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.     

Multiple-input microcantilever sensors

A surface-micromachined micro-electro-mechanical-system (MEMS) process has been used to demonstrate multiple-input chemical sensing using selectively coated cantilever arrays. Cantilever motion due to absorption-induced stress was readout using a custom-designed, eight-channel integrated circuit. Combined hydrogen and mercury vapor detection was achieved with a palm-sized, self-powered module with spread-spectrum telemetry reporting.     

An embedded polymer piezoresistive microcantilever sensor

We have developed a new type of chemical microsensor based on piezoresistive microcantilever technology. In this embedded polymer microsensor, a piezoresistive microcantilever is partially "embedded" into a polymeric material. Swelling of the polymer upon analyte exposure is measured as a simple resistance change in the embedded cantilever. Arrays of these sensors, each employing a different polymeric material, provide for the identification of a wide range of chemical vapor analytes. Advantages of this system over previous "surface" piezoresistive microcantilever chemical sensors include enhanced mechanical simplicity (no mechanical approach necessary), greater resistance to shock or movement, and lower cost.     

High-throughput combinatorial study of local stress in thin film composition spreads

We investigate the stresses in thin films with sub-millimeter lateral spatial resolution using a dense array of prefabricated cantilever beams prepared by microelectromechanical-system techniques. Stress induced deflection of the cantilever is interrogated by an optical (laser/position sensitive detector) measurement system. Composition spread films are deposited on the cantilever array using a three gun on-axis magnetron cosputtering system. The position dependent composition is inferred using rate calibrations and verified by electron microprobe/energy dispersive spectroscopy. We demonstrate the function of this system using an Fe-Ni-Al composition spread with approximately 1 at. % resolution. This approach allows for measurement of the composition dependence of other electromechanical properties such as the martensitic phase transition temperature of traditional and ferromagnetic shape-memory alloys, as well as the properties of hydrogen storage materials and the magnetic response of magnetostrictive materials.     

Pseudo-rigid-body model for corrugated cantilever beam used in compliant mechanisms

Common compliant joints generally have limited range of motion, reduced fatigue life and high stress concentration. To overcome these shortcomings, periodically corrugated cantilever beam is applied to design compliant joints. Basic corrugated beam unit is modeled by using pseudo-rigid-body method. The trajectory and deformation behavior of periodically corrugated cantilever beam are estimated by the transformation of coordinate and superposition of the deformation of corrugated beam units. Finite element analysis（FEA） is carried out on corrugated cantilever beam to estimate the accuracy of the pseudo-rigid-body model. Results show that the kinetostatic behaviors obtained by this method, which has a relative error less than 6%, has good applicability and corrugated cantilever beam has the characteristics of a large range of motion and high mechanical strength. The corrugated cantilever beam is then applied to design a flexible rotational joint to obtain a larger angle output. The paper proposes a pseudo-rigid-body model for corrugated cantilever beam and designed a flexible rotational joint with large angle output.     

Electroplated CoPt magnets for actuation of stiff cantilevers

A cantilever has been microfabricated for use in non-contact Atomic Force Microscopy (AFM) using a very thick magnetic film to actuate the cantilever motion. The thick magnetic block is deposited electrochemically over a defined area of the cantilever. This cantilever is particularly suitable for driving stiff AFM cantilevers in a liquid environment. Clean mechanical resonances are easily observed. Examples are given of a hard (CoPt) magnet of dimension 29 × 21 × 6 μm(3) electroplated on Silicon cantilevers of stiffness ~22 N/m, giving a static displacement of ~0.2 nm in an applied field of 10(-3) T.     

Dynamic response of rotating flexible cantilever pipe conveying fluid with tip mass

In this study the vibration system is consisted of a rotating cantilever pipe conveying fluid and a tip mass. The equation of motion is derived by using the Lagrange's equation. Also, the equation of motion is derived applying a modeling method that employs hybrid deformation variables. The influences of the rotating angular velocity and the velocity of fluid flow on the dynamic behavior of a cantilever pipe are studied by the numerical method. The effects of a tip mass on the dynamic behavior of a rotating cantilever pipe are also studied. The influences of a tip mass, the velocity of fluid, the angular velocity of a cantilever pipe and the coupling of these factors on the dynamic behavior of a cantilever pipe are analytically clarified. The natural frequencies of a cantilever pipe conveying fluid are proportional to the angular velocity of the pipe and a tip mass in both axial direction and lateral direction.     

