Microelectromechanical Systems Resonators Research Articles

Internal resonance between the extensional and flexural modes in micromechanical resonators

Internal resonance between different vibration modes in micromechanical devices has been widely studied due to its promising application prospects in microelectromechanical systems (MEMS) resonators and oscillators. In this paper, we investigated the 2:1 internal resonance between the extensional and flexural modes in a micromechanical cantilever beam resonator using open and closed loop testing methods. In the open loop test, energy transfer from the extensional mode to the flexural mode induced by internal resonance is directly observed. Amplitude saturation and internal resonance bandwidth change in the extensional mode are experimentally studied and theoretically verified with numerical simulation. In the closed loop system, internal resonance produces a bistable self-oscillation frequency. The oscillation frequency of the extensional mode will be locked to one of the two peaks induced by internal resonance. In addition, obvious improvement in short-term frequency stability of the closed loop system is observed with the help of internal resonance. The dynamic characteristics studied in this research can be potentially used to enhance the performance of MEMS vibration devices by internal resonance.

A T-Shape Aluminum Nitride Thin-Film Piezoelectric MEMS Resonant Accelerometer

In this paper, we report a novel aluminum nitride (AlN) resonant micro-electromechanical systems (MEMS) accelerometer. The spring beams are T-shaped with two masses hanged at the end. This accelerometer is sensitive to the $z$ -axis acceleration due to a thin thickness. Different from the working mechanism of the ordinary MEMS resonant accelerometers, masses of this accelerometer are excited to resonate in-plane. In addition the stiffness of spring beams changes significantly when an out plane ( $z$ -axis) inertial force applied on the structure. Therefore, the resonant frequency of the structure will change with the out-plane inertial force. The resonant properties and sensitivities of this AlN accelerometer are simulated by COMSOL Multiphysics. The accelerometer is fabricated and tested. The size of the whole structure is $464\times 650\,\,\mu \text{m}^{2}$ . The resonant frequency is 16.10925 kHz at the static state. The sensing-axis sensitivity of this accelerometer is 1.11 Hz/g (i.e., 68.9 ppm/g) tested from −5g to +5g. The linearity of the accelerometer is 0.9954. The cross-axis sensitivities are 0.053 Hz/g ( $x$ -axis) and 0.048 Hz/g ( $y$ -axis) respectively. The temperature coefficient of frequency (TCF) of this accelerometer is 0.815 Hz/ °C (i.e., 50.6 ppm/°C), tested from 0 °C to 50 °C. [2019-0062]

Interface Stress for Bidirectional Frequency Tuning of Prebuckled Vanadium Dioxide MEMS Resonators

AbstractInterface stress between structural materials and thin film coatings has a significant influence on the resonant frequency of microelectromechanical system (MEMS) resonators. In this work, the axial stress on different types of buckled bridge MEMS resonator structures is controlled through the solid‐to‐solid phase transition of a VO2 thin film coating. The devices have identical dimensions, but different buckling orientations and profiles due to the combined effect of overetching and residual thermal stress mismatch. Thermal actuation is used to tune the resonant frequency of the device, but the changes in frequency are found to be dependent on the type of buckling for the device. Thermal actuation is achieved by applying an electrical current to integrated heaters, or by uniform substrate heating. Bidirectional tunability is found when substrate heating is used, while Joule heating shows a monotonic change in frequency. This phenomenon can be attributed to the transition in boundary conditions, where the turning points are indicated by the prominent changes in buckling amplitude. In addition, devices with opposite buckling orientations exhibit different tuning behaviors which can be explained by different bending moments induced by beam stress interface modification.

High Q 2D-length extension mode resonators for potential time–frequency applications

This paper presents recent advances on two dimensional length-extension mode (2D-LEM) quartz resonators providing high quality (Q) factor on resonances at a few MHz. The resonators have been collectively manufactured using one or two steps quartz deep reactive-ion etching (DRIE) processes. These resonators combine the intrinsic qualities of quartz in comparison to silicon (i.e. high Q factor, low temperature sensitivity and piezoelectricity) and the advantages of microelectromechanical systems (MEMS) resonators: small dimensions, low power consumption and collective processes. Samples vibrating at frequencies f of 2.2, 3 and 4.5 MHz have shown promising results with very high Q factor. Q factor as high as 180,000 for fundamental mode vibrating at 2.2 MHz and 89,000 for harmonic mode at 8.9 MHz were measured which lead to quality factor and resonance frequency products (Q·f) figure of merit near 1012 Hz at the state of the art for 2D-LEM quartz resonators and the higher Q factor measured for DRIE made quartz resonators. Two designs, several dimensions and two processes have been investigated. Two main limiting damping mechanisms were identified and one of them is strongly linked to the technological limits of the etching process.

