Resonant Cantilever Research Articles

Ultrafine Aerosol Particle Sizer Based on Piezoresistive Microcantilever Resonators with Integrated Air-Flow Channel.

To monitor airborne nano-sized particles (NPs), a single-chip differential mobility particle sizer (DMPS) based on resonant micro cantilevers in defined micro-fluidic channels (µFCs) is introduced. A size bin of the positive-charged fraction of particles herein is separated from the air stream by aligning their trajectories onto the cantilever under the action of a perpendicular electrostatic field of variable strength. We use previously described µFCs and piezoresistive micro cantilevers (PMCs) of 16 ng mass fabricated using micro electro mechanical system (MEMS) technology, which offer a limit of detection of captured particle mass of 0.26 pg and a minimum detectable particulate mass concentration in air of 0.75 µg/m3. Mobility sizing in 4 bins of a nebulized carbon aerosol NPs is demonstrated based on finite element modelling (FEM) combined with a-priori knowledge of particle charge state. Good agreement of better than 14% of mass concentration is observed in a chamber test for the novel MEMS-DMPS vs. a simultaneously operated standard fast mobility particle sizer (FMPS) as reference instrument. Refreshing of polluted cantilevers is feasible without de-mounting the sensor chip from its package by multiply purging them alternately in acetone steam and clean air.

High Resolution and Fast Response of Humidity Sensor Based on AlN Cantilever With Two Groups of Segmented Electrodes

Resonant cantilever based on piezoelectric materials is one of the most promising platforms for real-time humidity sensing. In this letter, we propose a humidity sensor based on an AlN piezoelectric microcantilever with a high-order resonant mode and a sensing layer of MoS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . The top electrode of cantilever is designed into two groups of segmented electrodes in order to achieve a high intensity of the resonance peak of the cantilever resonator operated at a high-order mode. Compared with the humidity sensor based on a standard cantilever with the same dimension, the sensitivity of the newly proposed humidity sensor is increased from 5.99 to 778 Hz/%RH when the humidity is about 80%RH. The resolution is increased from 0.21%RH to 0.025%RH because of the improvement of the ratio of sensitivity to noise, which cannot be achieved simply by increasing the frequency. The sensor shows a low hysteresis (5.8%) in a wide humidity sensing range from 10%RH to 90%RH. Moreover, the proposed humidity sensor has good short-term repeatability, fast response (0.6 s) and recovery (8 s) to humidity changes, indicating its great potential for fast-response detection.

Cantilever magnetoelectric PZT/Tb–Fe–Co resonators for magnetic sensing applications

Magnetoelectric material-based cantilever resonators have been considered as a promising solution for magnetic sensing applications. However, most applications focus on bulk piezoelectric (e.g., PZT) laminated composites, which put a critical limit for miniaturizing into micrometer-sized devices. This work aims at demonstrating the potential of a micro-resonator approach with lower power consumption and smaller size. It reports on the fabrication and characterization of a resonant cantilever based on a freestanding multi-ferroic PZT/Tb–Fe–Co thin film multilayer, where the magnetic signal is sensed by measuring the shift of the device resonant frequency. The Tb–Fe–Co layer acts as a magnetic field sensing layer, while the PZT thin film integrated in the capacitor geometry acts as a micro-transducer to obtain an electrical signal. For a magnetic field less than 0.2 T, a sensitivity as high as 487 Hz/T is measured for the sensor under a vacuum environment. While the sensor design has to be further optimized to improve the performance, it is promising as a micro-magnetoelectric sensor for magnetic field sensing.

Frequency–amplitude response of superharmonic resonance of second order of electrostatically actuated MEMS cantilever resonators

