U-shaped Cantilever Research Articles

AFM probe with the U-shaped cross-sectional cantilever for measuring the ultra-low coefficient of friction of 10−6

Accurately measuring the coefficient of friction (COF) is the fundamental prerequisite of superlubricity research. This study aimed to reduce the COF measurement resolution Δμ of atomic force microscopy (AFM). Based on the theoretical model, a distinctive strategy was adopted to reduce Δμ by optimizing the cantilever’s cross-section of the AFM probe, inspired by civil engineering. Δμ can be reduced by decreasing the width of the horizontal side wR and the wall thickness t and increasing the width of the vertical side wH. Moreover, the I-shape demonstrates the highest reduction in Δμ, followed by the U-shape. Considering the processability, the AFM probe with the U-shaped cross-sectional cantilever was investigated further, and the dimensions are 35 µm wR, 3.5 µm wH, 0.5 µm t, 50 µm l (cantilever length), and 23 µm htip (tip height). The finite element analysis results confirm its reliability. After being fabricated and calibrated, the AFM probe achieves the minimal Δμ of 1.9×10−6 under the maximum normal force so far. Additionally, the friction detection capability of the fabricated AFM probe improves by 78 times compared to the commercial tipless-force modulation mode (TL-FM) AFM probe with the conventional solid rectangular cross-sectional cantilever. This study provides a powerful tool for measuring 10−6 COF.

Design and Fabrication of Mems U-Shaped Cantilever

MEMS are used in acceleration, flow, pressure and force sensing applications on the micro and macro levels. The fundamental part of every sensor is the transducer which converts the measurend of intrest into and interpretable output signal. The most prominent transducer is the piezoresistive cantilever which translates any signal into an electrical signal.This paper presents the deisgn and fabrication of U shaped cantilever with enhanced sensitivity and stiffness which gives better results than other cantilevers. The simulation results of the cantilevers are designed using COMSOL software. MEMS technology becomes more affordable better and easier to fabricate in increasing quantities. Each layer of fabrication process is quite complex and final fabricated product will tested and used for high end applications.

Carbon nanotubes enhanced bimorph effect of U-shaped flexure cantilever beam actuators made from polyethylene terephthalate and polymethyl methacrylate

U-shaped cantilever actuators made from PET and PMMA exhibit a bimorph effect upon radiation heating and beam always moves toward PMMA side with maximum displacement and displacing rate measured to be 2100 μm and 35 μm s−1. This number increases to 3300 μm and 55 μm s−1 while PET surfaces are coated with single-walled carbon nanotubes acting as heat reservoir. Actuations can be further improved by carbon nanotube resistive heating and improvement reaches two-fold (4100 μm and 68.3 μm s−1). Coated beam actuators exhibit an excellent stability over 2 h intermittent operations where the maximum displacement varies only in ±1%.

SOI-based micro-mechanical terahertz detector operating at room-temperature and atmospheric pressure

We present a micro-mechanical terahertz (THz) detector fabricated on a silicon on insulator substrate and operating at room-temperature. The device is based on a U-shaped cantilever of micrometric size, on top of which two aluminum half-wave dipole antennas are deposited. This produces an absorption extending over the ∼2–3.5 THz frequency range. Due to the different thermal expansion coefficients of silicon and aluminum, the absorbed radiation induces a deformation of the cantilever, which is read out optically using a 1.5 μm laser diode. By illuminating the detector with an amplitude modulated, 2.5 THz quantum cascade laser, we obtain, at room-temperature and atmospheric pressure, a responsivity of ∼1.5×108 pm W−1 for the fundamental mechanical bending mode of the cantilever. This yields noise-equivalent-power of 20 nW/Hz at 2.5 THz. Finally, the low mechanical quality factor of the mode grants a broad frequency response of approximately 150 kHz bandwidth, with a thermal response time of ∼ 2.5 μs.

A Multi-Mode Broadband Vibration Energy Harvester Composed of Symmetrically Distributed U-Shaped Cantilever Beams.

