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.     

Calibration of higher eigenmode spring constants of atomic force microscope cantilevers

Standard spring constant calibration methods are compared when applied to higher eigenmodes of cantilevers used in dynamic atomic force microscopy (dAFM).?Analysis shows that Sader's original method (Sader et al 1999 Rev. Sci. Instrum. 70 3967-9), which relies on a priori knowledge of the eigenmode shape, is poorly suited for the calibration of higher eigenmodes. On the other hand, the thermal noise method (Hutter and Bechhoefer 1993 Rev. Sci. Instrum. 64 1868-73) does not require knowledge of the eigenmode and remains valid for higher eigenmodes of the dAFM probe. Experimental measurements of thermal vibrations in air for three representative cantilevers are provided to support the theoretical results.     

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.     

Characterization of materials' nanomechanical properties by force modulation and phase imaging atomic force microscopy with soft cantilevers

Soft cantilevers, although having good force sensitivity, have found limited use for investigating materials' nanomechanical properties by conventional force modulation (FM) and intermittent contact (IC) atomic force microscopy. This is due to the low forces and small indentations that these cantilevers are able to exert on the surface, and to the high amplitudes required to overcome adhesion to the surface. In this paper, it is shown that imaging of local elastic properties of surface and subsurface layers can be carried out by employing electrostatic forcing of the cantilever. In addition, by mechanically exciting the higher vibration modes in contact with the surface and monitoring the phase of vibrations, the contrast due to local surface elasticity is obtained.     

原子力显微镜微悬臂梁杨氏模量动态测试方法

原子力显微镜微悬臂梁是微纳米领域重要的微力传感器,而微悬臂梁的杨氏模量又是决定其力学性能的重要参数.由于微悬臂梁的尺寸处于微米级,有些特征尺寸甚至达到纳米级,常规的测试结构材料特性的检测方法已经难以满足需求,急需研究新的测试方法和装置对微悬臂梁的机械特性进行研究和分析.本文提出了一种基于微悬臂梁振动固有频率测试的杨氏模量测试方法.使用本方法时,首先建立待测微悬臂梁在空气中的振动模型,并使用数值仿真的方法计算结构尺寸相同但杨氏模量不同的各种微悬臂梁在空气中的振动固有频率,然后实际测量微悬臂梁的振动固有频率,和实验结果最接近的仿真结果所对应的杨氏模量参数就是待测微悬臂梁的杨氏模量.本文最后对Mikromaseh公司生产的NSC型探针的杨氏模量进行了测试,实验结果证实了本文提出的方法的正确性.     

Lorentz force actuation of a heated atomic force microscope cantilever

We report Lorentz force-induced actuation of a silicon microcantilever having an integrated resistive heater. Oscillating current through the cantilever interacts with the magnetic field around a NdFeB permanent magnet and induces a Lorentz force that deflects the cantilever. The same current induces cantilever heating. With AC currents as low as 0.2 mA, the cantilever can be oscillated as much as 80 nm at resonance with a DC temperature rise of less than 5 °C. By comparison, the AC temperature variation leads to a thermomechanical oscillation that is about 1000 times smaller than the Lorentz deflection at the cantilever resonance. The cantilever position in the nonuniform magnetic field affects the Lorentz force-induced deflection, with the magnetic field parallel to the cantilever having the largest effect on cantilever actuation. We demonstrate how the cantilever actuation can be used for imaging, and for measuring the local material softening temperature by sensing the contact resonance shift.     

Uncertainty quantification in nanomechanical measurements using the atomic force microscope

Quantifying uncertainty in measured properties of nanomaterials is a prerequisite for the manufacture of reliable nanoengineered materials and products. Yet, rigorous uncertainty quantification (UQ) is rarely applied for material property measurements with the atomic force microscope (AFM), a widely used instrument that can measure properties at nanometer scale resolution of both inorganic and biological surfaces and nanomaterials. We present a framework to ascribe uncertainty to local nanomechanical properties of any nanoparticle or surface measured with the AFM by taking into account the main uncertainty sources inherent in such measurements. We demonstrate the framework by quantifying uncertainty in AFM-based measurements of the transverse elastic modulus of cellulose nanocrystals (CNCs), an abundant, plant-derived nanomaterial whose mechanical properties are comparable to Kevlar fibers. For a single, isolated CNC the transverse elastic modulus was found to have a mean of 8.1?GPa and a 95% confidence interval of 2.7-20?GPa. A key result is that multiple replicates of force-distance curves do not sample the important sources of uncertainty, which are systematic in nature. The dominant source of uncertainty is the nondimensional photodiode sensitivity calibration rather than the cantilever stiffness or Z-piezo calibrations. The results underscore the great need for, and open a path towards, quantifying and minimizing uncertainty in AFM-based material property measurements of nanoparticles, nanostructured surfaces, thin films, polymers and biomaterials.     

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.     

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.     

