式原子力声显微镜(AFAM)系统的动力学方程,并应用非线性动力学分析方法对AFAM微悬臂梁的振动特性进行研究。通过合理改变超声激励幅值、超声激励频率和针尖-样品初始间距等模型参数模拟得到微悬臂梁的超谐波、次谐波、准周期和混沌振动现象,采用时间序列、频谱、相空间、Poincare截面和Lyapunov指数等方法对不同非线性振动特性进行表征。通过分析不同模型参数条件下微悬臂梁针尖-样品作用力特性,探索了微悬臂梁不同非线性振动现象的产生机制。此外,研究了AFAM微悬臂梁运动的分岔特性,发现当超声激励幅值和针尖-样品初始间隙连续变化时,周期、准周期和混沌运动交替出现。研究结果对AFAM系统非线性动力学行为分析和混沌振动控制提供了理论参考。      

Theory of higher harmonics imaging in tapping-mode atomic force microscopy

The periodic impact force induced by tip-sample contact in tapping mode atomic force microscope (AFM) gives rise to non-harmonic response of a micro-cantilever. These non-harmonic signals contain the full characteristics of tip-sample interaction. A complete theoretical model describing the dynamical behaviour of tip--sample system was developed in this paper. An analytic formula was introduced to describe the relationship between time-varying tip--sample impact force and tip motion. The theoretical analysis and numerical results both show that the time-varying tip--sample impact force can be reconstructed by recording tip motion. This allows for the reconstruction of the characteristics of the tip--sample force, like contact time and maximum contact force. It can also explain the ability of AFM higher harmonics imaging in mapping stiffness and surface energy variations.     

Analyses of vibration responses on nanoscale processing in a liquid using tapping-mode atomic force microscopy

An analytical solution of the vibration responses of biological specimens using atomic force microscopy (AFM), which often requires operation in a liquid, is developed. In this study, the modal superposition method is employed to analyze the vibration responses of AFM cantilevers in tapping mode (TM) operated in a liquid and in air. The hydrodynamic force exerted by the fluid on AFM cantilevers is approximated by additional mass and hydrodynamic damping. The tip–sample interaction forces were transformed into axial, distributed transversal, and bending loading, and then applied to the end region of the AFM through the tip holder. The effects of transverse stress and bending stress were adopted to solve the dynamic model. With this model, a number of simulations were carried out to investigate the relationship between the transient responses of the cantilever in a liquid and the parameters considered in nanoscale processing. The simulations show that the vibration of AFM cantilevers in a liquid has dramatically different dynamic characteristics from these of that in air. The liquid reduces the magnitude of the transversal response and reduces the cantilever resonances. Moreover, the magnitudes of response become larger with increasing intermolecular distances and smaller with decreasing tip length. The cantilever vibration amplitudes significantly depend on the damping constant and the mass proportionality constant.     

Tapping mode atomic force microscope combined with reflection scanning near-field optical microscope (AF/RSNOM)

A new kind of scanning probe microscope is introduced in this paper, which is a combination of atomic force microscope and reflection scanning near field optical microscopy (AF/RSNOM) with equi-amplitude tapping mode. The principle and recent experiment result of AF/RSNOM are reported. Besides convenient operation, the bi-functional probe tip of AF/RSNOM brings an even illumination for every sampling position. Experiment result and analysis show that the signal to noise ratio (SNR) of AF/RSNOM optical image is much better than that of other RSNOM without tapping working mode.     

Modeling and simulating of V-shaped piezoelectric micro-cantilevers using MCS theory considering the various surface geometries

Atomic force microscopy (AFM) is widely used as a tool in studying surfaces and mechanical properties of materials at nanoscale. This paper deals with mechanical and vibration analysis of AFM vibration in the non-contact and tapping modes for V-shaped piezoelectric micro-cantilever (MC) with geometric discontinuities and cross section variation in the air ambient. In the vibration analysis, Euler-Bernoulli beam theory based on modified couple stress (MCS) theory has been used. The governing equation of motion has been derived by using Hamilton's principle. By adopting finite element method (FEM), the MC differential equation has been solved. Damping matrix was considered in the modal space. Frequency response was obtained by using Laplace transform, and it has been compared with experimental results. Newmark algorithm has been used based on constant average acceleration to analyze time response of MC, and then time response results in the vibration mode, far from the sample surface have been compared with experimental data. In vicinity of sample surface, MC is influenced by various nonlinear forces between the probe tip and sample surface, including van der Waals, contact, and capillary forces. Time response was examined at different distances between MC base and sample surface, and the best distance was selected for topography. Topography results of different types of roughness showed that piezoelectric MC has been improved in the air ambient. Topography showed more accurate forms of roughness, when MC passes through sample surface at higher frequencies. The surface topography investigation for tapping and non-contact modes showed that using of these two modes are suitable for topography.     

Imitation of non-contact mode while scanning in the presence of an electric double layer?

