Influence of Poisson's ratio variation on lateral spring constant of atomic force microscopy cantilevers

Atomic force microscopy (AFM) can be used to measure the surface morphologies and the mechanical properties of nanostructures. The force acting on the AFM cantilever can be obtained by multiplying the spring constant of AFM cantilever and the corresponding deformation. To improve the accuracy of force experiments, the spring constant of AFM cantilever must be calibrated carefully. Many methods, such as theoretical equations, the finite element method, and the use of reference cantilever, were reported to obtain the spring constant of AFM cantilevers. For the cantilever made of single crystal, the Poisson's ratio varies with different cantilever-crystal angles. In this paper, the influences of Poisson's ratio variation on the lateral spring constant and axial spring constant of rectangular and V-shaped AFM cantilevers, with different tilt angles and normal forces, were investigated by the finite element analysis. When the cantilever's tilt angle is 20 degrees and the Poisson's ratio varies from 0.02 to 0.4, the finite element results show that the lateral spring constants decrease 11.75% for the rectangular cantilever with 1muN landing force and decrease 18.60% for the V-shaped cantilever with 50nN landing force, respectively. The influence of Poisson's ratio variation on axial spring constant is less than 3% for both rectangular and V-shaped cantilevers. As the tilt angle increases, the axial spring constants for rectangular and V-shaped cantilevers decrease substantially. The results obtained can be used to improve the accuracy of the lateral force measurement when using atomic force microscopy.     

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。     

A force-matching method for quantitative hardness measurements by atomic force microscopy with diamond-tipped sapphire cantilevers

We present a new method to improve the accuracy of force application and hardness measurements in hard surfaces by using low-force (<50 μN) nanoindentation technique with a cube-corner diamond tip mounted on an atomic force microscopy (AFM) sapphire cantilever. A force calibration procedure based on the force-matching method, which explicitly includes the tip geometry and the tip-substrate deformation during calibration, is proposed. A computer algorithm to automate this calibration procedure is also made available. The proposed methodology is verified experimentally by conducting AFM nanoindentations on fused quartz, Si(1 0 0) and a 100-nm-thick film of gold deposited on Si(1 0 0). Comparison of experimental results with finite element simulations and literature data yields excellent agreement. In particular, hardness measurements using AFM nanoindentation in fused quartz show a systematic error less than 2% when applying the force-matching method, as opposed to 37% with the standard protocol. Furthermore, the residual impressions left in the different substrates are examined in detail using non-contact AFM imaging with the same diamond probe. The uncertainty of method to measure the projected area of contact at maximum force due to elastic recovery effects is also discussed.     

Dynamic spring constants for higher flexural modes of cantilever plates with applications to atomic force microscopy

In atomic force microscopy (AFM) a sharp tip fixed close to the free end of a cantilever beam interacts with a surface. The interaction can be described by a point-mass model of an equivalent oscillator with a single spring located at the position of the tip. However, other spring constants have to be used to describe the oscillation behavior correctly if forces are acting on the cantilever over an extended lateral range. A point-mass model is then no longer valid. In the present study we derive expressions for the spring constants of cantilevers that can interact with any part of their plan view area along the beam and for all flexural modes. The equations describe the oscillation behavior in the corresponding mass model and are based on the eigenfrequencies and modal shapes of the free cantilever. The results are of high practical relevance, for example if an AFM is operated in a higher flexural mode, if the tip is not located at the free end of the cantilever beam, or if the external conservative forces affecting cantilever movement are not restricted to a single point. The limitations of the approach are discussed.     

Investigation of penetration force of living cell using an atomic force microscope