This paper deals with the frequency–amplitude response of superharmonic resonance of second order (order two) of electrostatically actuated Micro-Electro-Mechanical System (MEMS) cantilever resonators. The structure of MEMS resonators consists of a cantilever resonator over a parallel ground plate, with a given gap in between, and under AC voltage. This resonance results from hard excitations and AC voltage frequency near one-fourth of the natural frequency of the resonator. The forces acting on the resonator are the nonlinear electrostatic force to include fringe effect, and a linear damping force. In order to solve the dimensionless partial differential equation of motion along with boundary and initial conditions, two types of models are developed, namely Reduced Order Models (ROMs), and Boundary Value Problem (BVP) model. The BVP model is essentially a finite difference model with a discretization in time only. ROMs are developed using one through five modes of vibration. The Method of Multiple Scales (MMS), numerical integrations using MATLAB, as well as a continuation and bifurcation analysis are used to solve the ROMs. The BVP model, resulting from using finite differences for time derivatives, is also numerically integrated. Five modes of vibration ROM is found to make accurate predictions in all amplitudes. A softening effect of the response is predicted. The response consists of a bifurcation with a bifurcation point of amplitude one fourth of the gap, and a stable branch in larger frequencies with a pull-in instability end point at three fourths of the gap. The bifurcation point shifts to lower frequencies as the voltage and/or fringe effect increase, and/or damping decreases. If damping increases, the branches coalesce, peak amplitude decreases, and a linear behavior is experienced.

Research on frequency bandwidth and phase difference of piezoelectric resonant cantilever based on mass

Research on frequency bandwidth and phase difference of piezoelectric resonant cantilever based on mass

Modeling the Piezoelectric Cantilever Resonator with Different Width Layers.

The piezoelectric cantilever resonator is used widely in many fields because of its perfect design, easy-to-control process, easy integration with the integrated circuit. The tip displacement and resonance frequency are two important characters of the piezoelectric cantilever resonator and many models are used to characterize them. However, these models are only suitable for the piezoelectric cantilever with the same width layers. To accurately characterize the piezoelectric cantilever resonators with different width layers, a novel model is proposed for predicting the tip displacement and resonance frequency. The results show that the model is in good agreement with the finite element method (FEM) simulation and experiment measurements, the tip displacement error is no more than 6%, the errors of the first, second, and third-order resonance frequency between theoretical values and measured results are 1.63%, 1.18%, and 0.51%, respectively. Finally, a discussion of the tip displacement of the piezoelectric cantilever resonator when the second layer is null, electrode, or silicon oxide (SiO2) is presented, and the utility of the model as a design tool for specifying the tip displacement and resonance frequency is demonstrated. Furthermore, this model can also be extended to characterize the piezoelectric cantilever with n-layer film or piezoelectric doubly clamped beam.

Exploring 1:3 internal resonance for broadband piezoelectric energy harvesting

Recent literature has shown that the spectral characteristics of a harvester can be significantly improved by invoking internal resonance between the modes. Taking motivation from this premise, the present work analyzes the nonlinear dynamics and harvesting performance of a 1:3 internally resonant piezoelectric cantilever beam with a lumped mass under harmonic excitation. The governing modal equations are derived using Galerkin’s approach and Hamilton’s principle of least action. The method of multiple scales has been used to study the dynamics of the harvester in the proximity of primary resonances. The steady state periodic responses of the harvester are obtained using a pseudo-arc continuation technique and subsequently, their implications on the harvested power are discussed. The frequency responses of the harvested power are shown to boast significantly high magnitudes across a wide frequency band due to the energy transfer between the modes near the primary resonances. Results presented in the study show that the higher mode invoked through internal resonance plays a significant role in broadband power generation. The transfer of energy between the modes is found to occur only within a certain threshold of excitation level which in turn affects the magnitude of harvested power. Numerical simulations have also been carried out the results of which are compared against the analytical results. The outcomes of this first-hand analysis shall aid in the proposition of an efficient design for a broadband energy harvester.

High-resolution measurement of atomic force microscope cantilever resonance frequency

The atomic force microscope (AFM) is widely used in a wide range of applications due to its high scanning resolution and diverse scanning modes. In many applications, there is a need for accurate and precise measurement of the vibrational resonance frequency of a cantilever. These frequency shifts can be related to changes in mass of the cantilever arising from, e.g., loss of fluid due to a nanolithography operation. A common method of measuring resonance frequency examines the power spectral density of the free random motion of the cantilever, commonly known as a thermal. While the thermal is capable of reasonable measurement resolution and speed, some applications are sensitive to changes in the resonance frequency of the cantilever, which are small, rapid, or both, and the performance of the thermal does not offer sufficient resolution in frequency or in time. In this work, we describe a method based on a narrow-range frequency sweep to measure the resonance frequency of a vibrational mode of an AFM cantilever and demonstrate it by monitoring the evaporation of glycerol from a cantilever. It can be seamlessly integrated into many commercial AFMs without additional hardware modifications and adapts to cantilevers with a wide range of resonance frequencies. Furthermore, this method can rapidly detect small changes in resonance frequency (with our experiments showing a resolution of ∼0.1 Hz for cantilever resonances ranging from 70 kHz to 300 kHz) at a rate far faster than with a thermal. These attributes are particularly beneficial for techniques such as dip-pen nanolithography.