Fabrication and characterization of PMN-PT single crystal cantilever array for cochlear-like acoustic sensor

We have successfully fabricated piezoelectric PMN-PT single crystal cantilever array. Each PMN-PT cantilever has a different length to achieve different resonance frequencies. The width and thickness of PMN-PT cantilever array are 200 μm and 10 μm, respectively. Resonance frequencies of PMN-PT cantilevers were measured with laser interferometer, and charge sensitivity was measured with charge-measuring device. PMN-PT cantilever array was installed in a noise-shield case. The array was then exposed to sound pressure frequency corresponding to resonance frequency to measure its sensitivity. The experimental results show that the PMN-PT cantilever array has high sensitivity to the sound pressure. This implies that the single crystal PMN-PT cantilever array is a potential candidate for a cochlear-like acoustic sensor.     

Expanded beam deflection method for simultaneous measurement of displacement and vibrations of multiple microcantilevers

Here we present an extension of optical beam deflection (OBD) method for measuring displacement and vibrations of an array of microcantilevers. Instead of focusing on the cantilever, the optical beam is either focused above or below the cantilever array, or focused only in the axis parallel to the cantilevers length, allowing a wide optical line to span multiple cantilevers in the array. Each cantilever reflects a part of the incident beam, which is then directed onto a photodiode array detector in a manner allowing distinguishing between individual beams. Each part of reflected beam behaves like a single beam of roughly the same divergence angle in the bending sensing axis as the incident beam. Since sensitivity of the OBD method depends on the divergence angle of deflected beam, high sensitivity is preserved in proposed expanded beam deflection (EBD) method. At the detector, each spot's position is measured at the same time, without time multiplexing of light sources. This provides real simultaneous readout of entire array, unavailable in most of competitive methods, and thus increases time resolution of the measurement. Expanded beam can also span another line of cantilevers allowing monitoring of specially designed two-dimensional arrays. In this paper, we present first results of application of EBD method to cantilever sensors. We show how thermal noise resolution can be easily achieved and combined with thermal noise based resonance frequency measurement.     

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.     

Development of a microlateral force sensor and its evaluation using lateral force microscopy

A microlateral force sensor (MLFS) was developed and evaluated using atomic force microscopy (AFM). The sensor was attached to a sensing table supported by a suspension system. The lateral motion of the sensing table was activated by a comb actuator. The driving voltage to the comb actuator was controlled to maintain a constant position of the sensing table by detecting the tunneling current at a detector, which consisted of two electrodes where the bias voltage was applied. An AFM was used to apply a lateral force to the sensing table of the sensor. When the probe of a cantilever was pressed against the sensing table and a raster scanning was conducted, the driving voltage of the comb actuator changed to compensate the friction force between the probe and sensing table. AFM measurements of an asperity array on the sensing table were conducted, and a lateral force microscopy image (LFM) was obtained from the change in driving voltage. The image by MLFS was very similar to the LFM image that was conventionally obtained from torsion of the cantilever. The LFM image strongly correlated with the gradient image calculated from the AFM topographic image. The force sensitivity of the MLFS was determined by comparing the LFM image obtained by using the MLFS with the tangential force derived from the gradient of the AFM image.     

Microthermogravimetry using a microcantilever hot plate with integrated temperature-compensated piezoresistive strain sensors

This paper reports thermogravimetric analysis of nanogram samples of paraffin using a microcantilever hot plate. The microcantilever hot plate has an integrated temperature-controlled heater and integrated temperature-compensated strain-sensing piezoresistors. The microcantilever vibration amplitude was measured using either a laser and a position sensitive photodiode, or using the piezoresistors. The cantilever resonance was measured as the cantilever was heated, such that the analyte mass could be measured as a function of temperature. Both optical and piezoresistive methods were employed to generate thermogravimetric curves for analytes in the range of 1-3 ng, and the results of the two methods compared well.     

Deconvolution of damping forces with a nonlinear microresonator

We report a fully electrical microcantilever device that utilizes capacitance for both actuation and detection and show that it can characterize various gases with a bare silicon microcantilever. We find the motion of the cantilever as it rings down when the oscillating force is removed, by measuring the voltage induced by the oscillating capacitance in the microcantilever∕counterelectrode system. The ringdown waveform was analyzed using an iterative numerical algorithm to calculate the oscillator motion, modeling the cantilever∕electrode capacitance to calculate the electrostatic force. We find that nonlinearity in the motion of the cantilever is not necessarily a disadvantage. After calibration, we simultaneously measure viscosity and density of several gaseous mixtures, yielding viscosities within ±2% and densities within ±6% of NIST values.     

Developments for inverted atomic force microscopy

Atomic force microscopy (AFM) has been used to study a wide range of systems. Chemically and biologically modified probes have extended AFM by coupling chemical and biological information with the physical measurements. In an effort to further expand the capabilities of modified AFM probes, previous studies investigated the use of an inverted AFM design (i-AFM), wherein a microfabricated tip array is used to image a cantilever-supported sample. This report details developments in cantilever and tip array fabrication which are aimed at improving the applicability and performance of this i-AFM design. Using an epoxy-based procedure, commercial cantilevers were modified with a series of standard substrates, including template-stripped gold, highly oriented pyrolytic graphite, and mica. The samples on these cantilevers were imaged with i-AFM, and lateral force images are obtained. This paper demonstrates the first use of i-AFM for measuring friction.     