Using the piezoelectric effect to harvest energy from surrounding vibrations is a promising alternative solution for powering small electronic devices such as wireless sensors and portable devices. A conventional piezoelectric energy harvester (PEH) can only efficiently collect energy within a small range around the resonance frequency. To realize broadband vibration energy harvesting, the idea of multiple-degrees-of-freedom (DOF) PEH to realize multiple resonant frequencies within a certain range has been recently proposed and some preliminary research has validated its feasibility. Therefore, this paper proposed a multi-DOF wideband PEH based on the frequency interval shortening mechanism to realize five resonance frequencies close enough to each other. The PEH consists of five tip masses, two U-shaped cantilever beams and a straight beam, and tuning of the resonance frequencies is realized by specific parameter design. The electrical characteristics of the PEH are analyzed by simulation and experiment, validating that the PEH can effectively expand the operating bandwidth and collect vibration energy in the low frequency. Experimental results show that the PEH has five low-frequency resonant frequencies, which are 13, 15, 18, 21 and 24 Hz; under the action of 0.5 g acceleration, the maximum output power is 52.2, 49.4, 61.3, 39.2 and 32.1 μW, respectively. In view of the difference between the simulation and the experimental results, this paper conducted an error analysis and revealed that the material parameters and parasitic capacitance are important factors that affect the simulation results. Based on the analysis, the simulation is improved for better agreement with experiments.

Integrated Electromechanical Transduction Schemes for Polymer MEMS Sensors.

Polymer Micro ElectroMechanical Systems (MEMS) have the potential to constitute a powerful alternative to silicon-based MEMS devices for sensing applications. Although the use of commercial photoresists as structural material in polymer MEMS has been widely reported, the integration of functional polymer materials as electromechanical transducers has not yet received the same amount of interest. In this context, we report on the design and fabrication of different electromechanical schemes based on polymeric materials ensuring different transduction functions. Piezoresistive transduction made of carbon nanotube-based nanocomposites with a gauge factor of 200 was embedded within U-shaped polymeric cantilevers operating either in static or dynamic modes. Flexible resonators with integrated piezoelectric transduction were also realized and used as efficient viscosity sensors. Finally, piezoelectric-based organic field effect transistor (OFET) electromechanical transduction exhibiting a record sensitivity of over 600 was integrated into polymer cantilevers and used as highly sensitive strain and humidity sensors. Such advances in integrated electromechanical transduction schemes should favor the development of novel all-polymer MEMS devices for flexible and wearable applications in the future.

Design and analysis of MEMS MWCNT/epoxy strain sensor using COMSOL

The design and performance of piezoresistive MEMS-based MWCNT/epoxy composite strain sensor using COMSOL Multiphysics Toolbox has been investigated. The proposed sensor design comprises su-8 based U-shaped cantilever beam with MWCNT/epoxy composite film as an active sensing element. A point load in microscale has been applied at the tip of the cantilever beam to observe its deflection in the proposed design. Analytical simulations have been performed to optimize various design parameters of the proposed sensor, which will be helpful at the time of fabrication.

Micromechanical contact stiffness devices and application for calibrating contact resonance atomic force microscopy

This paper reports the design, fabrication, and characterization of micromechanical devices that can present an engineered contact stiffness to an atomic force microscope (AFM) cantilever tip. These devices allow the contact stiffness between the AFM tip and a substrate to be easily and accurately measured, and can be used to calibrate the cantilever for subsequent mechanical property measurements. The contact stiffness devices are rigid copper disks of diameters 2–18 μm integrated onto a soft silicone substrate. Analytical modeling and finite element simulations predict the elastic response of the devices. Measurements of tip–sample interactions during quasi-static force measurements compare well with modeling simulation, confirming the expected elastic response of the devices, which are shown to have contact stiffness 32–156 N m−1. To demonstrate one application, we use the disk sample to calibrate three resonant modes of a U-shaped AFM cantilever actuated via Lorentz force, at approximately 220, 450, and 1200 kHz. We then use the calibrated cantilever to determine the contact stiffness and elastic modulus of three polymer samples at these modes. The overall approach allows cantilever calibration without prior knowledge of the cantilever geometry or its resonance modes, and could be broadly applied to both static and dynamic measurements that require AFM calibration against a known contact stiffness.

Fabrication of a 2-DOF electromagnetic energy harvester with in-phase vibrational bandwidth broadening

A vibration structure with two-degrees-of-freedom is proposed to increase the usable bandwidth of a micromachined electromagnetic energy harvester. Compared with the structure of a pure cantilever harvester, the proposed structure is formed by integrating a spiral diaphragm into a U-shaped cantilever diaphragm. By performing finite element analysis, the resonance frequencies of the two diaphragms are designed with a slight shift, both lower than 300 Hz. In addition, to achieve output bandwidth broadening, electroplated copper coils on the spiral and the U-shaped cantilever are coupled and the connection sequences of the coupled coils are arranged such that single- or duo-mode tuning of the energy harvester can be realized. The harvester delivers powers of 22.1 and 21.5 nW at two resonance frequencies of 211 and 274 Hz, respectively, in the duo-mode operation. The proposed spiral–cantilever coupled energy harvester has lower resonance frequencies and broader bandwidth than a pure cantilever-type harvester of equal area, and can therefore harvest more energy from the environment.

