Error in dynamic spring constant calibration of atomic force microscope probes due to nonuniform cantilevers

Many common atomic force microscope (AFM) spring constant calibration methods regard the AFM probe as a uniform cantilever, neglecting the tip mass and any nonuniformity in the thickness of the probe along its length. This work quantifies the error in the spring constant estimated by the Sader and thermal calibration methods due to nonuniformity in the thickness of the cantilever and the influence of the mass loading effect of the probe tip. Formulae are presented that can be used to compute the uncertainty in cantilever calibration for an arbitrary thickness nonuniformity, or to correct the calibration methods if the thickness nonuniformity is known. The results show that both methods are quite sensitive to nonuniformity. When the first dynamic mode is used in the calibration, the error in the spring constant estimated by either method is between - 4% and 9% for a cantilever whose thickness increases or decreases linearly by 30% along its length. The errors are several times larger if the second or higher dynamic modes are used. To illustrate the proposed methods, a commercial AFM probe that has significant nonuniformity is considered and the error in calibrating this probe is quantified and discussed. For this particular probe, variations in the thickness of the probe over the last 15% of its length are found to significantly reduce the accuracy of the calibration when the thermal method is used, since that method is sensitive to changes in the shape of the eigenmode of the probe near its free end.     

Atomic force microscope cantilever calibration using a focused ion beam

A calibration method is presented for determining the spring constant of atomic force microscope (AFM) cantilevers, which is a modification of the established Cleveland added mass technique. A focused ion beam (FIB) is used to remove a well-defined volume from a cantilever with known density, substantially reducing the uncertainty usually present in the added mass method. The technique can be applied to any type of AFM cantilever; but for the lowest uncertainty it is best applied to silicon cantilevers with spring constants above 0.7?N?m(-1), where uncertainty is demonstrated to be typically between 7 and 10%. Despite the removal of mass from the cantilever, the calibration method presented does not impair the probes' ability to acquire data. The technique has been extensively tested in order to verify the underlying assumptions in the method. This method was compared to a number of other calibration methods and practical improvements to some of these techniques were developed, as well as important insights into the behavior of FIB modified cantilevers. These results will prove useful to research groups concerned with the application of microcantilevers to nanoscience, in particular for cases where maintaining pristine AFM tip condition is critical.     

具有溯源性的原子力显微镜探针法向弹性常数标定系统

原子力显微镜(AFM)悬臂梁探针的弹性常数在微纳米尺度力学测试中十分重要,其准确程度直接影响力学测量结果的可靠性,故需对其进行精确标定.因天平法的测量结果可溯源,本文在已有天平法的基础上,研制了一套新型标定系统.该系统将AFM测头与超精密电磁天平相结合.微悬臂梁在精密位移台的带动下接触天平并产生弯曲,接触力由天平测得,微悬臂梁的弯曲量由光杠杆检测,并通过反馈系统进行精确控制,最后根据胡克定律计算出弹性常数.利用本系统对4种不同型号商用微悬臂梁探针的法向弹性常数进行了标定,标定结果表明本系统具有良好的测量重复性.通过进行不确定度分析,得到测量结果的相对标准不确定度优于2%.     

Calibration of silicon atomic force microscope cantilevers

We present a comparison of three different methods to calibrate the spring constant of two different types of silicon beam shaped atomic force microscope (AFM) cantilevers to determine each method's accuracy, ease of use and potential destructiveness. The majority of research in calibrating AFM cantilevers has been concerned with contact mode levers. The two types of levers we have studied are used in force modulation and tapping mode in air. Not only can these types of cantilevers have spring constants an order of magnitude greater than contact mode levers, but also their geometries can be quite different from the standard V-shape contact lever. In this work we experimentally determine the correction factors for two of the calibration methods when applied to the tapping mode cantilevers and also demonstrate that the force modulation levers can be calibrated easily and accurately using these same techniques.     

Variations in properties of atomic force microscope cantilevers fashioned from the same wafer

Variations in the mechanical properties of nominally identical V-shaped atomic force microscope (AFM) cantilevers sourced from the same silicon nitride wafer have been quantified by measuring the spring constants, resonant frequencies and quality factors of 101 specimens as received from the manufacturer using the thermal spectrum method of Hutter and Bechhoefer. The addition of thin gold coatings always lowers the resonant frequency but the corresponding spring constant can either increase or decrease as a result. The observed broad spread of spring constant values and the lack of correlations between the resonant frequency and spring constant can be attributed in part to the non-uniformity of composition and material properties in the thinnest dimension of such cantilevers which arise from the manufacturing process. The effects of coatings are dictated by the competing influence of differences in mass density and Young's modulus between the silicon nitride and the gold coating. An implication of this study is that cantilever calibration methods based on the assumption of uniformity of material properties of the cantilever in the thinnest dimension are unlikely to be applicable for such cantilevers.     