Model updating of a scaled piping system and vibration attenuation via locally resonant bandgap formation

This study presents a Finite Element (FE) model updating methodology of a piping system and demonstrates vibration attenuation at its resonant frequencies using tuned local resonators distributed along its length. An experimental laboratory scaled version of a prototype piping system inspired from existing piping structures in the oil and gas industry is assembled to study its dynamic behavior under laboratory conditions. A dynamic structural similitude analysis is carried out to derive scaling factors for frequencies and mode shapes between the prototype and scaled piping systems. These scaling factors are verified with the aid of both detailed and reduced-order FE models. Experimental natural frequencies and mode shapes are obtained based on the impact hammer modal test and the forced vibration sine sweep test and then compared with numerical results. Discrepancies between measured and computed results due to uncertainties in the FE model necessitate the use of an FE model updating technique to minimize the error between the predicted and the measured response. This updating strategy is carried out by iteratively adjusting parameters associated with the assumed boundary conditions until a relatively faithful computational model that can replicate the actual behavior of the structure is obtained. The updated reduced order model is then used to investigate the creation of locally resonant bandgaps centered at the first three resonant frequencies of the structure by embedding tuned resonant cantilever beams with tip masses along the length of the piping system. Using a harmonic response analysis, it is shown that an attenuation is obtained at all considered target frequencies with distinct edge frequencies appearing in the frequency response for the third mode of vibration.

Effect of Surface and Interfacial Tension on the Resonance Frequency of Microfluidic Channel Cantilever.

The bending resonance of micro-sized resonators has been utilized to study adsorption of analyte molecules in complex fluids of picogram quantity. Traditionally, the analysis to characterize the resonance frequency has focused solely on the mass change, whereas the effect of interfacial tension of the fluid has been largely neglected. By observing forced vibrations of a microfluidic cantilever filled with a series of alkanes using a laser Doppler vibrometer (LDV), we studied the effect of surface and interfacial tension on the resonance frequency. Here, we incorporated the Young–Laplace equation into the Euler–Bernoulli beam theory to consider extra stress that surface and interface tension exerts on the vibration of the cantilever. Based on the hypothesis that the near-surface region of a continuum is subject to the extra stress, thin surface and interface layers are introduced to our model. The thin layer is subject to an axial force exerted by the extra stress, which in turn affects the transverse vibration of the cantilever. We tested the analytical model by varying the interfacial tension between the silicon nitride microchannel cantilever and the filled alkanes, whose interfacial tension varies with chain length. Compared with the conventional Euler–Bernoulli model, our enhanced model provides a better agreement to the experimental results, shedding light on precision measurements using micro-sized cantilever resonators.

Photothermal excitation efficiency enhancement of cantilevers by electron beam deposition of amorphous carbon thin films

In recent years, the atomic force microscope has proven to be a powerful tool for studying biological systems, mainly for its capability to measure in liquids with nanoscale resolution. Measuring tissues, cells or proteins in their physiological conditions gives us access to valuable information about their real ‘in vivo’ structure, dynamics and functionality which could then fuel disruptive medical and biological applications. The main problem faced by the atomic force microscope when working in liquid environments is the difficulty to generate clear cantilever resonance spectra, essential for stable operation and for high resolution imaging. Photothermal actuation overcomes this problem, as it generates clear resonance spectra free from spurious peaks. However, relatively high laser powers are required to achieve the desired cantilever oscillation amplitude, which could potentially damage biological samples. In this study, we demonstrate that the photothermal excitation efficiency can be enhanced by coating the cantilever with a thin amorphous carbon layer to increase the heat absorption from the laser, reducing the required excitation laser power and minimizing the damage to biological samples.

