Fabrication and analysis of cylindrical resin AFM microcantilevers

In this paper a new method of fabricating cylindrical resin microcantilevers using the Direct Digital Manufacturing (DDM) technique of Micro-stereolithography (MSL) is described. The method is rapid and commercially viable, allowing the fabrication of atomic force microscope (AFM) cantilevers which exhibit much larger spring constants than those currently commercial available. This allows for experimentation in a force regime orders of magnitude higher than currently possible using the AFM. This makes these cantilevers ideally suited for AFM-based depth sensing indentation. Due to their geometry, the assumptions used in the standard Euler-Bernoulli beam theory usually used to analyse AFM cantilevers may no longer be valid. Therefore approximate analytical solutions based on Timoshenko beam theory have been derived for the stiffness and resonant frequency of these cantilevers. Prototypes of the cantilevers have been fabricated and tested. Results show good agreement between experiment and theory.     

Nondestructive and noncontact method for determining the spring constant of rectangular cantilevers

We present here an experimental setup and suggest an extension to the long existing added-mass method for the calibration of the spring constant of atomic force microscope cantilevers. Instead of measuring the resonance frequency shift that results from attaching particles of known masses to the end of cantilevers, we load them with water microdrops generated by a commercial inkjet dispenser. Such a device is capable of generating drops, and thus masses, of extremely reproducible size. This makes it an ideal tool for calibration tasks. Moreover, the major advantage of water microdrops is that they allow for a nearly contactless calibration: no mechanical micromanipulation of particles on cantilevers is required, neither for their deposition nor for removal. After some seconds the water drop is completely evaporated, and no residues are left on the cantilever surface or tip. We present two variants: we vary the size of the drops and deposit them at the free end of the cantilever, or we keep the size of the drops constant and vary their position along the cantilever. For the second variant, we implemented also numerical simulations. Spring constants measured by this method are comparable to results obtained by the thermal noise method, as we demonstrate for six different cantilevers.     

Finite element calculations and fabrication of cantilever sensors for nanoscale detection

Finite element analysis (FEA) is used to study the effect of geometric variations on the properties of rectangular cantilevers and U-shaped Joule-heated cantilevers. Simulations of locally thinned cantilevers as well as of cantilevers modified by the implementing of a hole or a side cut are compared with fabricated cantilevers, which are tuned by focused ion beam (FIB) milling. By locally thinning the cantilevers, the resonance frequency and the spring constant are reduced. For a hole, the internal stress is increased while for a side cut, the lateral spring constant is decreased. Good agreement between the measured and the simulated resonance frequencies is observed. Simulations of the current density and the temperature distributions attained during the passage of current through a doped silicon layer are performed to optimize the design of Joule-heated cantilevers (U-shaped) for thermal gravimetric applications. A very uniform temperature distribution over a region near the apex can be realized by slitting the U-shaped cantilever. In such a way, the heating power can be minimized by effecting only a small variation in the geometry of a U-shaped cantilever. A simple fabrication process for the fabrication of Joule-heated cantilevers is presented, which consists mainly of a uniform conductive p-doped layer.     

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.     

Highly sensitive polymer-based cantilever-sensors for DNA detection

We present a technology for the fabrication of cantilever arrays aimed to develop an integrated biosensor microsystem. The fabrication process is based on spin coating of the photosensitive polymer and near-ultraviolet exposure. Arrays of up to 33 microcantilevers are fabricated in the novel polymer material SU-8. The low Young's modulus of the polymer, 40 times lower than that of silicon, enables to improve the sensitivity of the sensor device for target detection. The mechanical properties of SU-8 cantilevers, such as spring constant, resonant frequency and quality factor are characterized as a function of the dimensions and the medium. The devices have been tested for measurement of the adsorption of single stranded DNA and subsequent interstitial adsorption of lateral spacer molecules. We demonstrate that sensitivity is enhanced by a factor of six compared to that of commercial silicon nitride cantilevers.     

Calibration and examination of piezoresistive Wheatstone bridge cantilevers for scanning probe microscopy

This paper describes the method of determining the force constant and displacement sensitivity of piezoresistive Wheatstone bridge cantilevers applied in scanning probe microscopy (SPM). In the procedure presented here, the force constant for beams with various geometry is determined based on resonance frequency measurement. The displacement sensitivity is measured by the deflection of the cantilever with the calibrated piezoactuator stage. Preliminary results show that our method is capable of measuring the force constant of Wheatstone bridge cantilevers with an accuracy of better than 5% and this is used as feedback for improvement of sensor micromachining process.     

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.     