Non-contact atomic force microscopy (NCAFM) minimizes the physical interaction between the AFM tip and the surface of interest. Several recent studies have reported observation of single atom defects using this technique. The repulsive force is presumably the primary interatomic force (cf. our paper on pseudo-non-contact mode in this issue) responsible for the reported atomic resolution in these studies. The combination of these factors, minimal tip–sample deformation and repulsive force interaction, are responsible for the observation of the single atom defects. In the present study, we show that similar resolution can be achieved utilizing the same two factors but which employs scanning in a surfactant. The method decreases the tip–sample interaction by eliminating the attractive forces between the tip and sample. The surfactant solution induces an electrical double-layer (EDL) on the surface of the tip and sample. This EDL creates additional repulsion that is distributed over a large area, and hence does not contribute noticeably to the image contrast during scanning. However, it does compensate for the high pressures normally experienced by the tip in the absence of surfactant. In addition, the presence of the EDL enhances tip stability during the image scan. This method has been tested on surfaces of such minerals as mica, chlorite, and anhydrite.     

Image dipole approach and polarization effects in scanning near-field optical microscopy

A coupled-dipole approach is proposed in order to study the coupling between the probe tip and the rough sample in SNOM. In the present model both the optical probe tip and the sample protrusions are represented by polarizable dipole spheres. The induced polarization effects on the sample surface can be replaced by the image dipoles in the circumstance of quasi-static electromagnetic field approximation. Applying the radiation theory of the dipole, we have established a set of self-consistent equations to describe the field distribution at the sites of the probe tip and the sample protrusions. The results are completely the same as those obtained by means of the dyadic electromagnetic propagator formalism and also the derivation procedure is relatively simple. This method permits us to analyze the physical mechanisms of the interaction between the probe tip and the rough surface in SNOM intuitively. Based on this approach, we further discuss the influence of polarization of the incident light on the imaging quality. The calculating result shows that the shape and the contrast of the images of the sample are both sensitive to the field polarization, and the z-polarized mode is proved to give better resolution in SNOM.     

AFM tip gauge by nuclear tracks methodology

Atomic force microscopy (AFM) instrumentation in the different modes of operation is a metrologic system for evaluating some surface properties of solid and semisolid materials. The resolution of this instrument depends strongly on the tip sharpness, which can be changed by contamination of the AFM tip apex due to wearing and/or breaking. In order to assess new and old tips, scanning electron microscopy (SEM) inspection is often used, which is not very convenient due to the availability and demand of SEM services. In the market there are some expensive devices for verification of the tip geometry, and for the particular case of AFM in the tapping mode, a simple proposal has been published based on fiber-like samples. In this work, we present an AFM tip gauge device based on the use of a pattern of etched tracks on CR-39 material. For the preparation of the device, the requirements are a radioactive alpha particle source with specific energy, controlled temperature bath and KOH solution, with all these parameters optimized for the tip evaluation, based on the AFM profilometry image. This work shows another interesting and a very useful application of nuclear tracks methodology (NTM).     

Thin film piezoelectric response characterisation using atomic force microscopy with standard contact mode imaging

This article introduces a technique for observing and quantifying the piezoelectric response of thin films, using standard atomic force microscopes (AFMs). The technique has been developed and verified using strontium-doped lead zirconate titanate (PSZT) thin films, which are known for their high piezoelectric response. Quantification of the electro-mechanical voltage coefficient d(33) (pm/V) is made directly based on the applied peak-to-peak voltage and the corresponding peak-to-peak displacement in the obtained scan image. Under the proposed technique the AFM is configured in contact mode, where the silicon nitride tip is set to follow the film displacement at a single point. A known sinusoidal voltage is applied across the film and the displacement determined as a function of time, rather than the typical AFM measurement of displacement versus tip position. The resulting raster image contains several bands, which are directly related to the AFM scan frequency and the applied sinusoidal voltage and its frequency. Different combinations of the AFM scan frequency and the applied sinusoid frequency have been used to characterise the PSZT thin films, with estimated values of d(33) between 109 and 205 pm/V.     

Exploring the facets of “soft crystals” using an Atomic Force Microscope

We obtained monocrystalline droplets in a thermotropic cubic phase, of approximate size 100μm, deposited on a flat surface. The facets of these soft crystals are explored using both an optical microscope and an AFM. The height of individual steps on the principal facets and the lateral distance between steps in vicinal facets are measured using AFM in imaging (tapping) mode. Moreover, the elastic modulus is measured locally, using the AFM tip (in contact mode) as a local rheological probe.     

偏压在隧道效应中的作用

从隧道扫描势垒模型出发。用量子力学导出隧道电流与针尖间的偏压、间距及它们的逸出功之间的关系,并从能带模型的角度导出样品与针尖的间距不变时,隧道电流与偏压成正比关系．指出偏压的作用主要是提高针尖上电子的能量,使针尖上的电子比样品上的电子更容易穿过势垒,从而形成隧道电流．     

原子力显微术轻敲模式中探针样品接触过程及相位衬度研究

借助简单的有阻尼受迫振子模型，研究了原子力显微术轻敲模式中探针与样品接触时间t_c、样品的表面形变D_z和相位衬度对探针设置高度z_c及样品杨氏模量E_s的依赖关系.结果发现,t_c与D_z均随E_s及z_c的增大而减小，同时探针与样品作用过程伴随很小的能量耗散.对轻敲过程中相移量φ的研究表明，E_s较大的样品有较小的φ，且φ随 关键词： 原子力显微术 轻敲模式 相位衬度