Ultrasensitive detection of antigen–antibody interaction and triglycerides in liquid ambient using polysilicon cantilevers

Measurement in liquid media is a major challenge in real-time detection using resonant cantilevers. This is addressed in the present study by fabricating sub-micron thick cantilevers followed by functionalization for biomolecule detection.The fabricated cantilever resonator beams of thickness 165 nm were used for measurements in two systems: (i) human immunoglobulin (HIgG) as the antibody on the cantilever sensing mouse immunoglobulin (MIgG) as corresponding antigen, and (ii) detection of triglyceride (TG) based on the enzymatic hydrolysis with lipase, using tributyrin as a model. In both cases, the beams were functionalized for covalent bonding of the protein receptor. The label-free detection was carried out by measuring the shift in resonance frequency at higher modes, using a laser Doppler vibrometer in liquid and in air.The calibration showed a linear correlation between the bioanalyte concentration and change in the resonance frequency. Notably, detection of antigen mass as low as 434 ± 59fg and triglyceride concentration in the nM range with limit of detection as 7 nM in liquid interface was achieved, greatly improving the sensitivity of bioanalyte detection in liquid samples.Although frequency-based methods are highly sensitive, the issues with measurement liquid medium limit theirapplication. In the present report, these issues were addressed by fabricatingsub-micron thick cantilever beam, choosing an appropriate functionalizationmethod without affecting the sensitivity, and measurement at higher modes. Thesehave resulted in circumventing issues like damping and hydrodynamic loadingthus improving its potential as real-time sensor.

Temperature Compensation of Thermally Actuated, In-Plane Resonant Gas Sensor Using Embedded Oxide-Filled Trenches

We report the implementation of a passive temperature compensation technique in thermally actuated, silicon-based, resonant cantilever gas sensors vibrating in their fundamental in-plane resonant mode. The temperature compensation technique utilizes oxide-filled trenches along the edges of the cantilever structure and adds a single additional mask to the overall fabrication process. The trench width for effective temperature compensation was optimized using finite element simulation. The fabricated resonators exhibit a temperature coefficient of frequency (TCF) as low as 1.7 ppm/°C, which represents a 15x improvement compared to the same resonators without oxide trenches. Quality factors of devices with oxide compensation are similar to those measured in non-compensated counterparts. The temperature compensation technique addresses a key limitation of silicon-based, mass-sensitive chemical microsensors, namely their temperature instability due to inherent temperature-dependent material properties. Compared to our previous work, the improved frequency and baseline stability yields an almost order-of-magnitude improvement in the extrapolated limit of detection, approaching 100 ppb for toluene. [2020-0154]

Analysis of Coupled Dynamic and Voltage Models of Piezoelectric Cantilever Energy Harvester using Differential Transformation Method

In this work, differential transformation method with after treatment technique is applied to develop analytical models for the prediction of the behavior and output voltage of cantilever piezoelectric energy harvesters. The analytical results are in a good agreement with the experimental results in literature. The first mode of vibration has the lowest resonant frequency, and typically provides the most deflection and therefore electrical energy. The output voltage increases with the length of the beam but increase in the thickness of the beam decreases the output voltage. The results depict that the shape of the cantilever energy harvester plays an important role in improving the harvester’s efficiency. It is established that under the same loading, material and geometrical conditions, triangular cantilever beams are more efficient than rectangular ones. From the results, it is also established that that among all the cantilever beams with uniform thickness, the triangular cantilever, can lead to highest resonance frequency. Therefore, in order to obtain more wideband piezoelectric energy harvester, the geometrical and material designs of piezoelectric resonant cantilevers must be properly analyzed.