Quality factor improvement of piezoelectric MEMS resonator by the conjunction of frame structure and phononic crystals

Recently, piezoelectric resonators fabricated by using MEMS (i.e., micro-electro-mechanical systems) technology have received increasing attention in a large and diverse set of applications, including sensors, filters and timing references. One of the critical challenges for the actual application of MEMS resonators is further improving their quality factors (Qs) to respond the urgent demand of performance enhancement. Herein, a strategy by employing suspended frame structure and phononic crystals (PnC) was proposed to reduce the energy dissipation, and thus AlN-on-SOI MEMS resonators with high Q were successfully implemented. The suspended frame structure isolates the mechanical vibration between the resonant body and the anchoring substrate, while PnC arrays serve as a frequency-selective reflector to reduce the energy leakage. The multi-physics finite-element-analysis (FEA) and the experimental comparison were employed to systematically investigate the underlying mechanisms of the energy dissipation reduction of the proposed strategy. The unloaded Qs (i.e., Qu) of proposed resonators achieved maximum 7.8-fold and 1.5-fold improvements compared with that of bared resonators and that of those with only suspended frame structure, respectively.

Energy Loss in a MEMS Disk Resonator Gyroscope.

Analysing and minimizing energy loss is crucial for high performance disk resonator gyroscopes (DRGs). Generally, the primary energy loss mechanism for high vacuum packaged microelectromechanical system (MEMS) resonators includes thermoelastic damping, anchor loss, and electronic damping. In this paper, the thermoelastic damping, anchor loss, and electronic damping for our DRG design are calculated by combining finite element analysis and theoretical derivation. Thermoelastic damping is the dominant energy loss mechanism and contributes over 90% of the total dissipated energy. Benefiting from a symmetrical structure, the anchor loss is low and can be neglected. However, the electronic damping determined by the testing circuit contributes 2.6%–9.6% when the bias voltage increases from 10 V to 20 V, which has a considerable impact on the total quality factor (Q). For comparison, the gyroscope is fabricated and seal-packaged with a measured maximum Q range of 141k to 132k when the bias voltage varies. In conclusion, thermoelastic damping and electronic damping essentially determine the Q of the DRG. Thus, optimizing the resonance structure and testing the circuit to reduce energy loss is prioritized for a high-performance DRG design.

Leveraging of MEMS Technologies for Optical Metamaterials Applications

AbstractTunable metamaterial devices have experienced explosive growth in the past decades, driving the traditional electromagnetic (EM) devices to evolve into diversified functionalities by manipulating EM properties such as amplitude, frequency, phase, polarization, and propagation direction. However, one of the bottlenecks of these rapidly developed metamaterials technologies is limited tunability caused by the intrinsic frequency‐dependent property of exotic tunable material. To overcome such limitation, the microelectromechanical system (MEMS) enabling micro/nanoscale manipulation is developed to actively control “meta‐atom” in terahertz and infrared region, which brings frequency‐scalable tunability and complementary metal‐oxide‐semiconductor‐compatible functional meta‐devices. Beyond tunability, novel chemical sensing platforms of molecular identification and dynamic monitoring of the biochemical process can be achieved by integrating micro/nanofluidics channels with metamaterial resonators. Additionally, incorporating metamaterial absorbers with MEMS resonators brings another research interest in MEMS zero‐power devices and radiation sensors. Furthermore, moving from 2D metasurfaces to 3D metamaterials, enhanced EM properties like novel resonance mode, giant chirality, and 3D manipulation reinforce the application in biochemical and physical sensors as well as functional meta‐devices, paving the way to realize multi‐functional sensing and signal processing on a hybrid smart‐sensor microsystem for booming healthcare, environmental monitoring, and the Internet of Things applications.

Dimensional dependence of the radiation damage in microelectromechanical system resonators

The effect of 10 keV x-ray and 255 nm UV radiation on MEMS resonators of different sizes were tested. The change in resonance frequency of the resonator during and after radiation was tracked, and a dimensional dependent resonance frequency reduction was observed for both x-ray and UV irradiation. The dimensional dependence of the resonance frequency shift indicates that surface effects are an important factor in both types of radiation damage. We propose two theoretical models that successfully explain the dimensional dependencies of x-ray and UV radiation damage. The x-ray model is based on hydrogen diffusion in silicon and the UV model is based on radiation induced charging of the native oxide. The models show that larger surface-to-volume ratio devices are more susceptible to radiation and need to be considered when scaling MEMS devices.