Seismic Earth Pressures on Retaining Structures and Basement Walls in Cohesionless Soils

Observations of the performance of basement walls and retaining structures in recent earthquakes show that failures of basement or deep-excavation walls in earthquakes are rare even if the structures were not designed for the actual magnitude of the earthquake loading. For instance, no significant damage or failures of retaining structures occurred in the recent Wenchuan earthquake in China (2008) or in the subduction earthquakes in Chile (2010) and Japan (2011). To develop a better understanding of the distribution and magnitude of the seismic earth pressures on cantilever retaining structures, a series of centrifuge experiments were performed on model retaining and basement structures with medium dense cohesionless backfill. This paper provides a general overview of the research program and its results. Two sets of centrifuge-scale experiments were carried out on the centrifuge at the Center for Geotechnical Modeling at UC Davis. Three different types of prototype retaining structure were modeled in this research effort as follows: (1) a nondisplacing cross-braced (basement) structure with a stem stiffness of 5.92×1010 lb-in.2 per ft width (5.57×1005 kN-m2 per m width) and 1.04×1010 lb-in.2 per ft width (9.79×1004 kN-m2 per m width); (2) a nondisplacing U-shaped cantilever structure with a stem stiffness of 5.92 and 1.04×1010 lb-in.2 per ft width (9.79×1004 kN-m2 per m width); and (3) a free standing, cantilever retaining wall with a stem stiffness of 2.4×1010 lb-in.2 per ft width (2.26×1005 kN-m2 per m width). Overall, for the structures examined [i.e., wall heights in the range 6.1–9.15 m (20–30 ft)], the centrifuge data consistently show that the maximum dynamic earth pressure increases with depth and can be reasonably approximated by a triangular distribution. This suggests that the result of the dynamic earth pressure increment acts near 0.33H above the footing as opposed to 0.5–0.6 H recommended by most current design procedures. The current data also suggest that cantilever walls can resist ground accelerations up to 0.4 g if designed with an adequate static factor of safety.

Improving picogram mass sensitivity via frequency doubling in coupled silicon micro-cantilevers

Two geometrically different cantilevers, with primary frequencies of 182.506 kHz (u-shaped cantilever for sensing) and 372.503 kHz (rectangular cantilever for detecting), were coupled by two symmetrical coupling overhangs for oscillation-based mass sensing verification with phase-locking. Based on a lumped element model, a theoretical expression, containing a nonlinear spring constant and a term corresponding to the effect of the coupling spring, was proposed to consider the factors influencing the entrainment range, which is defined as a plateau with a frequency ratio (resonant frequency of rectangular cantilever to that of u-shaped cantilever) of 2.000 in present study. A picogram order mass sensing by applying a polystyrene microsphere as a small mass perturbation onto the tip of the u-shaped cantilever was demonstrated. By varying driving voltages, two entrainment regions with and without microsphere were experimentally measured and comparatively shown. At a driving voltage of 1 Vpp, when the u-shaped cantilever was excited at its shifted frequency of 180.29 kHz, the frequency response of the coupled rectangular cantilever had a peak at double the shifted frequency of 360.58 kHz of the u-shaped cantilever. The frequency shift for picogram mass sensing was thus doubled from 2560 Hz to 5133 Hz due to phase-locking. A mass of 3.732 picogram was derived based on the doubled frequency shift corresponding to a calculated mass of 3.771 picogram from measured diameter and reported density. Both experimental demonstration and theoretical discussions from the viewpoint of entrainment range elicits the possibility of increasing the mass sensitivity via phase-locking in the coupled silicon micro-cantilevers.

Multifunctional atomic force microscope cantilevers with Lorentz force actuation and self-heating capability

This paper reports the development of microcantilevers capable of self-heating and Lorentz-force actuation, and demonstrates applications to thermal topography imaging. Electrical current passing through a U-shaped cantilever in the presence of a magnetic field induces a Lorentz force on the cantilever free end, resulting in cantilever actuation. This same current flowing through a resistive heater induces a controllable temperature increase. We present cantilevers designed for large actuation forces for a given cantilever temperature increase. We analyze the designs of two new cantilevers, along with a legacy cantilever design. The cantilevers are designed to have a spring constant of about 1.5 N m−1, a resonant frequency near 100 kHz, and self-heating capability with temperature controllable over the range 25–600 °C. Compared to previous reports on self-heating cantilevers, the Lorentz–thermal cantilevers generate up to seven times as much Lorentz force and two times as much oscillation amplitude. When used for thermal topography imaging, the Lorentz–thermal cantilevers can measure topography with a vertical resolution of 0.2 nm.