Recently, the manipulation of a single cell has been receiving much attention in transgenesis, in-vitro fertilization, individual cell based diagnosis, and pharmaceutical applications. As these techniques require precise injection and manipulation of cells, issues related to penetration force arise. In this work the penetration force of living cell was studied using an atomic force microscope (AFM). L929, HeLa, 4T1, and TA3 HA II cells were used for the experiments. The results showed that the penetration force was in the range of 2∼22 nN. It was also found that location of cell penetration and stiffness of the AFM cantilever affected the penetration force significantly. Furthermore, double penetration events could be detected, due to the multi-membrane layers of the cell. The findings of this work are expected to aid in the development of precision micro-medical instruments for cell manipulation and treatment. This paper was presented at the 9^th Asian International Conference on Fluid Machinery (AICFM9), Jeju, Korea, October 16–19, 2007.recommended for publication in revised form by Associate Editor Keum-Sik Hong Eun-Young Kwon received her B.S. and M.S degrees in Mechanical Engineering from Yonsei University, Korea, in 2005 and 2007, respectively. Ms. Kwon is currently an Engineer at Digital Printing Division of Samsung Electronics. Her research interests include biotribology, tribology, and electrophotography. Young-Tae Kim received his B.S. in Automotive Engineering from Seoul National University of Technology, Korea, in 2003. He then received his M.S. degree from Yonsei University in Seoul, Korea in 2005. Mr. Kim is currently a Ph. D. candidate at the Graduate School of Mechanical Engineering at Yonsei University in Seoul, Korea. His research interests include biotribology, tribology, and biomechanics. Dae-Eun Kim received his B.S. in Mechanical Engineering from Tufts University, USA, in 1984. He then received his M.S. and Ph.D. degrees from M.I.T. in 1986 and 1991, respectively. Dr. Kim is currently a Professor at the School of Mechanical Engi-neering at Yonsei University in Seoul, Korea. His research interests include tribology, functional surfaces, and micromachining.     

Design of a sample approach mechanism for a metrological atomic force microscope

In order to obtain the high accuracy required for a metrological atomic force microscope, the sample approach mechanism meets strict specifications. The design presented in this paper offers a stiff construction, which limits the influences of floor vibrations on the measurement. Next to this, thermal considerations in the design decrease the uncertainties introduced by temperature variations of the environment. Uncertainties can also be caused by misalignment of the sample holder with respect to the measurement system of three interferometers. To limit these uncertainties, the approach mechanism provides sufficient alignment possibilities. The performance of the sample approach mechanism was evaluated by means of a finite element simulation of its dynamic stiffness. A series of experiments provide the unknown parameters to the simulation model. The dynamic stiffness lies around 395 Hz, which is sufficiently high to provide accurate measurements.     

Force-gradient-induced mechanical dissipation of quartz tuning fork force sensors used in atomic force microscopy

We have studied the dynamics of quartz tuning fork resonators used in atomic force microscopy taking into account the mechanical energy dissipation through the attachment of the tuning fork base. We find that the tuning fork resonator quality factor changes even in the case of a purely elastic sensor-sample interaction. This is due to the effective mechanical imbalance of the tuning fork prongs induced by the sensor-sample force gradient, which in turn has an impact on dissipation through the attachment of the resonator base. This effect may yield a measured dissipation signal that can be different from the one exclusively related to the dissipation between the sensor and the sample. We also find that there is a second-order term in addition to the linear relationship between the sensor-sample force gradient and the resonance frequency shift of the tuning fork that is significant even for force gradients usually present in atomic force microscopy, which are in the range of tens of N/m.     

原子力显微镜在聚合物研究中的应用

原子力显微镜以其分辨率高、样品无需特殊制备、实验可在大气环境中进行等优点而广泛应用于聚合物研究之中,弥补扫描隧道显微镜不能观测非导电样品的缺憾。近年来,其应用已由对聚合物表面几何形貌的观测发展到纳米级结构和表面性能的研究领域。在介绍原子力显微镜工作原理的基础上,简要回顾其在聚合物研究方面的若干新应用,并对其应用前景作展望。     

X轴分离式高速原子力显微镜系统设计

为了提高原子力显微镜(Atomic Force Microscope,AFM)的成像速度,本文提出了一种新的AFM结构设计方案并搭建了相应的实验系统。在该方案中,Y、Z扫描器集成于测头内驱动探针进行慢轴扫描和形貌反馈;X扫描器与测头分离,驱动样品做快轴扫描。X扫描器采用高刚性的独立一维纳米位移台,能够承载尺寸和质量较大的样品高速往复运动而不易发生共振;同时Z扫描器的载荷实现最小化,固有频率得以显著提高。为了避免测头的扫描运动引起检测光束与探针相对位置的偏差,设计了一种随动式光杠杆光路;为了便于装卸探针以及精确调整激光在探针上的反射位置,设计了基于磁力的探针固定装置和相应的光路调节方案。对所搭建的AFM系统的初步测试结果表明,该系统在采用三角波驱动和简单PID控制算法的情况下,可搭载尺寸达数厘米且质量超过10g的较大样品实现13μm×13μm范围50Hz行频的高速成像。     