Design and fabrication of a microelectromechanical system resonator based on two orthogonal silicon beams with integrated mirror for monitoring in-plane magnetic field

We present a resonant magnetic field sensor based on microelectromechanical systems technology with optical detection. The sensor has single resonator composed of two orthogonal silicon beams (600 µm × 26 µm × 2 µm) with an integrated mirror (50 µm × 34 µm × 0.11 µm) and gold tracks (16 µm × 0.11 µm). The resonator is fabricated using silicon-on-insulator wafer in a simple bulk micromachining process. The sensor has easy performance that allows its oscillation in the first bending vibration mode through the Lorentz force for monitoring in-plane magnetic field. Analytical models are developed to predict first bending resonant frequency, quality factor, and displacements of the resonator. In addition, finite element method models are obtained to estimate the resonator performance. The results of the proposed analytical models agree well with those of the finite element method models. For alternating electrical current of 30 mA, the sensor has a theoretical linear response, a first bending resonant frequency of 43.8 kHz, a sensitivity of 46.1 µm T−1, and a power consumption close to 54 mW. The experimental resonant frequency of the sensor is 53 kHz. The proposed sensor could be used for monitoring in-plane magnetic field without a complex signal conditioning system.

An Analytical Study for Nonlinear Free and Forced Vibration of Electrostatically Actuated MEMS Resonators

This work aims to construct accurate and simple lower-order analytical approximation solutions for the free and forced vibration of electrostatically actuated micro-electro-mechanical system (MEMS) resonators, in which geometrical and material nonlinearities are induced by the mid-plane stretching, dynamic pull-in characteristics, electrostatic forces and other intrinsic properties. Due to the complexity of nonlinear MEMS systems, the quest of exact closed-form solutions for these problems is hardly obtained for system design and analysis, in particular for harmonically forced nonlinear systems. To examine the simplicity and effectiveness of the present analytical solutions, two illustrative cases are taken into consideration. First, the free vibration of a doubly clamped microbeam suspended on an electrode due to a suddenly applied DC voltage is considered. Based on the Euler–Bernoulli beam theory and the von Karman type nonlinear kinematics, the dynamic motion of the microbeam is further discretized by the Galerkin method to an autonomous system with general nonlinearity, which can be solved analytically by using the Newton harmonic balance method. In addition to large-amplitude free vibration, the primary resonance response of a doubly clamped microbeam driven by two symmetric electrodes is also investigated, in which the microbeam is actuated by a bias DC voltage and a harmonic AC voltage. Following the same decomposition approach, the governing equation of a harmonically forced beam model can be transformed to a nonautonomous system with odd nonlinearity only. Then, lower-order analytical approximation solutions are derived to analyze the steady-state resonance response of such a problem under a combination of various DC and AC voltage effects. Finally, the analytical approximation results of both cases are validated, and they are in good agreement with those obtained by the standard Runge–Kutta method.

Single-crystal diamond microelectromechanical resonator integrated with a magneto-strictive galfenol film for magnetic sensing

Single-crystal diamond (SCD) is a promising material for micro-electromechanical system (MEMS) devices to achieve high performance and reliability due to its prominent mechanical and physical properties. However, the application of SCD MEMS has not been practically achieved due to the lack of device concept for SCD MEMS. Here, the SCD MEMS resonator based magnetic sensor is successfully realized with integrating of a large magneto-strictive galfenol film on SCD mechanical resonator with high performance. It is concluded that SCD provides a suitable substrate for galfenol film with excellent magnetic properties. Along with the high-quality factor of the SCD MEMS resonator, a high magnetic field sensitivity of 4.83 Hz/mT and an extremely low detectable force of 2.14 × 10−12 N are achieved. Based on the experimental results, the estimated minimum detectable force, magnetic field and energy reach 1.76 × 10−14 N, 1.42 × 10−10 T and 8.4 × 10−29 J. The successful fabrication of SCD MEMS magnetic sensor provides a promising strategy for broadening the application of SCD MEMS with merits super to other ones, such as nanoscale to microscale spatial resolution, wide-range magnetic field sensing, high sensitivity, high temperature operation, and facile integration with CMOS.

Fabrication and characterization of zinc oxide piezoelectric MEMS resonator

Micro electromechanical system resonators (MEMS) are being explored to fulfil the demands of speedy wireless communication circuits, which may be utilized as oscillators and/or filters in radio transceivers. Micro resonators of radio frequency range are involved in variety of commercial applications as a replacement of traditional bulky devices due to their small size, high quality factor and most importantly CMOS compatibility. In this work, the design and fabrication of laterally vibrating contour mode MEMS resonator of global system for mobile communication range frequency is presented. Zinc oxide (ZnO), a green piezoelectric material has been used. The ZnO films can also be deposited at low temperature thus reduces thermal budget. An excellent biocompatible/biodegradable property of ZnO may also be useful in resonators used as the detector for mass/pressure sensing for medical applications. The performance of fabricated MEMS resonator is validated by numerical simulations and experimental electrical characterization. The results show that the resonator may be deployed for radio frequency communication. The process to fabricate the resonator has been developed and the devices have been fabricated by surface micromachining techniques on silicon wafer using two electron beam, two optical lithography processes and simple and cost-effective wet etching method used for ZnO etching over costly DRIE process.