Characterizing the free and surface-coupled vibrations of heated-tip atomic force microscope cantilevers**Publication of NIST, an agency of the US government, not subject to copyright.

Combining heated-tip atomic force microscopy (HT-AFM) with quantitative methods for determining surface mechanical properties, such as contact resonance force microscopy, creates an avenue for nanoscale thermomechanical property characterization. For nanomechanical methods that employ an atomic force microscope cantilever’s vibrational modes, it is essential to understand how the vibrations of the U-shaped HT-AFM cantilever differ from those of a more traditional rectangular lever, for which analytical techniques are better developed. Here we show, with a combination of finite element analysis (FEA) and experiments, that the HT-AFM cantilever exhibits many more readily-excited vibrational modes over typical AFM frequencies compared to a rectangular cantilever. The arms of U-shaped HT-AFM cantilevers exhibit two distinct forms of flexural vibrations that differ depending on whether the two arms are vibrating in-phase or out-of-phase with one another. The in-phase vibrations are qualitatively similar to flexural vibrations in rectangular cantilevers and generally show larger sensitivity to surface stiffness changes than the out-of-phase vibrations. Vibration types can be identified from their frequency and by considering vibration amplitudes in the horizontal and vertical channels of the AFM at different laser spot positions on the cantilever. For identifying contact resonance vibrational modes, we also consider the sensitivity of the resonant frequencies to a change in applied force and hence to tip–sample contact stiffness. Finally, we assess how existing analytical models can be used to accurately predict contact stiffness from contact-resonance HT-AFM results. A simple two-parameter Euler–Bernoulli beam model provided good agreement with FEA for in-phase modes up to a contact stiffness 500 times the cantilever spring constant. By providing insight into cantilever vibrations and exploring the potential of current analysis techniques, our results lay the groundwork for future use of HT-AFM cantilevers for accurate nanomechanical property measurements.

Principles of nonlinear MEMS-resonators regarding magnetic-field detection and the interaction with a capacitive read-out system

This paper presents a magnetic field sensor with capacitive read-out, whose active element is a micromachined mechanical resonator. The MEMS magnetic field sensor exploits the Lorentz force to detect external magnetic flux density through the displacement of the resonant structure, which can be measured with optical and capacitive sensing techniques. The micromachined U-shaped cantilever features a length of 2 mm, a base width of 90 μm and a thickness of 20 μm, and is manufactured in SOI technology. The designed sensor has a measured resonant frequency of 4.359 kHz for the fundamental mode and a calculated mass of the flexible structure of 24.5 ng. A quality factor in the order of 104 at an ambient pressure of 0.3 Pa has been measured where a magnetic field resolution of 15 nT can be achieved. Although these arrangements are well suited to capacitively sense the vibrations caused by the Lorentz force on the current lead on the silicon part, care has to be taken to avoid undesired mutual interferences. A serious interference was observed in case of a DC bias voltage at the readout capacitance and a significant voltage drop caused by the current needed for the generation of the Lorentz force. This work investigates in detail this phenomenon as well as the complete physical transduction chain and improves the understanding of such microelectromechanical systems significantly. An analytical model of the electrostatic system is established including all relevant components and their interactions as well as the motion of the MEMS part. The importance of electrostatic back-action for a feasible detection limit for magnetic fields was recognized for the first time.

1011 同期共振を利用した微小共振子に関する研究とその応用(第2報)(OS8-1 オーガナイズドセッション《マイクロマシンとG-MEMS/N-MEMS》)

A novel oscillation system, which consists of a U-shaped cantilever and a beam-shaped cantilever, was designed, fabricated and characterized for synchronized oscillation-based applications. Two geometrically different cantilevers, with resonant frequencies of 372.503 kHz (beam-shaped for detecting) and 182.506 kHz (U-shaped for sensing), are coupled by two coupling overhangs. Under synchronized oscillation, the frequency response was found to double from 182.850 kHz to 365.713 kHz from low frequency cantilever (U-shaped) to high frequency cantilever (beam-shaped). A plateau with a frequency ratio of 2.000 was observed, which corresponds to a synchronization region or bandwidth. The synchronization bandwidth was observed to be expanded from 70 Hz to over 500 Hz by increasing the driving voltage. This expansion is believed to be related to nonlinear characteristic of coupled oscillator, which needs further studied.

