A new detection system for extremely small vertically mounted cantilevers

Detection techniques currently used in scanning force microscopy impose limitations on the geometrical dimensions of the probes and, as a consequence, on their force sensitivity and temporal response. A new technique, based on scattered evanescent electromagnetic waves (SEW), is presented here that can detect the displacement of the extreme end of a vertically mounted cantilever. The resolution of this method is tested using different cantilever sizes and a theoretical model is developed to maximize the detection sensitivity. The applications presented here clearly show that the SEW detection system enables the use of force sensors with sub-micron size, opening new possibilities in the investigation of biomolecular systems and high speed imaging. Two types of cantilevers were successfully tested: a high force sensitivity lever with a spring constant of 0.17?pN?nm(-1) and a resonant frequency of 32?kHz; and a high speed lever with a spring constant of 50?pN?nm(-1) and a resonant frequency of 1.8?MHz. Both these force sensors were fabricated by modifying commercial microcantilevers in a focused ion beam system. It is important to emphasize that these modified cantilevers could not be detected by the conventional optical detection system used in commercial atomic force microscopes.     

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.     

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.     

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.     

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.     

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.     

基于小波有限元的悬臂梁裂纹识别

研究了悬臂梁裂纹识别中的正反问题．即通过裂纹位置和尺寸求解梁的固有频率以及利用梁的固有频率．识别裂纹位置和尺寸。以矩形截面裂纹悬臂梁为例，利用小波有限元方法建立了梁自由振动的有限元模型．其中裂纹被看作为一刚度已知的扭转线弹簧，求解出了系统的固有频率；通过行列式变换，将反问题求解简化为只含线弹簧刚度一个未知数的一元二次方程求根问题，分别做出了以不同固有频率作为输入值时裂纹位置与弹簧刚度之间的解曲线，曲线交点预测出裂纹的位置与尺寸。数值算例证实了算法的有效性，为工程结构裂纹故障预示与诊断提供了新的方法。     

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%.     

Design optimization and fatigue testing of an electronically-driven mechanically-resonant cantilever spring mechanism

A light scanning device consisting of an electronically-driven mechanically-resonant cantilever spring-mirror system has been developed for innovative lighting applications. The repeated flexing of the cantilever spring during operation can lead to premature fatigue failure. A model was created to optimize the spring design. The optimized spring design can reduce stress by approximately one-third from the initial design. Fatigue testing showed that the optimized spring design can operate continuously for over 1 month without failure. Analysis of failures indicates surface cracks near the root of the spring are responsible for the failures.     

Measurement of Local Si‐Nanowire Growth Kinetics Using In situ Transmission Electron Microscopy of Heated Cantilevers

A technique to study nanowire growth processes on locally heated microcantilevers in situ in a transmission electron microscope has been developed. The in situ observations allow the characterization of the nucleation process of silicon wires, as well as the measurement of growth rates of individual nanowires and the ability to observe the formation of nanowire bridges between separate cantilevers to form a complete nanowire device. How well the nanowires can be nucleated controllably on typical cantilever sidewalls is examined, and the measurements of nanowire growth rates are used to calibrate the cantilever‐heater parameters used in finite‐element models of cantilever heating profiles, useful for optimization of the design of devices requiring local growth.     

Self-heating in piezoresistive cantilevers

We report experiments and models of self-heating in piezoresistive microcantilevers that show how cantilever measurement resolution depends on the thermal properties of the surrounding fluid. The predicted cantilever temperature rise from a finite difference model is compared with detailed temperature measurements on fabricated devices. Increasing the fluid thermal conductivity allows for lower temperature operation for a given power dissipation, leading to lower force and displacement noise. The force noise in air is 76% greater than in water for the same increase in piezoresistor temperature.     