Exploring the cantilever: teaching tools for atomic force microscopy

This paper presents a series of experiments that aim to aid with the understanding of some of the fundamental concepts pertaining to the resonance of cantilevers. The goal is to provide an accessible platform for exploring how the cantilever, one of the fundamental components in non-contact scanning probe/atomic force microscopy, is utilized in measuring forces. A straightforward experiment that utilizes a piezo buzzer and oscilloscope to measure the natural resonance frequency of a cantilever is showcased. This information is used to demonstrate how the frequency is related to the length and to extract information about the Young’s modulus of the material. It also presents how one is able to utilize a piezo-driven craft stick to measure masses within a 100th of a gram. Utilizing the same driven craft sticks, are a series of experiments exhibited that employ the use of a magnetic probe to explore the differences between attractive and repulsive forces. In addition, a discussion of how these results relate to the tip-sample interactions in atomic force microscopy will be displayed. The experiments presented were developed as part of an undergraduate modern physics laboratory and a scanning probe microscopy course. A review of how these experiments were implemented in these courses will be presented. The experiments highlighted in this manuscript were employed as part of a distance learning kit for a modern laboratory, that was converted to an e-learning classroom due to social distancing restrictions. A description of the kits utilized will be provided.

Enhancement of the low-frequency acoustic energy harvesting with auxetic resonators

A new concept to enhance efficiency of the acoustic energy harvesting is presented and experimentally tested in this paper. An auxetic latticed resonator backed by an acoustic rectangular tube is proposed for this purpose. The concept is tested and proved by comparing the extracted power against performance of a conventional cantilever resonator at resonant-resonant condition. The problem is modeled by the Finite Element Method. The models are validated using experimental tests. The energy harvesting performance is numerically evaluated in different sound powers, geometrical aspects and electrical properties. In a parametric study, performance of the proposed auxetic resonator is compared with a plain one. It is shown that employing the concept can remarkably enhance performance of the acoustic energy harvesting system. At low frequencies, 138 Hz in this study, at an optimum situation we could arrive at a large magnification factor around 10.5 for 100 dB sound pressure level.

Optomechanical probe of an axial-vector mediated interaction in the quantum regime.

We present an atomic, molecular, and optical physics based method to search for axial-vector mediated dipole-dipole interaction between electrons. In our optomechanical scheme, applying a static magnetic field and a pump beam and a probe beam to a hybrid mechanical system composed of a nitrogen-vacancy center and a cantilever resonator, we could obtain a probe absorption spectrum. Based on the study of the relationship between this spectrum and the exotic dipole-dipole interaction, we put forward our detection principle and then provide a prospective constraint most stringent at a rough interaction range from 4 × 10-8 to 2 × 10-7m. Our results indicate that this scheme could be put into consideration in relevant experimental searches.