原子力显微镜原理与应用技术

本文简述原子力显微镜的工作原理,对比说明敲击模式的优越性,指出针尖-样品卷积效应和假象产生的原因,并例证其应用领域及其测试效果。     

无线控制式原子力显微镜系统

提出了一种基于嵌入式系统和WiFi无线控制的接触模式原子力显微镜(AFM)系统。该AFM系统直接由迷你型移动电源给扫描与反馈电路及嵌入式系统等供电;嵌入式系统由微型电脑树莓派和微小型ADDA模块构成,通过WiFi与笔记本电脑实现无线数据通信。利用这一方法,成功研发了无线控制式AFM系统,并开展了微纳米样品的扫描成像实验。实验结果表明,该AFM系统的横向分辨率达到纳米量级,纵向分辨率达到0.1nm,最大扫描范围为3.6μm×3.6μm。该系统的显著特点是无需交流市电供电,无需直流高压电源,也无需与计算机之间的线缆连接,可在约100m远处通过无线控制的方式实现AFM的扫描成像。这一新型AFM系统,不仅能够在微纳米技术的常规领域得到应用,而且在野外考察、隔离环境、真空条件、气体氛围环境及星际探测等特殊领域具有广阔的应用前景。     

Dynamic friction measurements with an atomic force microscope on polymer surfaces

The combination of scanning friction force microscopy (SFFM) and lock‐in techniques leads to dynamic SFFM (DSFFM) and provides great advantages in friction force studies with sub‐micrometre resolution. In this paper are presented measurements on thin adsorbed organic films on polymers (polymer blend of 75% poly(allylaminehydrochloride) (PAA) and 25% poly(diallyl‐dimethylammonium chloride) (PDDAC)) and on mica (as a reference). The amplitude and phase response as a function of the excitation amplitude can be explained on hard surfaces by a simple static and dynamic friction model. This model allows us further to distinguish static friction forces and kinetic friction forces in a quantitative way. Furthermore, we demonstrate the use of these spectra to determine the correct modulation amplitude of the excitation to achieve the optimal friction contrasts directly. Polymer data suggest that the viscoelastic shear flow under the atomic force microscope (AFM) tip is responsible for the shape of the phase and amplitude spectrum. Lastly, we demonstrate that DSFFM is a useful technique for surface characterisation in situations where SFFM may not be adequate.     

Calibration of AFM cantilever stiffness: a microfabricated array of reflective springs

Calibration of the spring constant of atomic force microscope (AFM) cantilevers is necessary for the measurement of nanonewton and piconewton forces, which are critical to analytical applications of AFM in the analysis of polymer surfaces, biological structures and organic molecules.

We have developed a compact and easy-to-use reference standard for this calibration. The new artifact consists of an array of 12 dual spiral-cantilever springs, each supporting a mirrored polycrystalline silicon disc of 160 μm in diameter. These devices were fabricated by a three-layer polysilicon surface micromachining method, including a reflective layer of gold on chromium. We call such an array a Microfabricated Array of Reference Springs (MARS). These devices have a number of advantages. Cantilever calibration using this device is straightforward and rapid. The devices have very small inertia, and are therefore resistant to shock and vibration. This means they need no careful treatment except reasonably clean laboratory conditions.

The array spans the range of spring constant from around 0.16 to 11 N/m important in AFM, allowing almost all contact-mode AFM cantilevers to be calibrated easily and rapidly. Each device incorporates its own discrete gold mirror to improve reflectivity. The incorporation of a gold mirror both simplifies calibration of the devices themselves (via Doppler velocimetry) and allows interferometric calibration of the AFM z-axis using the apparent periodicity in the force–distance curve before contact. Therefore, from a single force–distance curve, taking about one second to acquire, one can calibrate the cantilever spring constant and, optionally, the z-axis scale. These are all the data one needs to make accurate and reliable force measurements.     