High-throughput characterization of stresses in thin film materials libraries using Si cantilever array wafers and digital holographic microscopy

We report the development of an advanced high-throughput stress characterization method for thin film materials libraries sputter-deposited on micro-machined cantilever arrays consisting of around 1500 cantilevers on 4-inch silicon-on-insulator wafers. A low-cost custom-designed digital holographic microscope (DHM) is employed to simultaneously monitor the thin film thickness, the surface topography and the curvature of each of the cantilevers before and after deposition. The variation in stress state across the thin film materials library is then calculated by Stoney's equation based on the obtained radii of curvature of the cantilevers and film thicknesses. DHM with nanometer-scale out-of-plane resolution allows stress measurements in a wide range, at least from several MPa to several GPa. By using an automatic x-y translation stage, the local stresses within a 4-inch materials library are mapped with high accuracy within 10 min. The speed of measurement is greatly improved compared with the prior laser scanning approach that needs more than an hour of measuring time. A high-throughput stress measurement of an as-deposited Fe-Pd-W materials library was evaluated for demonstration. The fast characterization method is expected to accelerate the development of (functional) thin films, e.g., (magnetic) shape memory materials, whose functionality is greatly stress dependent.     

Calibration of the normal spring constant of microcantilevers in a parallel fluid flow

We demonstrate a novel approach to determine the normal spring constant of microcantilevers. The cantilevers are placed parallel to a fluid flow thus establishing one of the walls of the flow channel. Resonance frequencies are recorded depending on the velocity of the fluid. The pressure gradient resulting from the flow causes the resonance frequency to change. This change can be exploited to deduce the cantilever spring constant with high precision. The method we present can be performed in situ and does not involve any contact of the cantilever with a surface thus having great potential for the calibration of modified probes and for being incorporated in microfluidic systems. In case the spring constant is known, the setup can also be employed to determine the velocity of fluid flows and the flow rate with high precision and up to high speeds.     

基于激光多普勒技术的微悬臂梁机械特性的测量

介绍了一种微悬臂梁离面运动测试系统。结合显微激光多普勒技术,分析了用于间接测量微悬臂梁机械特性的方法,采用虚拟仪器技术建立控制系统,编辑器件激励和数据采集、处理软件,实现了对微悬臂梁的动态特性和杨氏模量、弹性系数等机械特性的测量。最后利用该测试系统对矩形、三角形微悬臂梁杨氏模量进行了实验研究,并计算了两种微悬臂梁的弹性系数。经实验证明,用该方法测量悬臂梁机械特性得到的弹性系数和杨氏模量误差小于7．5％。     

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.     

Direct measurement of cantilever spring constants and correction for cantilever irregularities using an instrumented indenter

A method is presented that allows direct measurement of a wide range of spring constants of cantilevers using an indentation instrument with an integrated optical microscope. An uncertainty of less than 10% can be achieved for spring constants from 0.1 to 10(2) Nm. The technique makes it possible to measure the spring constant at any desired location on a cantilever of any shape, particularly at the tip location of an atomic force microscopy cantilever. The article also demonstrates a technique to detect and correct apparent length anomalies of cantilevers by analyzing spring constants at multiple positions.     

Micromechanical sensor for studying heats of surface reactions, adsorption, and cluster deposition processes

We present a newly designed highly sensitive micromechanical sensor devoted to thermodynamic studies involving supported clusters. The thermally sensitive element of the sensor consists of a micromachined silicon cantilever array, onto which a thin metal film is evaporated. Due to the difference between the thermal expansion coefficients of silicon and the metal employed, thermal bending is observed when heat is exchanged with the cantilever. The sensitivity and the response time of the cantilever are studied as a function of the film material (gold or aluminum) and the thickness of the metal film. With our routinely prepared cantilevers, a minimum power of 120 nW is measurable with a submillisecond response time, corresponding to a limit of detection in the femtojoule range. The high sensitivity of the sensor is demonstrated by measuring the heat exchange which occurs during the deposition of clusters on the cantilever. Experimentally, we illustrate the 1,3-butadiene hydrogenation reaction using a cluster model catalysts created by soft-landing palladium clusters onto the cantilever surface.     

Quantum size aspects of the piezoresistive effect in ultra thin piezoresistors

Proximal probe sensors with an ability to detect extremely small forces (10(-15)-10(-18)N) play significant role in scanning probe microscopy applications. The detection of extremely low forces, require producing micromachined cantilevers with as small as possible spring constants, which is considered by the optimization of the sensor design. In the last year many papers describing the fabrication process of producing ultrathin cantilevers (below 100nm) with integrated piezoresistors for deflection read-out have been published. In the case of such cantilevers the required thickness of piezoresistors is in the range of 50nm. From a quantum mechanical point of view, an electrical carrier transport confinement in direction perpendicular to the cantilever surface can be expected and in this manner we have to consider the quantum size effect.The goal of the project described in this paper is to calculate and determine the piezoresistive coefficients in p type Si thin (under 50nm) piezoresistors taking into account the quantum size effect and to compare them with the corresponding coefficients for bulk material. The calculation of the band structure will use the mathematical apparatus of an exact analytical diagonalization six-band k.p model, modified with the envelope function approximation.The behaviour of the thin piezoresistors employed as integrated deflection read-out will be also discussed. Moreover, critical issues in the realization of piezoresistors formed by MOS transistor channel will be presented.     

