Effect of tip mass on frequency response and sensitivity of AFM cantilever in liquid

The effect of tip mass on the frequency response and sensitivity of atomic force microscope (AFM) cantilever in the liquid environment is investigated. For this purpose, using Euler–Bernoulli beam theory and considering tip mass and hydrodynamic functions in a liquid environment, an expression for the resonance frequencies of AFM cantilever in liquid is derived. Then, based on this expression, the effect of the surface contact stiffness on the flexural mode of a rectangular AFM cantilever in fluid is investigated and compared with the case where the AFM cantilever operates in the air. The results show that in contrast with an air environment, the tip mass has no significant impact on the resonance frequency and sensitivity of the AFM cantilever in the liquid. Hence, analysis of AFM behaviour in liquid environment by neglecting the tip mass is logical.     

Surface defects characterization with frequency and force modulation atomic force microscopy using molecular dynamics simulations

This paper is devoted to the characterization of the surface defects using a recently developed AFM technique called frequency and force modulation AFM (FFM–AFM). The simulated system includes a recently developed gold coated AFM probe which interacts with a sample including single-atom vacancy and impurities. In order to examine the behavior of the above system on different transition metals, the molecular dynamics (MD) simulation with Sutton–Chen (SC) inter-atomic potential is used. In this study, an online imaging simulation of the probe and sample is performed, and the effects of the horizontal scan speed, the effective frequency set-point, the cantilever stiffness, the tip-sample rest position and the cantilever quality factor on the resulting images are investigated. Using a proposed optimum controlling scheme for the excitation force amplitude, the cantilever horizontal speed can be increased.     

Material anisotropy revealed by phase contrast in intermittent contact atomic force microscopy

Phase contrast in intermittent-contact atomic force microscopy (AFM) reveals in-plane structural and mechanical properties of polymer monolayers. This is surprising, because measurements of nanoscale in-plane properties typically require contact mode microscopies. Our measurements are possible because the tip oscillates not just perpendicular but also parallel to the sample surface along the long axis of the cantilever. This lateral tip displacement is virtually universal in AFM, implying that any oscillating-tip AFM technique is sensitive to in-plane material properties.     

Evaluation of the contact resonance frequencies in atomic force microscopy as a method for surface characterisation (invited)

The combination of ultrasound with atomic force microscopy (AFM) opens the high lateral resolution of scanning probe techniques in the nanometer range to ultrasonics. One possible method is to observe the resonance frequencies of the AFM sensors under different tip-sample interaction conditions. AFM sensors can be regarded as small flexible beams. Their lowest flexural and torsional resonance frequencies are usually found to be in a range between several kHz and several MHz depending on their exact geometrical shape. When the sensor tip is in a repulsive elastic contact with a sample surface, the local indentation modulus can be determined by the contact resonance technique. Contact resonances in the ultrasonic frequency range can also be used to improve the image contrast in other dynamic techniques as, for example, in the so-called piezo-mode. Here, an alternating electric field is applied between a conducting cantilever and a piezoelectric sample. Via the inverse piezoelectric effect, the sample surface is set into vibration. This excitation is localised around the contact area formed by the sensor tip and the sample surface. We show applications of the contact resonance technique to piezoelectric ceramics.     

Frequency shifts of cantilever in AFM

The frequency shift and frequency shift image of cantilever in AFM have been studied by numerical integration of the equation of motion of cantilever for silicon tip with rutile TiO₂(0 0 1) surface in UHV conditions and by the Hamaker summation method for the tip-surface interaction forces. The effects of the excitation frequency at the cantilever base and the equilibrium position of the tip on the frequency shift have been calculated and the results showed the same phenomena as those measured, e.g., the frequency shift increased dramatically or rapidly before the contact point and was then almost level off after the contact point. The effects of scanning speed and the initial closest distance of tip to the contact point have been calculated at different excitation frequencies at the cantilever base and the results showed that proper frequency shift image could be obtained either by noncontact mode at the excitation frequency slightly less than the resonance frequency of free cantilever, or by tapping mode at the excitation frequency a few times smaller than the resonance frequency of free cantilever.     

Simultaneous imaging of tunneling current and damping energy by noncontact-AFM in ultra-high vacuum

We have simultaneously observed the images of tunneling current and damping energy with the nc-AFM (noncontact atomic force microscopy) image of Si(111)7ǻ. When inverted contrast is observed in the constant frequency shift nc-AFM image, the current image is not inverted, and vice versa. On the other hand, the damping images show a contrast similar to that of the nc-AFM images; the damping decreases at a narrow separation between the tip and the sample. This possibly indicates that the damping decreases as the attractive interaction increases under a constant oscillation amplitude of the cantilever. To keep the oscillation amplitude constant under an attractive interaction between a tip and a sample, the total energy of the cantilever oscillation is reduced and the oscillation velocity of the cantilever decreases. An explanation is proposed that the change in energy dissipation occurs in the cantilever oscillation, depending on the oscillation velocity of the cantilever, and the value is estimated from a simple model.     