Calibration of the scanning (atomic) force microscope with gold particles

Scanning force microscopy (SFM) holds great promise for biological research. Two major problems that have confronted imaging with the scanning force microscope have been the distortion of the image and overestimation in measurements of lateral size due to the varying geometry and characteristics of the scanning tip. In this study, spherical colloidal gold particles (10, 20 and 40 nm in diameter) were used to determine (1) tip parameters (size, shape and semivertical angle); (2) the distortion of the image caused by the tip; and (3) the overestimation or broadening of lateral dimensions. These gold particles deviate little in size, are rigid and have a size similar to biological macromolecules. Images of the colloidal gold particles by SFM were compared with those obtained by electron microscopy (EM). The height of the gold particles as measured by SFM and EM was comparable and was little affected by the tip geometry. The measurements of the lateral dimensions of colloidal gold, however, showed substantial differences between SFM and EM in that SFM resulted in an overestimate of the lateral dimensions. Moreover, the distortion of images and broadening of lateral dimensions were specific to the SFM tip used. The calibration of the SFM tip with mica provided little clue as to the type of distortion and the amount of lateral broadening observed when the larger gold particles were scanned. The SFM image also depended on the orientation of the tip with respect to the specimen. Our results suggest that quantitative SFM imaging requires calibration to identify and account for both the distortions and the magnitude of lateral broadening caused by the cantilever tip. Calibration with gold particles is fast and nondestructive to the tip. The raw imaging data of the specimen can be corrected for the tip effect and true structural information can be derived. In summary, we present a simple and practical method for the calibration of the SFM tip using gold particles with a size in the range of biomacromolecules that allows: (1) selection of a cantilever tip that produces an image with minimal distortion; (2) quantitative determination of tip parameters; (3) reconstruction of the shape of the tip at different heights from the tip apex; (4) appreciation of the type of distortion that may be introduced by a specific tip and quantification of the overestimation of the lateral dimensions; and (5) calculation of the true structure of the specimen from the image data. The significance is that such calibration will permit quantitative and accurate imaging with SFM.     

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.     

Fabrication of ball-shaped atomic force microscope tips by ion-beam-induced deposition of platinum on multiwall carbon nanotubes

Ball-shaped atomic force microscope (AFM) tips (ball tips) are useful in AFM metrology, particularly in critical dimension AFM metrology and in micro-tribology. However, a systematic fabrication method for nano-scale ball tips has not been reported. We report that nano-scale ball tips can be fabricated by ion-beam-induced deposition (IBID) of Pt at the free end of multiwall carbon nanotubes that are attached to AFM tips. Scanning electron microscopy and transmission electron microscopy analyses were done on the Pt ball tips produced by IBID in this manner, using ranges of Ga ion beam conditions. The Pt ball tips produced consisted of aggregated Pt nano-particles and were found to be strong enough for AFM imaging.     

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.     

A symmetrical stretching stage for electrical atomic force microscopy

We present a remotely-controlled device for sample stretching, designed for use with atomic force microscopy (AFM) and providing electrical connection to the sample. Such a device enables nanoscale investigation of electrical properties of thin gold films deposited on polydimethylsiloxane (PDMS) substrate as a function of the elongation of the structure. Stretching and releasing is remotely controlled with use of a dc actuator. Moreover, the sample is stretched symmetrically, which gives an opportunity to perform AFM scans in the same site without a time-consuming finding procedure. Electrical connections to the sample are also provided, enabling Kelvin probe force microscopy (KPFM) investigations. Additionally, we present results of AFM imaging using the stretching stage.     

Phase imaging with intermodulation atomic force microscopy

Intermodulation atomic force microscopy (IMAFM) is a dynamic mode of atomic force microscopy (AFM) with two-tone excitation. The oscillating AFM cantilever in close proximity to a surface experiences the nonlinear tip-sample force which mixes the drive tones and generates new frequency components in the cantilever response known as intermodulation products (IMPs). We present a procedure for extracting the phase at each IMP and demonstrate phase images made by recording this phase while scanning. Amplitude and phase images at intermodulation frequencies exhibit enhanced topographic and material contrast.     

Improved estimation of contact compliance via atomic force microscopy using a calibrated cantilever as a reference sample

A method to improve accuracy of surface compliance determination by atomic force microscopy is presented, based on using calibrated cantilevers as the reference samples. During each work session, a 1-D compliance map of a reference cantilever is calculated from force–indentation curves along its axis, by the standard ‘indentation mode’. An independent measurement of local compliance on the reference cantilever is obtained by 2-D imaging in constant deflection and using analytical equations based on its known geometry and material properties, called ‘imaging mode’. A re-mapping of the apparent (‘indentation mode’) to the true (‘imaging mode’) compliance is thus obtained, which is applied on ‘indentation mode’ measurements of an unknown sample. This method demonstrates correction in the right direction for a polystyrene plate and a Teflon foil reference samples. The method is then applied on an unknown sample of flat agarose gel patterned with spots of polylysine protein.