Nanomechanical detection of cholera toxin using microcantilevers functionalized with ganglioside nanodiscs

The label-free detection of cholera toxin is demonstrated using microcantilevers functionalized with ganglioside nanodiscs. The cholera toxin molecules bind specifically to the active membrane protein encased in nanodiscs, nanoscale lipid bilayers surrounded by an amphipathic protein belt, immobilized on the cantilever surface. The specific molecular binding results in cantilever deflection via the formation of a surface stress-induced bending moment. The nanomechanical cantilever response is quantitatively monitored by optical interference. The consistent and reproducible nanomechanical detection of cholera toxin in nanomolar range concentrations is demonstrated. The results validated with such a model system suggest that the combination of a microcantilever platform with receptor nanodiscs is a promising approach for monitoring invasive pathogens and other types of biomolecular detection relevant to drug discovery.     

Detection of CrO4(2-) using a hydrogel swelling microcantilever sensor

Hydrogels containing various mounts of tetraalkylammonium salts were used to modify microcantilevers for measurements of the concentration of CrO4(2-) in aqueous solutions. These microcantilevers undergo bending deflection upon exposure to solutions containing various CrO4(2-) concentrations as a result of swelling or shrinking of the hydrogels. The microcantilever deflection as a function of the concentration of CrO4(2-) ions is nearly linear in most concentration ranges. It was found that a concentration of 10(-11) M CrO4(2-) can be detected using this technology in a fluid cell. Other ions, such as Br-, HPO4(2-), and NO3-, have minimal effect on the deflection of this cantilever. The anions SO4(2-) and CO3(2-) could interfere with the CrO4(2-) detection, but only at high concentrations (> 10(-5) M). Such hydrogel-coated microcantilevers could potentially be used to prepare microcantilever-based chemical and biological sensors when molecular recognition agents are immobilized in the hydrogel.     

Accurate and precise calibration of AFM cantilever spring constants using laser Doppler vibrometry

Accurate cantilever spring constants are important in atomic force microscopy both in control of sensitive imaging and to provide correct nanomechanical property measurements. Conventional atomic force microscope (AFM) spring constant calibration techniques are usually performed in an AFM. They rely on significant handling and often require touching the cantilever probe tip to a surface to calibrate the optical lever sensitivity of the configuration. This can damage the tip. The thermal calibration technique developed for laser Doppler vibrometry (LDV) can be used to calibrate cantilevers without handling or touching the tip to a surface. Both flexural and torsional spring constants can be measured. Using both Euler-Bernoulli modeling and an SI traceable electrostatic force balance technique as a comparison we demonstrate that the LDV thermal technique is capable of providing rapid calibrations with a combination of ease, accuracy and precision beyond anything previously available.     

Label-free sugar detection using phenylboronic acid-functionalized piezoresistive microcantilevers

By appropriate surface functionalization using a thiolated phenylboronic acid derivative, gold-coated piezoresistive microcantilevers responsive to analytes having vicinal cis-diols were fashioned. A reference, uncoated cantilever permitted reliable subtraction of background signal (i.e., differential measurement). Experiments carried out in static mode under flow conditions, using the monosaccharide D-(-)-fructose as a test analyte in aqueous buffer, showed that the measured stationary-state surface stress was linear in analyte concentration over the 0-25 mM range, allowing this sugar to be readily detected at physiologically meaningful concentrations and at neutral pH. This approach offers a simple, reagentless, and flexible format for polyol screening that does not require aqueous alkaline solutions, suggesting potential applications in biomass process monitoring and glucose assay.     

Atomic Force Microscope Cantilever Flexural Stiffness Calibration: Toward a Standard Traceable Method

The evolution of the atomic force microscope into a useful tool for measuring mechanical properties of surfaces at the nanoscale has spurred the need for more precise and accurate methods for calibrating the spring constants of test cantilevers. Groups within international standards organizations such as the International Organization for Standardization and the Versailles Project on Advanced Materials and Standards (VAMAS) are conducting studies to determine which methods are best suited for these calibrations and to try to improve the reproducibility and accuracy of these measurements among different laboratories. This paper expands on a recent mini round robin within VAMAS Technical Working Area 29 to measure the spring constant of a single batch of triangular silicon nitride cantilevers sent to three international collaborators. Calibration techniques included reference cantilever, added mass, and two forms of thermal methods. Results are compared to measurements traceable to the International System of Units provided by an electrostatic force balance. A series of guidelines are also discussed for procedures that can improve the running of round robins in atomic force microscopy.     