Effects of geometrical dimensions and liquid properties on frequency response of resonating microcantilevers in the vicinity of a surface

Frequency response of an atomic force microscopy cantilever immersed in liquid near a surface strongly depends on the hydrodynamic forces specially the squeezed film damping, mechanical properties of the liquid including the dynamic viscosity and the density and the geometrical dimensions of the cantilever. For a slightly inclined magnetically oscillated cantilever with the approximate hydrodynamic forces acting on it, the analytical solution of the equation of motion has already been acquired. In this paper, the effects of geometrical dimensions of the cantilever on the resonance frequency, the motion amplitude and the quality factor are observed and then any increase in the kinematic viscosity of the liquid is studied through the simulation of the oscillatory motion of the cantilever. The acquired amplitude–frequency curves indicate that with an appropriate proportion between the cantilever dimensions, it is possible to optimize the quality factor for extremely small tip-sample separations. Also, if the thickness is increased and the width is reduced with the cross section area being held constant, the resonance will occur at higher frequency and the quality factor will be enhanced. Adding glycerol to water will result in the reduction of resonance frequency of the cantilever near the surface due to the viscous friction and squeezed film damping. Consequently the quality factor is decreased as a result of viscosity increase in the simulations.     

Design optimization of piezoelectric energy harvester subject to tip excitation

This research proposes a new design for a cantilever-type piezoelectric energy harvester in which a free tip is excited by any rotary motion of mechanical devices. A coupled field finite element model for the harvester is constructed using ANSYS and verification study is performed. Design optimization on the shape of the harvester is done to maximize output power. The design optimization result shows excellent performance when compared to a simple rectangular cantilever or the well-known tapered cantilever. The design results are prototyped and their improved performances are experimentally attested.     

Piezoresistive cantilever array sensor for consolidated bioprocess monitoring

Cellulolytic microbes occur in diverse natural niches and are being screened for industrial modification and utility. A microbe for consolidated bioprocessing (CBP) development can rapidly degrade pure cellulose and then ferment the resulting sugars into fuels. To identify and screen for novel microbes for CBP, we have developed a piezoresistive cantilever array sensor which is capable of simultaneous monitoring of glucose and ethanol concentration changes in a phosphate buffer solution. 4‐mercaptophenylboronic acid and polyethyleneglycol‐thiol are employed to functionalize each piezoresistive cantilever for glucose and ethanol sensing, respectively. Successful concentration measurements of glucose and ethanol with minimal interferences are obtained with our cantilever array sensor. SCANNING 31: 204–210, 2009. © 2009 Wiley Periodicals, Inc.     

The effect of off-end tip distance on the nanomanipulation based on rectangular and V-shape cantilevered AFMs

The AFM system, which is used as a nanomanipulator, includes a probe consistent of a cantilever and a tapered tip. In cantilevers, the tip can be located in different distances from the cantilever free end. This causes to change in stiffness of the cantilever and therefore changing in pushing force of the nanomanipulation. In this paper, the effect of the tip distance on the cantilever stiffness is studied using the equations of Hazel, and Neumeister and Ducker (ND), and a new equation to correct the torsional stiffness of V-shaped cantilevers (VSC) is proposed, which is based on the ND equation. Then, the effect of distance on pushing force of AFM-based nanomanipulations with rectangular cantilevered (RC) and VSC AFMs is simulated. The obtained results using proposed equation show that increasing of distance causes to non-linear increment of torsional stiffness of VSC. Error of the proposed equation is achieved less than 3% in comparison with result of torsional stiffness equation of ND. Moreover, it is observed that the torsional stiffness of VSC predicted by Hazel’s equation is considerably inaccurate. In nanomanipulation studies, the necessary pushing forces of nanoparticle motion are increased by increment of distance, for both types of cantilevers (RC and VSC). Moreover, critical time for RC AFM increases, but in the case of VSC AFM, the critical time decreases at first, then it is almost constant at a limited range of d, and finally it starts to increase by increasing the distance.     

Influence of tip mass on dynamic behavior of cracked cantilever pipe conveying fluid with moving mass

In this paper, we studied about the effect of the open crack and a tip mass on the dynamic behavior of a cantilever pipe conveying fluid with a moving mass. The equation of motion is derived by using Lagrange’s equation and analyzed by numerical method. The cantilever pipe is modelled by the Euler-Bernoulli beam theory. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influences of the crack, the moving mass, the tip mass and its moment of inertia, the velocity of fluid, and the coupling of these factors on the vibration mode, the frequency, and the tip-displacement of the cantilever pipe are analytically clarified.