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.     

Lateral force microscope calibration using a modified atomic force microscope cantilever

A proof-of-concept study is presented for a prototype atomic force microscope (AFM) cantilever and associated calibration procedure that provide a path for quantitative friction measurement using a lateral force microscope (LFM). The calibration procedure is based on the method proposed by Feiler et al. [Rev. Sci. Instrum. 71, 2746 (2000)] but allows for calibration and friction measurements to be carried out in situ and with greater precision. The modified AFM cantilever is equipped with lateral lever arms that facilitate the application of normal and lateral forces, comparable to those acting in a typical LFM friction experiment. The technique allows the user to select acceptable precision via a potentially unlimited number of calibration measurements across the full working range of the LFM photodetector. A microfabricated version of the cantilever would be compatible with typical commercial AFM instrumentation and allow for common AFM techniques such as topography imaging and other surface force measurements to be performed.     

Manipulation, dissection, and lithography using modified tapping mode atomic force microscope

A modified tapping mode of the atomic force microscope (AFM) was introduced for manipulation, dissection, and lithography. By sufficiently decreasing the amplitude of AFM tip in the normal tapping mode and adjusting the setpoint, the tip-sample interaction can be efficiently controlled. This modified tapping mode has some characteristics of the AFM contact mode and can be used to manipulate nanoparticles, dissect biomolecules, and make lithographs on various surfaces. This method did not need any additional equipment and it can be applied to any AFM system.     

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.     

Precise atomic force microscope cantilever spring constant calibration using a reference cantilever array

A method for calibrating the stiffness of atomic force microscope (AFM) cantilevers is demonstrated using an array of uniform microfabricated reference cantilevers. A series of force-displacement curves was obtained using a commercial AFM test cantilever on the reference cantilever array, and the data were analyzed using an implied Euler-Bernoulli model to extract the test cantilever spring constant from linear regression fitting. The method offers a factor of 5 improvement over the precision of the usual reference cantilever calibration method and, when combined with the Systeme International traceability potential of the cantilever array, can provide very accurate spring constant calibrations.     

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.     

A more comprehensive modeling of atomic force microscope cantilever

This paper focuses on the development of a complete model of an atomic force microscope (AFM) micro-cantilever beam, based on considering the effects of four major factors in modeling the cantilever. They are: rotary inertia and shear deformation of the beam and mass and rotary inertia of the tip. A method based on distributed-parameter modeling approach is proposed to solve the governing equations. The comparisons generally show a very good agreement between the present results and the results of other investigators. As expected, rotary inertia and shear deformation of the beam decrease resonance frequency especially at high ratio of cantilever thickness to its length, and it is relatively more pronounced for higher-order frequencies, than lower ones. Mass and rotary inertia of the tip have similar effects when the mass-ratio of the tip to the cantilever is high. Moreover, the influence of each of these four factors, thickness of the cantilever, density of the tip and inclination of the cantilever on the resonance frequencies has been investigated, separately. It is felt that this work might help the engineers in reducing AFM micro-cantilever design time, by providing insight into the effects of various parameters with the micro-cantilever.     

Direct measurement of tapping force with a cantilever deflection force sensor

An experimental set up dedicated to the measurement of atomic force microscope tapping force was developed. In the set-up, a standard TappingMode™ probe cantilever was used to tap another cantilever equipped with its own low noise and high sensitivity deflection detection system for force measurement. The amplitude and phase change of the tapping lever as well as the deflection of the sensing lever were simultaneously recorded as a function of tip/surface separation. Since the deflection of the sensing cantilever reflects the average force over one interaction cycle, we measured the total average force quantitatively after calibrating the spring constant and deflection sensitivity of the sensing lever. Considerable effort was made to achieve the same force curve in the tapping force measurement as occur during imaging of conventional samples such that the detected tapping force reflects the same interaction of the imaging process.     