High throughput optical readout of dense arrays of nanomechanical systems for sensing applications

We present an instrument based on the scanning of a laser beam and the measurement of the reflected beam deflection that enables the readout of arrays of nanomechanical systems without limitation in the geometry of the sample, with high sensitivity and a spatial resolution of few micrometers. The measurement of nanoscale deformations on surfaces of cm(2) is performed automatically, with minimal need of user intervention for optical alignment. To exploit the capability of the instrument for high throughput biological and chemical sensing, we have designed and fabricated a two-dimensional array of 128 cantilevers. As a proof of concept, we measure the nanometer-scale bending of the 128 cantilevers, previously coated with a thin gold layer, induced by the adsorption and self-assembly on the gold surface of several self-assembled monolayers. The instrument is able to provide the static and dynamic responses of cantilevers with subnanometer resolution and at a rate of up to ten cantilevers per second. The instrumentation and the fabricated chip enable applications for the analysis of complex biological systems and for artificial olfaction.     

Atomic force microscopy: loading position dependence of cantilever spring constants and detector sensitivity

A simple and accurate experimental method is described for determining the effective cantilever spring constant and the detector sensitivity of atomic force microscopy cantilevers on which a colloidal particle is attached. By attaching large (approximately 85 microm diameter) latex particles at various positions along the V-shaped cantilevers, we demonstrate how the normal and lateral spring constants as well as the sensitivity vary with loading position. Comparison with an explicit point-load theoretical model has also been used to verify the accuracy of the method.     

Using FIB-processed AFM cantilevers to determine microtribology characteristics

Microtribology characteristics were determined by using a combination of single asperities and three types of FIB (focused ion beam)-processed cantilevers for AFM (atomic force microscope). First, single gold asperities were rubbed with single and parallel leaf springs. For the parallel leaf spring, the pull-off force was proportional to the worn area of the gold asperity peak. The total volume of the gold asperity only slightly changed with rubbing. Second, the friction force on a worn asperity was measured by using a double parallel leaf spring, and the results showed that the friction force was proportional to the sum of the normal load and the pull-off force.     

Effect of cantilevers' dimensions on phase contrast in multifrequency atomic force microscopy

During the past years, different theoretical and experimental works are done to enhance the observables (mostly higher eigenmode's phase contrast) in multifrequency atomic force microscopy methods. In this study, the geometry of rectangular cantilevers is studied and an optimum dimension that can provide maximum phase contrast for a given set of samples is found. The analysis is done both numerically and experimentally. A sensitivity analysis is provided to demonstrate which dimension (length, width, thickness, tip‐radius, and cantilever and sample angle) of the cantilever has a higher effect on the results. The effects of geometrical dimensions are categorized into to: (a) effect on dynamics of the cantilever (b) effects on cantilever's specifications (i.e., spring constant and quality factor). Length and width of the cantilever dominates the static behavior of the cantilever. While thickness (for lower values), tip radius, and approach angle mostly affect the dynamic behavior of the cantilever. Theoretically, it is found as the length increases the phase contrast increase. This relationship is opposite for width. It was also observed that the effect of thickness for a specific range on the phase contrast depends on the 1st eigenmode amplitude setpoint. This study shows for having higher contrast, lower tip‐radius is needed. The optimum angle between cantilever and sample to enhance bimodal atomic force microscopy imaging is also found. Based on the commercially available cantilevers, the optimum cantilever dimension is provided. Three different cantilevers with similar dimensions are experimentally tested and theoretical results are verified.     

涡流检波器串动态特性测试夹具的改进与试验

地震勘探多采用多通道数据采集。为了得到有效的地质数据，不同地震通道的接 收特性（包括有效带宽、灵敏度、信噪比等）必须一致，这对不同通道所连接的检波器 特性的一致性提出了很高的要求。为了确保一致性及测试的可靠性和准确性，对检 波器的各项性能参数进行定期检测是十分必要的。对涡流检波器串动态特性测试设 备的夹具进行了动力学分析与测试，发现原设备的动态特性不能满足测试要求，因 此在分析计算的基础上对原设备夹具进行了改进设计。试验结果表明，改进后的设 备性能有较大改善。     

截止波导介质腔介电常数测量理论与方法研究

本文提出了用截止波导介质谐振腔测量微波材料相对介电常数和微波损耗的方法.利用开波导法给出了腔中TE0ml谐振模的电磁场,导出了利用此模测量介电常数和微波损耗的公式;通过测量频率和谐振曲线,就能算出材料的复介电常数,并对谐振模TE0ml进行了讨论;比较了这种测量方法与原有的短路金属板介质谐振腔法的优劣,结果表明采用截止波导介质谐振腔测量材料的微波损耗时更有优越性.