SiOCH Hits the Gas

There is an increasing need for on-site and real-time analyses of complex gas mixtures in many application fields such as industry, air quality, security and medicine. One challenge consists in developing complete and portable multi-gas analysis systems allowing in situ and real-time quantitative analysis of complex gas mixtures. A promising approach is based on the integration of resonating devices on silicon chips by using “standard” microelectronic technologies. The fabrication of these gravimetric gas sensors based on Nano Electro Mechanical System (NEMS) requires the use of a chemical sensitive layer to ensure a better collection and concentration of the target molecules. This enhances the sensitivity in conjunction with the limit of detection. The integration of a chemical sensitive layer on to NEMS fabricated on Si wafers leads to specific material requirements. The use of solvent is prohibited in order to avoid the degradation of the Si nanocantilevers due to capillarity forces,Very thin film thickness (less than few hundred of nanometers) should be deposited on the Si beam in order to avoid filling the gap between the resonant cantilever and the electrodes,The deposition technique should provide good uniformity over a large surface (typically on 200 mm Si wafers) for a collective sensor fabrication.And the material should be optimized to absorb the highest level of targeted gas for a given thickness, reversibly and quickly. In this work, the objective was to develop materials deposited using microelectronic compatible techniques in order to detect light alkanes and aromatic volatile organic compounds such as BTEX (for Benzene, Toluene Ethylbenzene and Xylene). Organosilicate materials are potentially good candidates for this application especially because they are nonpolar or weakly polar materials. In order to better understand the impact of the material chemistry on the detection of hydrocarbon gas and optimize the sensitivity of the chemical layer, a large panel of organosilicate thin films were deposited by different chemical vapor deposition (CVD) techniques. First, SiOCH were deposited by Plasma Enhanced Chemical Vapor Deposition (PECVD), this technique being the most used in the microelectronic industry for dielectric thin-film deposition. Several precursors (diethoxymethylsilane, trimethylsilane or octamethyltrisiloxane) and deposition conditions were used in order to vary their chemical composition and their physical properties. In these SiOCH, the carbon content is mainly under the form of methyl groups bonded to silicon. At the same time, to allow a better flexibility in term of chemical functions, filament assisted chemical vapor deposition (FACVD) was used for the deposition of organosilicate thin films. Indeed, FACVD allow a better control over the precursor fragmentation pathway in comparison to plasma-based techniques. Then, it is possible to add polar groups (such as ethoxy to in case of FACVD of methyltriethoxysilane) or to introduce siloxane rings in the materials (in case of initiated CVD of cyclosiloxane). Finally, the introduction of additional porosity was investigated as another way to potentially improve the sensitivity of the chemical sensitive layers. By using a porogen approach, it is possible to introduce up to 40 % porosity in a PECVD SiOCH. Using a foaming approach, we can go even further (> 50 %). Film properties after deposition and after potential annealing were investigated using multiple characterization techniques (ellipsometry, FTIR and Tof-SIMS). Porosity was characterized by ellipsometric porosimetry and grazing incidence small angle X-ray Scattering. In these material, pores (if any) are nanometrics and porosity is mainly open and interconnected. Thin film response under toluene or pentane exposures was studied using Quartz Crystal Microbalance functionalized with the different SiOCH.Through the synthesis and characterization of these various SiOCH thin films, the role of hydrophobicity, carbon content and specific chemical bonding can be highlighted. It is shown that the hydrophobic nature of SiOCH materials composed of a Si-O-Si backbone with methyl groups bonded to silicon, combined with the presence nanoporosity, lead to very high sensibility. The presence of isolated polar bonds such as ethoxy groups seems beneficial especially for BTEX detection. High partition coefficients toward toluene and pentane can be obtained, at least ten time higher than those measured on more classical polymers such as PDMS. Both deposition techniques (PECVD or FACVD) are able to produce good chemical sensitive layers for the detection of light alkanes and aromatics VOCs and these organosilicates constitute promising solution for the functionalization of NEMS-based gas sensors.Acknowledgment: Developments on FACVD were performed in the frame of a collaboration with TEL, US-Technology Development Center, America.

Signal enhancement of FBG-based cantilever accelerometer by resonance suppression using magnetic damper

In this work, we propose the use of a magnetic damper in the FBG-based cantilever accelerometer (FCA) to reduce the distortion of signal due to the infinite signal amplification at the resonant frequency. The magnetic damper comprises a permanent magnet and a U-shape aluminum structure. The permanent magnet serves as a load and is attached to one end of the cantilever whereas the aluminum structure serves as a damper to suppress the cantilever resonance. In the experiment, it is found that the distortion on the detected signal by FCA is reduced when the damper is incorporated, and the detected signal has a higher cross-correlation coefficient (CCC) with a reference signal from a standard capacitive based accelerometer. The introduction of a magnetic damper enables the vibration detection of the FCA in the resonant frequency region with reduced signal distortion and it widens the detection range of the FCA.

Evaluation and calculations of modes resonant cantilever for laser optical fiber assembly

&lt;p&gt;Biosensors depend on cantilevers have developed a promising tool for detecting biomedical, optical laser communication and many fields of interactions with high accuracy. We modeled the operation of cantilevers&lt;strong&gt; &lt;/strong&gt;with two magnetic and coil using Ansys program. This simulation technique can capably be used to select the appropriate design and dimensions of cantilever with the geometry of system. The primary main of the magnetic design is to improve the geometry of the coil and shape to yield a highly uniform for 3D of optical fiber includes Silica Glass and Nickel cantilever, two magnets and one coil that apply to force on the cantilever cylinder is using as a cantilever in the designing of this case.In conclusion,resonant frequency( tuning applying cantilivier presented in the resracher have larger variable range by using 2-magnets with the coil.However,the adjusting of the system and changing the deminsions.Resolutions to this problematic contain tuning the modes of resonant frequency to produce by cantilivier with 2-magnets and coil when the signal pass from laser source. Based on these simulations and characterization results, the proposed assembly can be a good applicant for evolving a low price, high material platform for many biological, laser optical fiber, communication, machine learning, biosensors and biomedical applications.&lt;/p&gt;