Optimizing AC-mode atomic force microscope imaging

We have operated an atomic force microscope in ambient air with several oscillating cantilever modes to establish the optimal scanning parameters to maximize image resolution and to minimize probe and sample damage. This was done by scanning a surface in air and correlating scan parameters such as oscillation amplitude and damping with image resolution. We also examined the geometry of the probe with a scanning electron microscope, before and after scanning, in order to determine whether the scanning technique had an effect on the geometry of the probe tip. If the probe is oscillated such that it contacts the surface on each oscillation, substantial damage or “wear” to the probe occurs and significant degradation of image quality was observed. In ambient air, the optimal conditions are achieved when the probe penetrates the contamination layer and reverses direction before touching the surface. Under these “near-contact” conditions no probe damage is observed and high-image resolution can be maintained indefinitely.     

Analytical evaluation of describing functions arising from harmonic balance analysis of tapping mode atomic force microscope

A new algorithm of harmonic balance analysis of tapping mode atomic force microscopes has been developed. The new algorithm is applicable to analytical evaluation of a large class of common tip-sample interaction potentials. The extensive test calculations show that the proposed algorithm in this work is the efficient one in practical computations. The comparative values presented in tables are acceptable and have the excellent agreement with the numerical results.     

Note: ferrule-top atomic force microscope. II. Imaging in tapping mode and at low temperature

In a recent paper [D.Chavan et al., Rev. Sci. Instrum. 81, 123702 (2010)] we have demonstrated that ferrule-top cantilevers, obtained by carving the end of a ferruled fiber, can be used for contact mode atomic force microscopy in ambient conditions. Here we show that those probes can provide tapping mode images at both room and cryogenic temperatures (12 K).     

Coupled lateral bending-torsional vibration sensitivity of atomic force microscope cantilever

We study the influence of the contact stiffness and the ration between cantilever and tip lengths on the resonance frequencies and sensitivities of lateral cantilever modes. We derive expressions to determine both the effective resonance frequency and the mode sensitivity of an atomic force microscope (AFM) rectangular cantilever. Once the contact stiffness is given, the resonance frequency and the sensitivity of the vibration modes can be obtained from the expression. The results show that each mode has a different resonant frequency to variations in contact stiffness and each frequency increased until it eventually reached a constant value at very high contact stiffness. The low-order vibration modes are more sensitive to vibration than the high-order mode when the contact stiffness is low. However, the situation is reversed when the lateral contact stiffness became higher. Furthermore, increasing the ratio of tip length to cantilever length increases the vibration frequency and the sensitivity of AFM cantilever.     

一种新颖的点衍射干涉轻敲模式原子力显微镜

论述了一种新颖的原子力显微镜,它利用硅微探针的特殊结构和相关光学系统所引起的点衍射干涉现象[1]来扫描成像,因为硅微探针被用作反射型点衍射板,故光路完全共路,再结合锁相检测技术,使得该仪器抗干扰力极强且结构精巧紧凑,可适用于测试软硬不同材料样品,对软质高分子膜材料检测得到了实际的链状结构。     

Studies of tip wear processes in tapping mode atomic force microscopy

Tip integrity is crucial to atomic force microscope image quality. Tip wear not only compromises image resolution but also introduces artifacts. However, the factors that govern wearing have not been systematically studied. The results presented here of tip wearing on a rough titanium surface were determined by monitoring changes in tip shape and the evolution of histograms of complex surface curvatures under different control parameters. In contrast with the common assumption that operating at a low set point (the ratio of tapping amplitude to free oscillation amplitude) wears the tip quickly, we observed that a low set point actually minimizes tip wear on a hard surface regardless of the free amplitude. The results can be interpreted qualitatively with theoretical calculations based on momentum exchange at tapping impact. Operating at a low set point allows more robust scanning than with a high set point (tapping near free amplitude), providing a method to slow down tip wear. Another advantage of a low set point is that amplitude error grows faster than with a high set point by nearly an order of magnitude, permitting an increase in scanning speed.     