原子力显微镜探针悬臂弹性常数校正技术进展

利用原子力显微镜对材料表面的力学性能进行定量表征时,需要准确知道原子力显微镜探针悬臂的弹性常数,所以对弹性常数进行校正十分重要。该文综述近年来对探针悬臂弹性常数的校正方法,主要包括维度法、静态挠度法、动态挠度法。维度法对不同悬臂形状(主要针对矩形、V型)进行阐述,分析不同方法使用的数学模型与优缺点;静态挠度法不仅对方法的数学模型进行阐述,还着重介绍近年来对该方法精确度的改进研究;动态挠度法以附加质量法、Sader法与热调谐法分别阐述,比较3种方法的模型特点与先进性;最后分析常用探针适合使用的校正方法,对今后校正方法的发展提供参考。     

Microfluidics and chromatography with an atomic force microscope

A combined atomic force microscope (AFM) and Raman spectrometer is presented as a microfluidic device for pumping, sampling, and trace chemical analysis. The AFM tip-cantilever provides a mechanism for shear-driven pumping of fluids in microchannels. Shear-driven pumping allows rapid flow rates and avoids the limitations of conventional pumping. The AFM's ability to translate sub-femtoliter volumes of fluid also proves a mechanism for fluidic switching and sample injection. In addition, the AFM is used to image liquid surfaces in microchannels and remove samples for very sensitive spectral analysis. Surface-enhanced Raman spectroscopy localized near the AFM tip provides chemical information of the sampled fluids. The results demonstrate the feasibility of integrating the AFM with microfluidic circuits and shear-driven chromatography and the potential for nanometer-scale chromatography.     

一种用于纳米计量的原子力显微镜测头的设计

介绍了我们研制的一种高精度、具有计量学意义的原子力显微镜测头.该显微测头与其它部件协同工作在50 mm×50 mm×2 mm的测量范围内实现纳米级精度的测量.测头采用光束偏转法检测探针悬臂的微小偏移,由单模保偏光纤引入半导体激光作为光源.该测头安装有3个立体反射镜作为激光干涉仪的参考镜.样品与原子力显微镜测头的相对位置可以由激光干涉仪直接读数,可溯源到米国际定义及国家基准上.激光干涉仪的布置无阿贝误差.测头采用立体光路设计,结构紧凑.测头厚度小于20 mm,质量约200 g,却实现了100 mm的反射光程.使用该测头测得与量块表面的力-距离曲线,还测得标称高度300 nm SiO2台阶样板的图像,分辨率优于0.05 nm.     

恒撞击力轻敲模式AFM的设计及研究

在轻敲模式AFM中,利用DMT模型与光探针点衍射理论结合来检测微探针的振动,并对振动信号进行频率域分析,通过检测和控制信号中高次谐波分量使针尖-样品间撞击力保持恒定。测试实验表明,该系统具有结构简单、可测不同材料的样品和对软质材料样品损伤小的优点,其测量重复性可达1%,分辩力可达1~5nm。     

Characterization of titanium polycide films by atomic force microscope

Non-destructive methods are required for in-line process control in VLSI circuits. In this study, mean roughness values as obtained from AFM analysis have been used to follow phase transformation of Ti-polycide films formed by annealing Ti films on polysilicon. The results are supported from XRD analysis of the TiSi₂ films.     

Thin films of porphyrin molecules imaged with the atomic force microscope

The assembly of two-dimensional molecular structures of zinc porphyrin molecules arising from the dewetting of a porphyrin solution on mica and graphite is investigated using atomic force microscopy. Both a near equilibrium nucleation and growth process, and a far from equilibrium spinodal dewetting process are observed. Nucleation and growth around pre-existing surface defects on mica produces single layer disks, ∼ 10 μm in diameter, of densely packed molecules. Spinodal dewetting gives rise to the formation of much smaller, single layer, molecular islands of various sizes on both mica and graphite.     

High-rate tunable ultrasonic force regulated nanomachining lithography with an atomic force microscope

This paper describes a high-rate tunable nanomachining-based nanolithography technique using an atomic force microscope (AFM). Controlled vibration between the cantilever tip and the sample is introduced to increase the lithographical speed and controllability of the nanomachining process. In this approach, an ultrasonic z?vibration of the sample and the resulting ultrasonic force from the nonlinear force-distance interaction between the sample and the cantilever tip are utilized to regulate fabrication depth. A high frequency in-plane circular vibration is introduced between the tip and the sample to control the width of the fabricated features, and to improve the speed of nanolithography. Features (e.g.?slots) with dimensions spanning from tens of nanometers to hundreds of nanometers are fabricated in one scan. A lithography speed of tens of microns per second can be achieved, which is significantly higher than other known mechanical-modification-based nanolithography methods. The patterns, that are machined on a thin PMMA film, are transferred to silicon substrate through a reactive ion etching process, which provides a cost-effective tunable approach for the fabrication of nanostructures.     

Coaxial atomic force microscope probes for imaging with dielectrophoresis

We demonstrate atomic force microscope (AFM) imaging using dielectrophoresis (DEP) with coaxial probes. DEP provides force contrast allowing coaxial probes to image with enhanced spatial resolution. We model a coaxial probe as an electric dipole to provide analytic formulas for DEP between a dipole, dielectric spheres, and a dielectric substrate. AFM images taken of dielectric spheres with and without an applied electric field show the disappearance of artifacts when imaging with DEP. Quantitative agreement between our model and experiment shows that we are imaging with DEP.     

The direct measurement of linewidth using an atomic force microscope

A method for directly measuring linewidth with an atomic force microscope using the first derivative of the signal is presented. The method showed that it is possible to make a direct measurement of the size of the upper base of a trapezoidal protrusion down to 30 nm. __________ Translated from Izmeritel’naya Tekhnika, No. 5, pp. 10–12, May, 2008.