原子力显微镜高次谐波幅度对样品弹性性质表征的研究

轻敲模式下原子力显微镜微悬臂探针在接近其基态共振频率的外加驱动下振荡, 其末端针尖周期性靠近、远离样品, 产生于针尖与样品非线性相互作用过程中的高次谐波信号包含更多的待测样品表面纳米力学特性等方面的信息. 通过理论分析、计算, 系统地研究了针尖与样品接触时间受样品弹性模量的影响, 以及高次谐波幅度与接触时间的关系, 获得了通过高次谐波幅度区分待测样品表面弹性性质差异的规律. 并在自制的高次谐波成像实验装置上, 得到了与理论预期一致的实验结果. 关键词： 轻敲模式原子力显微镜 接触时间 高次谐波幅度 弹性模量     

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.     

原子力显微镜探针悬臂几何结构变化对高次谐波信息增强的研究

轻敲模式原子力显微镜高次谐波信号包含待测样品表面纳米力学特性等方面的信息, 但是传统原子力显微镜的高次谐波信号非常微弱. 里兹法证明在探针悬臂的特定位置打孔可以实现探针的内共振从而增强高次谐波信号强度. 本文通过有限元仿真计算获得探针第一共振频、第二共振频及其比值随着孔的尺寸和位置变化的规律. 在实验上通过聚焦离子束在探针悬臂上打孔使其第二共振频约为第一共振频的6倍, 提高了第6次谐波信号的信噪比, 并在实验室研制的高次谐波成像实验装置上获得了6次谐波图像. 关键词： 轻敲模式原子力显微镜 探针悬臂几何结构 高次谐波 聚焦离子束加工     

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.     

Dynamics of high quality factor force microscope microcantilevers operated in contact mode

In AFM system with contact mode operation, the surface structure is determined by measuring the variation of the microcantilever tip deflection as the tip scans across the sample. Therefore, the dynamic characteristics of the microcantilever, including the stability, rapidity and accuracy performances, are extremely important parameters in determining the performance of AFM. In this paper, we obtain the analytical expressions of the deflection, overshoot, and adjustment time of the cantilever by using the Laplace transform theorem. The influence of the intrinsic parameters on the system dynamics is discussed in detail, which provides theoretical guidance for selecting samples in the experiments. Moreover, we propose a new control method based on the velocity feedback control in order to enhance the dynamic features of the system. The results indicate that the new control method can effectively improve the dynamic characteristics of the microcantilever.     

Detection of single-electron charging in an individual InAs quantum dot by noncontact atomic-force microscopy

Single-electron charging in an individual InAs quantum dot was observed by electrostatic force measurements with an atomic-force microscope (AFM). The resonant frequency shift and the dissipated energy of an oscillating AFM cantilever were measured as a function of the tip-back electrode voltage, and the resulting spectra show distinct jumps when the tip was positioned above the dot. The observed jumps in the frequency shift, with corresponding peaks in dissipation, are attributed to a single-electron tunneling between the dot and the back electrode governed by the Coulomb blockade effect, and are consistent with a model based on the free energy of the system. The observed phenomenon may be regarded as the "force version" of the Coulomb blockade effect.     

Physical properties of dynamic force microscopies in contact and noncontact operation

In the field of Scanning Force Microscopy several dynamical contact and noncontact modes have been introduced increasing the range of detectable surface and interface properties, and allowing to detect material properties such as elasticity and mass density on the nanometer scale. A detailed understanding of tip/surface interactions and the dynamic processes involved is required to understand the origin of a material contrast using these techniques. Here a general method to solve the equation of motion of a vibrating SFM cantilever/tip system in an external force field is presented. Contact modes as well as intermittent contact modes are discussed using a single set of equations describing the cantilever/tip motion, and by varying the size of amplitudes of the vibrating cantilever/tip system. To quantitatively describe the oscillation behavior of the SFM cantilever at large amplitudes the computer simulations are based on the MYD/BHW model providing a realistic contact model with respect to the contact area, the size of the contact forces as well as the transition from repulsive to attractive forces. The results are compared with the experiment and with different approaches based on analytical and numerical models.     

Strongly nonlinear beats in the dynamics of an elastic system with a strong local stiffness nonlinearity: Analysis and identification

We consider a linear cantilever beam attached to ground through a strongly nonlinear stiffness at its free boundary, and study its dynamics computationally by the assumed-modes method. The nonlinear stiffness of this system has no linear component, so it is essentially nonlinear and nonlinearizable. We find that the strong nonlinearity mostly affects the lower-frequency bending modes and gives rise to strongly nonlinear beat phenomena. Analysis of these beats proves that they are caused by internal resonance interactions of nonlinear normal modes (NNMs) of the system. These internal resonances are not of the classical type since they occur between bending modes whose linearized natural frequencies are not necessarily related by rational ratios; rather, they are due to the strong energy-dependence of the frequency of oscillation of the corresponding NNMs of the beam (arising from the strong local stiffness nonlinearity) and occur at energy ranges where the frequencies of these NNMs are rationally related. Nonlinear effects start at a different energy level for each mode. Lower modes are influenced at lower energies due to larger modal displacements than higher modes and thus, at certain energy levels, the NNMs become rationally related, which results in internal resonance. The internal resonances of NNMs are studied using a reduced order model of the beam system. Then, a nonlinear system identification method is developed, capable of identifying this type of strongly nonlinear modal interactions. It is based on an adaptive step-by-step application of empirical mode decomposition (EMD) to the measured time series, which makes it valid for multi-frequency beating signals. Our work extends an earlier nonlinear system identification approach developed for nearly mono-frequency (monochromatic) signals. The extended system identification method is applied to the identification of the strongly nonlinear dynamics of the considered cantilever beam with the local strong nonlinear stiffness at its free end.     