原子力显微镜矩形测力臂弹性系数计算方法研究

原子力显微镜测力臂弹性系数的准确性直接影响其测量精度,是仪器标定的一个重要指标。分别运用理论计算方法、动态计算方法和静态计算方法计算原子力显微镜测力臂弹性系数。以矩形测力臂为例,对其进行灵敏度分析,找出影响测力臂弹性系数的参数。分别选取矩形测力臂原始参数值及参数上下极限值,构成3组实验数据。利用上述3种计算方法,分别计算出3组不同参数值的矩形测力臂的弹性系数,然后对这3种计算方法计算所得的弹性系数进行分析并和生产商给出的名义值进行比较,所得结果为原子力显微镜矩形测力臂弹性系数的精确计算提供参考。     

Retrofitting an atomic force microscope with photothermal excitation for a clean cantilever response in low Q environments

It is well known that the low-Q regime in dynamic atomic force microscopy is afflicted by instrumental artifacts (known as "the forest of peaks") caused by piezoacoustic excitation of the cantilever. In this article, we unveil additional issues associated with piezoacoustic excitation that become apparent and problematic at low Q values. We present the design of a photothermal excitation system that resolves these issues, and demonstrate its performance on force spectroscopy at the interface of gold and an ionic liquid with an overdamped cantilever (Q < 0.5). Finally, challenges in the interpretation of low-Q dynamic AFM measurements are discussed.     

Immobilization method of yeast cells for intermittent contact mode imaging using the atomic force microscope

The atomic force microscope (AFM) is widely used for studying the surface morphology and growth of live cells. There are relatively fewer reports on the AFM imaging of yeast cells [1] (Kasas and Ikai, 1995), [2] (Gad and Ikai, 1995). Yeasts have thick and mechanically strong cell walls and are therefore difficult to attach to a solid substrate. In this report, a new immobilization technique for the height mode imaging of living yeast cells in solid media using AFM is presented. The proposed technique allows the cell surface to be almost completely exposed to the environment and studied using AFM. Apart from the new immobilization protocol, for the first time, height mode imaging of live yeast cell surface in intermittent contact mode is presented in this report. Stable and reproducible imaging over a 10-h time span is observed. A significant improvement in operational stability will facilitate the investigation of growth patterns and surface patterns of yeast cells.     

Electrostatic interactions observed when imaging proteins with the atomic force microscope

The atomic force microscope (AFM) is now an established and valuable tool for the study of biological macromolecules in aqueous environments. In this paper we form a patterned boundary via the microcontact printing of individually isolated proteins, covalently attached to a solid support. We use this boundary to investigate electrostatic interactions that can occur between an AFM tip and a protein surface during imaging in solution. The observed height variations of the protein film are found to be a combination of not only structural considerations and thickness of the protein film, but also the repulsive contribution from electrostatic interactions between the AFM tip and the sample. These variations in measured heights of the protein surface can be described by Derjaguin, Landau, Verway, Overbeek (DLVO) theory. Our experimental results show that height measurements can be manipulated either negatively or positively by adjusting the pH and concentration of the electrolyte buffer that is utilised.     

Ferrule-top atomic force microscope

Ferrule-top cantilevers are a new generation of all-optical miniaturized devices for utilization in liquids, harsh environments, and small volumes [G. Gruca et al., Meas. Sci. Technol. 21, 094033 (2010)]. They are obtained by carving the end of a ferruled fiber in the form of a mechanical beam. Light coupled from the opposite side of the fiber allows detection of cantilever deflections. In this paper, we demonstrate that ferrule-top cantilevers can be used to develop ultra compact AFMs for contact mode imaging in air and in liquids with sensitivity comparable to that of commercial AFMs. The probes do not require any alignment procedure and are easy to handle, favoring applications also outside research laboratories.     

Nanodissection and noncontact imaging of plasmid DNA with an atomic force microscope

In this paper we report that a combination of noncontact and contact atomic force microscopy is a convenient and reliable method for imaging and dissecting single plasmid deoxyribonucleic acid (DNA) strands on mica at ambient conditions without leaving feedback and without damage to the scanning tips. The width and thickness measured at different points of the DNA strands agree with literature data and are the same before and after dissection.