Determining Mechanical Properties of Carbon Microcoils Using Lateral Force Microscopy

Mechanical properties of amorphous carbon microcoil (CMC) synthesized by thermal chemical vapor deposition method were examined in compression and tension tests, using the lateral force mode of atomic force microscope (AFM). The AFM cantilever tip was manipulated by a piezoelectric scanner to contact, pull, and push an individual CMC. The lateral force that was exerted by the CMC deformation causes the twist of the AFM cantilever. It was monitored by the laser and photodetector of the AFM during the experiments. A linear response of the CMC was observed in the range of 25 nm to 5 mum of tension experiments. The results show that the spring constant of the CMC is reasonably proportional to the coil number. The shear modulus of the amorphous CMC is estimated to be 3 plusmn 0.2 GPa. The proposed method is promising to manipulate the compression and tension of the CMC and to measure the lateral force exerted in an ambient environment.     

Accuracy of the spring constant of atomic force microscopy cantilevers by finite element method

Atomic force microscopy (AFM) probe with different functions can be used to measure the bonding force between atoms or molecules. In order to have accurate results, AFM cantilevers must be calibrated precisely before use. The AFM cantilever's spring constant is usually provided by the manufacturer, and it is calculated from simple equations or some other calibration methods. The spring constant may have some uncertainty, which may cause large errors in force measurement. In this paper, finite element analysis was used to obtain the deformation behavior of the AFM cantilever and to calculate its spring constant. The influence of prestress, ignored by other methods, is discussed in this paper. The variations of Young's modulus, Poisson's ratio, cantilever geometries, tilt angle, and the influence of image tip mass were evaluated to find their effects on the cantilever's characteristics. The results were compared with those obtained from other methods.     

Enhanced Accuracy of Force Application for AFM Nanomanipulation Using Nonlinear Calibration of Optical Levers

The atomic force microscope (AFM) has been widely used as a nano-effector with a function of force sensing to detect interaction forces between an AFM tip and a sample, thereby controlling the process of the nanomanipulation. However, both the extent and accuracy of force application are significantly limited by the nonlinearity of the commonly used optical lever with a nonlinear position-sensitive detector (PSD). In order to compensate the nonlinearity of the optical lever, a nonlinear calibration method is presented. This method applies the nonlinear curve fit to a full-range position-voltage response of the photodiode, obtaining a continuous function of its voltage-related sensitivity. Thus, interaction forces can be defined as integrals of this sensitivity function between any two responses of photodiode voltage outputs, instead of rough transformation with a single conversion factor. The lateral position-voltage response of the photodiode, a universally acknowledged puzzle, was directly characterized by an accurately calibrated force sensor composed of a tippless piezoresistive microcantilever and corresponding electronics, regardless of any knowledge of the cantilevers and laser measuring system. Experiments using a rectangular cantilever (normal spring constant 0.24 N/m) demonstrated that the proposed nonlinear calibration method restrained the sensitivity error of normal position-voltage responses to 3.6% and extended the force application range.     

Techniques for imaging human metaphase chromosomes in liquid conditions by atomic force microscopy

The purpose of this study was to obtain three-dimensional images of wet chromosomes by atomic force microscopy (AFM) in liquid conditions. Human metaphase chromosomes-obtained either by chromosome spreads or by an isolation technique-were observed in a dynamic mode by AFM in a buffer solution. Under suitable operating conditions with a soft triangular cantilever (with the spring constant of 0.08-0.4?N?m(-1)), clear images of fixed chromosomes in the chromosome spread were obtained by AFM. For imaging isolated chromosomes with the height of more than 400?nm, a cantilever with a high aspect ratio probing tip was required. The combination of a Q-control system and the sampling intelligent scan (SIS) system in dynamic force mode AFM was useful for obtaining high-quality images of the isolated chromosomes, in which globular or cord-like structures about 50?nm thick were clearly observed on the surface of each chromatid.     