Functionalized mesoporous silica for microgravimetric sensing of trace chemical vapors

Featuring a huge surface-to-volume ratio, synthesized SBA-15 mesoporous silica is functionalized by inner-channel-wall modification of sensing groups for highly specific chemical-vapor detection at trace level. With the developed sensing material loaded on resonant microcantilevers, the specifically adsorbed chemical-vapor molecules act as an added mass to shift the cantilever resonant frequency for gravimetric sensing signal readout. Two kinds of sensing materials for trinitrotoluene (TNT) and ammonia/amine are respectively prepared by inner-wall layer-by-layer grafting functionalization. By using hexafluoro-2-propanol-functionalized mesoporous silica (HFMS), experimental results show highly specific and rapid detection of TNT vapor, with a ppt-level detection limit; functionalized with a carboxyl (COOH) group, the mesoporous silica is loaded onto the cantilever resonating sensor that experimentally exhibits an ultrafine detection limit of tens of ppb to ammonia/amine gases.     

Polyelectrolyte brush amplified electroactuation of microcantilevers

This paper describes the electroactuation of microcantilevers coated on one side with cationic polyelectrolyte brushes. We observed very strong cantilever deflection by alternating the potential on the cantilever between +0.5 and -0.5 V at frequencies up to 0.25 Hz. The actuation resulted from significant increases in the expansive stresses in the polymer brush layer at both negative and positive potentials. However, the deflection at negative bias was significantly larger. We have developed a theoretical framework that correlates conformational changes of the polymer chains in the brush layer with the reorganization of ions due to the potential bias. The model predicts a strong increase in the polymer volume fraction, close to the interface, which results in large expansive stresses that bend the cantilever at negative potentials. The model also predicts that the actuation responds much stronger to negative potentials than positive potentials, as observed in the experiments.     

Ultrasensitive detection of CrO4(2-) using a microcantilever sensor

Microcantilevers modified with a self-assembled monolayer respond sensitively to specific ion concentrations. Here, we report the detection of trace amounts of CrO4(2-) using microcantilevers modified with a self-assembled monolayer of triethyl-12-mercaptododecylammonium bromide. The self-assembled monolayer was prepared on a silicon microcantilever coated with a thin layer of gold on one side. The microcantilever undergoes bending due to sorption of CrO4(2-) ions on the monolayer-modified side. It was found that a concentration of 10(-9) M CrO4(2-) can be detected using this technology in a flow cell. Other anions, such as Cl-, Br-, CO3(2-) (or HCO3-), and SO4(2-), have minimal effect on the deflection of this cantilever. The mechanics of the bending and the chemistry of cantilever modification are discussed.     

Gravimetric analysis of CO2 adsorption on activated carbon at various pressures and temperatures using piezoelectric microcantilevers

We investigated the adsorption and desorption of CO(2) on activated carbon using piezoelectric microcantilevers. After coating the free end of a cantilever with activated carbon, variations in the resonance frequency of the cantilever were measured as a function of CO(2) pressure, which is related to mass changes due to the adsorption or desorption of CO(2). The pressure-dependent viscous damping effects were compensated in the calculation of the CO(2) adsorption capacity of the activated carbon by comparing the frequency differences between the coated and uncoated cantilevers. The mass sensitivity of the piezoelectric cantilever was found to be better than 1 pg. The fractional coverage of CO(2) agreed with a Langmuir adsorption isotherm, indicating that a submonolayer of adsorbed CO(2) occurred on the surface of the activated carbon under the experimental conditions. The heat of adsorption was determined using the Clausius-Clapeyron relation and the fractional coverage of CO(2) at various temperatures and pressures.