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.     

Imaging of chemical reactivity and buckled dimers on Si(100)2×1 reconstructed surface with noncontact AFM

We have investigated the force interactions between the Si tip and the Si(100)2×1 reconstructed surface in the noncontact atomic-force microscopy (AFM) measurement. We observed two types of frequency shift curves without and with discontinuity, similar to the Si(111)7×7 surface. The image contrast changes drastically whether the frequency shift curve shows discontinuity or not. In the case of the frequency shift curves without discontinuity, the noncontact AFM images almost reflect the surface topography including dimers and adsorbates. In the case of the frequency shift curves with discontinuity, they reflect strongly the chemical reactivity of surface. Furthermore, in the case of the frequency shift curves without discontinuity, for the first time, the stabilize-buckling of dimers induced by a defect can be observed. This suggests that the force interactions during the noncontact AFM measurement hardly influence the surface dynamics.     

Electrical Measurement Techniques in Atomic Force Microscopy

A conductive tip in an atomic force microscope (AFM) has extended the capability from conventional topographic imaging to electrical surface characterization. The conductive tip acts as a voltage electrode to provide stimuli and monitor electrical surface properties. In this review article, we have organized the AFM electrical techniques based on whether the electrical properties are monitored at the cantilever tip or across the sample. Furthermore, the techniques are organized based on probe detection signal. A number of acronyms are used in the literature, and the more commonly used ones are identified. The principle of each technique is described, and representative applications are presented. A better understanding of the spectrum of techniques should serve as the driver to expand the application of electrical techniques to study interdisciplinary phenomena at the nanoscale.     

Tip-based nanoscale selective growth of discrete silicon nanowires by near-field laser illumination

Growth of discrete silicon nanowires is reported with nanoscale location selectivity by employing near-field laser illumination. An uncoated dielectric atomic force microscope (AFM) tip provides a nanometer-scale light source that is sufficiently localized to induce nucleation and subsequent growth of a single nanowire under its optical near-field. Far-field laser-induced heating is additionally supplied to the substrate to both relieve the required near-field light budget and also assist stable epitaxial growth. Specific catalysts are selected for the nanowire growth by non-contact mode AFM imaging. Through real-time monitoring of the deflection of the AFM cantilever during the growth process, the gap between the tip and the sample and hence truly near-field illumination are maintained throughout the growth process. The study shows that tip-based near-field laser illumination could be an effective tool for the direct integration of semiconductor nanowires.     

新型AFM探针的制备及应用

采用熔拉 -腐蚀复合方法 ,将普通单模石英光纤制成直锥形光纤探针。利用自制工具将探针打弯 ,制成悬臂式光纤探针 ,在AFM上取得了较理想的测试结果。将自制光纤探针和商用硅材料探针获得的两种扫描图像进行了对比 ,分析了悬臂式光纤探针的特点     

Giant enhancement of noncontact friction between closely spaced bodies by dielectric films and two-dimensional systems

The effect of an external bias voltage and spatial variations of the surface potential on the damping of cantilever vibrations in an atomic force microscope (AFM) is considered. The damping is due to an electrostatic friction that arises due to dissipation of the energy of an electromagnetic field generated in the sample by oscillating static charges induced on the surface of the AFM probe tip by the bias voltage or spatial variations of the surface potential. A similar effect appears when the tip is oscillating in an electrostatic field created by charged defects present in the dielectric sample. The electrostatic friction is compared to the van der Waals (vdW) friction between closely spaced bodies, which is caused by a fluctuating electromagnetic field related to the quantum and thermal fluctuations of current density inside the bodies. It is shown that the electrostatic friction and the vdW friction can be strongly enhanced in the presence of dielectric films or two-dimensional (2D) structures—such as a 2D electron system or an incommensurate layer of adsorbed ions exhibiting acoustic oscillations—on the probe tip and sample surfaces. It is also shown that the damping of cantilever oscillations caused by the electrostatic friction in the presence of such 2D structures can have the same order of magnitude and the same dependence on the distance as observed in experiment by Stipe et al. [Phys. Rev. Lett. 87, 096801 (2001)]. At small distances, the vdW friction can be large enough to be measured in experiment. In interpreting the experimental data that obey a quadratic dependence on the bias voltage, one can reject a phonon mechanism according to which the friction depends on the fourth power of the voltage.