微悬臂梁法向弹性系数的标定方法与分析

微机械加工制造的微悬臂梁/探针在科学研究和工业生产中有着重要的应用,作为原子力显微镜中的关键核心组件,微悬臂/探针结构在许多领域如表面特性研究和微加工等领域扮演着重要的角色.目前,尤其在生物、化学、和危险物品的检测上已经成为一个重要的平台.除了尺度测量外,当人们对表面力和原子间的相互作用力需要更准确和绝对的数值时,需要对微悬臂的弹性系数进行准确的标定,弹性系数的测量精度影响测量力学量的最终结果.本文对目前发展起来的几种标定方法,如参考悬臂梁的标定方法、悬臂梁的共振法和悬臂梁的热噪声振动法,从原理上和试验上进行总结和分析,对相应测试方法和影响测试精度的相关因素进行评述.     

Nanometer-scale flow of molten polyethylene from a heated atomic force microscope tip

We investigate the nanometer-scale flow of molten polyethylene from a heated atomic force microscope (AFM) cantilever tip during thermal dip-pen nanolithography (tDPN). Polymer nanostructures were written for cantilever tip temperatures and substrate temperatures controlled over the range 100-260?°C and while the tip was either moving with speed 0.5-2.0 μm s(-1) or stationary and heated for 0.1-100 s. We find that polymer flow depends on surface capillary forces and not on shear between tip and substrate. The polymer mass flow rate is sensitive to the temperature-dependent polymer viscosity. The polymer flow is governed by thermal Marangoni forces and non-equilibrium wetting dynamics caused by a solidification front within the feature.     

Teleoperated 3-D Force Feedback From the Nanoscale With an Atomic Force Microscope

In this study, 3-D experimental teleoperated force feedback during contact with nanoscale surfaces is demonstrated using an atomic force microscope (AFM) on the slave side and a haptic device on the master side. To achieve 3-D force feedback, coupling between one of the horizontal forces and the vertical force is a crucial bottleneck. To solve this coupling issue, a novel force decoupling algorithm is proposed. This algorithm uses local surface slopes, an empirical friction force model, and the haptic device motion angle projected onto the surface to estimate the friction value during experiments. With this estimation, it is possible to decouple the three orthogonal forces acting on the tip of the AFM cantilever. Moreover, using an adaptive observer, parameters of the friction model can be changed online, removing the necessity to calibrate the friction model initially. Finally, a modified passivity-based bilateral control is used to reflect the scaled nanoscale forces to the master side and the operator. The performance of the system is demonstrated on experimental results for flat and non-flat, and hard and soft surfaces.      

Noncontact electrochemical imaging with combined scanning electrochemical atomic force microscopy

Combined scanning electrochemical atomic force microscopy (SECM-AFM) is a recently introduced scanned probe microscopy technique where the probe, which consists of a tip electrode and integrated cantilever, is capable of functioning as both a force sensor, for topographical imaging, and an ultramicroelectrode for electrochemical imaging. To extend the capabilities of the technique, two strategies for noncontact amperometric imaging-in conjunction with contact mode topographical imaging-have been developed for the investigation of solid-liquid interfaces. First, SECM-AFM can be used to image an area of the surface of interest, in contact mode, to deduce the topography. The feedback loop of the AFM is then disengaged and the stepper motor employed to retract the tip a specified distance from the sample, to record a current image over the same area, but with the tip held in a fixed x-y plane above the surface. Second, Lift Mode can be employed, where a line scan of topographical AFM data is first acquired in contact mode, and the line is then rescanned to record SECM current data, with the tip maintained at a constant distance from the target interface, effectively following the contours of the surface. Both approaches are exemplified with SECM feedback and substrate generation-tip collection measurements, with a 10-microm-diameter Pt disk UME serving as a model substrate. The approaches described allow electrochemical images, acquired with the tip above the surface, to be closely correlated with the underlying topography, recorded with the tip in intimate contact with the surface.     

基于AFM氮化硅探针刻蚀方法制作聚碳酸酯纳米光栅

基于原子力显微镜(AFM)探针的纳米机械刻蚀技术以其成本低、分辨率高的优势被广泛应用于各种纳米元器件的制造中.为了得到最优的光栅结构,首先通过单次刻蚀实验定量分析了刻蚀方向、加载力和刻蚀速率等3个主要加工参数对所得纳米沟槽形貌和尺寸的影响,给出了普通氮化硅探针对聚碳酸酯(PC)的加工特性及加工效率.然后通过改变沟槽间距(100~500 nm)得到了不同周期的纳米光栅结构,并确定了这种探针与样品的组合对间距的要求及最佳加工参数:沿垂直于微悬臂长轴向右刻蚀,加载力2.3μN,刻蚀速率2.6μm/s.最后利用该技术对实验室已有原子光刻技术所得周期为213 nm的一维Cr原子光栅结构进行了复制加工,得到了均匀的213 nm一维光栅,证明这种基于AFM探针的纳米机械刻蚀技术可被广泛应用于纳米加工.     