Characterisation of micromechanically coupled U-shaped cantilever-based oscillators with and without micromechanical elements for synchronised oscillation-based applications

Two novel oscillation systems, consisting of a U-shaped cantilever and a beam-shaped cantilever, were designed, fabricated and comparatively characterised for synchronised oscillation-based applications. In the case of without mechanical elements, two geometrically different cantilevers, with resonant frequencies of 182.506 kHz (detecting) and 372.503 kHz (sensing), respectively, are coupled by two coupling overhangs. Under synchronised oscillation, the frequency response was found to double from 182.850 to 365.713 kHz from a low-frequency cantilever (U shaped) to a high-frequency cantilever (beam shaped). A plateau with a frequency ratio of 2.000 was observed for both systems, which corresponds to a stable synchronisation region. This demonstrates the possibility of increasing the frequency response signal from the low-frequency cantilever to the high-frequency cantilever based on this super harmonic synchronisation. However, based on the comparative studies of two systems with and without mechanical systems, it is found that enhancing the nonlinearity without increasing energy loss (support loss in the present study) seems to be necessary to widen the frequency entrainment range for real applications.

Improved energy harvesting from wideband vibrations by nonlinear piezoelectric converters

Vibration harvesters typically are linear mass-spring devices working at resonance. A different approach is here proposed based on nonlinear converters that exploit stochastic resonance with white-noise excitation. It consists of a piezoelectric beam converter coupled to permanent magnets to create a bistable system. Under proper conditions, the system bounces between two stable states in response to random excitation, which significantly improves energy harvesting from wide-spectrum vibrations. The background theory is discussed based on a simplified monodimensional model which includes nonlinearity. A cantilever beam with added nonlinearity was simulated by using a MATLAB ® Stochastic Differential Equation (SDE) Toolbox demonstrating the expected improvement under white-noise vibrations. Nonlinear converters were then realized by screen printing low-curing-temperature lead zirconate titanate (PZT) films on steel cantilevers equipped with magnets. Experimental tests were performed by measuring both the beam deflection and the output voltage under excitation by random vibrations at varying degree of nonlinearity added to the system. The obtained results show that the performances of the converter in terms of output voltage at parity of mechanical excitation are markedly improved when the system is made bistable. Furthermore, the principle was also preliminarily validated on a MEMS U-shaped cantilever beam that was purposely designed and fabricated in SOI technology. This demonstrates the possibility to downscale the principle here proposed in the perspective of a MEMS harvester based on nonlinear piezoelectric converters.

Crystalline silicon cantilevers for piezoresistive detection of biomolecular forces

In order to obtain a sensor with force resolution better than 100pN for biomolecular detection, U-shaped piezoresistive cantilevers made of crystalline silicon have been fabricated. The resistors have been defined by ionic implantation of As+, yielding a shallow and thin resistor and they have been patterned parallel to the (100) crystallographic direction, attaining a maximum for the piezoresistive factor. The sensitivity of the devices is characterized together as the force resolution, being both of them 60μV/pN and 65pN, respectively, for a cantilever with a length of 250μm, a width of 8μm and a thickness of 340nm.

Lorentz force based magnetic field sensor with optical readout

A miniaturized sensor capable for measuring high magnetic flux densities is presented. The magnetic flux density is converted into a movement of a micro machined U-shaped cantilever, which bears a thin film lead. The cantilever movement is accomplished by the Lorentz force acting on the electrical current. The cantilever poses as a deflecting mirror in an optical readout system. The ratio of the intensity of the light reflected by the front side of the cantilever to the intensity of the incident light is analyzed. The optical conversion principle was proven experimentally. It is well described by an optical near field model. To overcome measurement problems caused by the deformation due to mechanically prestressed cantilevers, an ac excitation was used for sensor characterization. A measurement range of the current–flux density product of 2.2 mA T was achieved by evaluating the peak light intensity. Beyond this limit more sophisticated signal analysis has to be applied. Depending on the rest position, a magnetic flux density of about 10 mT can be resolved with a current of 10 mA. The target of an upper limit of 50 T can be achieved by reducing the electrical current.

A study of U-shaped micromachined cantilever array

In order to increase the resolution and realize the versatility of cantilever, U-shaped piezoresistive cantilever array has been designed and fabricated in this research. The optimized geometries of cantilever and piezoresistor were determined by analyzing the stress, noise and sensitivity of piezoresistive cantilever from theory. Based on silicon micromachining technology, the piezoresistive cantilevers were fabricated by using polysilicon as the piezoresistive materials. With the measurement results of noise and sensitivity, the Hooge factor was calculated to be 3×10-3, the gauge factor is 27, and the minimum detectable deflection of piezoresistive cantilever was calculated to be 0.5nm at a 6V bias voltage and a 1000Hz measurement bandwidth. The noise sources of polysilicon pizeoresistor are also discussed in this paper.