A method to quantitatively measure the elastic modulus of materials in nanometer scale using atomic force microscopy

A method is proposed for quantitatively measuring the elastic modulus of materials using atomic force microscopy (AFM) nanoindentation. In this method, the cantilever deformation and the tip-sample interaction during the early loading portion are treated as two springs in series, and based on Sneddon's elastic contact solution, a new cantilever-tip property α is proposed which, together with the cantilever sensitivity A, can be measured from AFM tests on two reference materials with known elastic moduli. The measured α and A values specific to the tip and machine used can then be employed to accurately measure the elastic modulus of a third sample, assuming that the tip does not get significantly plastically deformed during the calibration procedure. AFM nanoindentation tests were performed on polypropylene (PP), fused quartz and acrylic samples to verify the validity of the proposed method. The cantilever-tip property and the cantilever sensitivity measured on PP and fused quartz were 0.514?GPa and 51.99?nm?nA(-1), respectively. Using these measured quantities, the elastic modulus of acrylic was measured to be 3.24?GPa, which agrees well with the value measured using conventional depth-sensing indentation in a commercial nanoindenter.     

A new method for the analysis of compaction processes in high-porosity agglomerates

Mechanical properties of high-porous microscopic agglomerates have been investigated. For this purpose we installed an atomic force microscope (AFM) cantilever in a scanning electron microscope (SEM) using a nanomanipulator. The nanomanipulator is piezoelectric controlled with increments of 5 nm in the rotational and 0.5 nm in the translational direction. Thus, this tool allows the precise positioning and movement of an AFM cantilever under SEM observation. Depending on the spring constant of the cantilever and the step size of the motion—both quantities determining the sensitivity of the instrument—different aspects of the deformation of dust-aggregate structures, e.g., the behaviour of single particle chains, can be analysed.     

The noise of coated cantilevers

In atomic force microscopy, cantilevers with a reflective coating are often used to reduce optical shot noise for deflection detection. However, static AFM experiments can be limited by classical noise and therefore may not benefit from a reduction in shot noise. Furthermore, the cantilever coating has the detrimental side-effect of coupling light power fluctuations into true cantilever bending caused by time-varying thermal stresses. Here, we distinguish three classes of noise: detection, force, and displacement noise. We discuss these noises with respect to cantilever coating in the context of both static and dynamic AFM experiments. Finally, we present a patterned cantilever coating which reduces the impact of these noises.     

High spatial resolution Kelvin probe force microscopy with coaxial probes

Kelvin probe force microscopy (KPFM) is a widely used technique to measure the local contact potential difference (CPD) between an AFM probe and the sample surface via the electrostatic force. The spatial resolution of KPFM is intrinsically limited by the long range of the electrostatic interaction, which includes contributions from the macroscopic cantilever and the conical tip. Here, we present coaxial AFM probes in which the cantilever and cone are shielded by a conducting shell, confining the tip-sample electrostatic interaction to a small region near the end of the tip. We have developed a technique to measure the true CPD despite the presence of the shell electrode. We find that the behavior of these probes agrees with an electrostatic model of the force, and we observe a factor of five improvement in spatial resolution relative to unshielded probes. Our discussion centers on KPFM, but the field confinement offered by these probes may improve any variant of electrostatic force microscopy.     

Design and characterization of nanoknife with buffering beam for in situ single-cell cutting

A novel nanoknife with a buffering beam is proposed for single-cell cutting. The nanoknife was fabricated from a commercial atomic force microscopy (AFM) cantilever by focused-ion-beam (FIB) etching technique. The material identification of the nanoknife was determined using the energy dispersion spectrometry (EDS) method. It demonstrated that the gallium ion pollution of the nanoknife can be ignored during the etching processes. The buffering beam was used to measure the cutting force based on its deformation. The spring constant of the beam was calibrated based on a referenced cantilever by using a nanomanipulation approach. The tip of the nanoknife was designed with a small edge angle 5° to reduce the compression to the cell during the cutting procedure. For comparison, two other nanoknives with different edge angles, i.e. 25° and 45°, were also prepared. An in situ single-cell cutting experiment was performed using these three nanoknives inside an environmental scanning electron microscope (ESEM). The cutting force and the sample slice angle for each nanoknife were evaluated. It showed the compression to the cell can be reduced when using the nanoknife with a small edge angle 5°. Consequently, the nanoknife was capable for in situ single-cell cutting tasks.