Characteristics of phase delay in capacitive pick‐off circuits for MEMS resonators

In this Letter, the authors theoretically and experimentally investigate the characteristics of phase delay in capacitive pick-off circuits for micro-electromechanical systems (MEMS) resonators for the first time in history. An analytical model considering the phase delay for capacitive pick-off circuits is built up in theory. Only when they use their proposed novel modified double side-band demodulation configuration for resonators to extract motional amplitude and phase, the phase delay of pick-off circuits can be eliminated and extracted meanwhile in real time. Experiments show that the changing feature of phase delay primarily depends on temperature rather than drive frequency. Experimental results agree well with the theoretical model and reveal the relatively high correlation between the phase delay and temperature. This work provides a new indicator of temperature for resonators, using this phase delay of the pick-off interface, to make temperature compensation.

Direct Detection of Akhiezer Damping in a Silicon MEMS Resonator

Silicon Microelectromechanical Systems (MEMS) resonators have broad commercial applications for timing and inertial sensing. However, the performance of MEMS resonators is constrained by dissipation mechanisms, some of which are easily detected and well-understood, but some of which have never been directly observed. In this work, we present measurements of the quality factor, Q, for a family of single crystal silicon Lamé-mode resonators as a function of temperature, from 80–300 K. By comparing these Q measurements on resonators with variations in design, dimensions, and anchors, we have been able to show that gas damping, thermoelastic dissipation, and anchor damping are not significant dissipation mechanisms for these resonators. The measured f · Q product for these devices approaches 2 × 1013, which is consistent with the expected range for Akhiezer damping, and the dependence of Q on temperature and geometry is consistent with expectations for Akhiezer damping. These results thus provide the first clear, direct detection of Akhiezer dissipation in a MEMS resonator, which is widely considered to be the ultimate limit to Q in silicon MEMS devices.

Hydrogel Microelectromechanical System (MEMS) Resonators: Beyond Cost‐Effective Sensing Platform

AbstractMechanical resonators have been used for various applications including timing references, filters, accelerometers, and inertial sensors. Mostly, silicon‐based materials have been thought to be ideal considering robustness and stability and thus used to fabricate micro and nanoscale mechanical resonators. When enhanced sensitivity becomes more important than long‐term stability, materials repertoires other than silicon might be better suited. Herein, a novel manufacturing approach is proposed, which rapidly fabricates microelectromechanical system resonators with hydrogel by single UV exposure via dynamic mask and dry‐state “plugging out” sacrificial process where hydrogel structures are defined by spatially modulated UV light. For practical demonstrations, rectangular cantilevers and closed circular membranes are employed for humidity and pressure sensing applications, respectively. The cost‐effective fabrication route suggested herein not only enables rapid prototyping of suspended hydrogel structures outside a cleanroom, but also offers spatially tunable elastic modulus. Most remarkably, sensitivity enhancement resulting from high swelling rate and/or low elastic modulus exceeds stability deterioration, one of the major concerns for polymeric materials. Such exclusive beneficial features, yet demonstrated with any microfabrication materials and methods or their combinations, open a new avenue for photocurable polymeric materials to be used for specific applications as well as fundamental investigations.

Fabrication and Characterization of Carbon Nanotube Channel on the Electrodes for the Development of Resonant Gate Transistor

Background: New application can be obtained by the integration between carbon nanotube technology Nano-Electro-Mechanical system (NEMs) and Micro-Electro-Mechanical system (MEMs). The new application is a transistor, which uses carbon nanotube as the channel between the source and drain, while MEMs resonator bridges are used as suspending gates. Methods: preparation process of the electrodes (source/drain), carbon nanotube growth between electrodes and the characterization of carbon nanotube channel using Raman spectroscopy to study the time and temperature effect on the quality of Carbon Nanotube channel (CNT-channel), field emission scanning electron microscope/Energy Dispersive X-ray Analysis (FESEM) to study CNT structure. Results: The result shows the increasing of quality with the increase of both temperature and time. Carbon nanotubes exist between electrodes, and the growth direction follow ethanol direction from source to drain. However, the carbon nanotube growth randomly not aligned. The channel between electrodes were well etched, this has been approved by EDX result. Conclusion: The characterization confirmed the CNT presence between source and drain. Increasing the growth temperature from 700 to 725 °C enhanced the quality of growing CNTs, which is clearly shown from Raman information. While, increasing growth time decreased quality, but the effect not that significant. FESEM characterization shows that CNT growth follows the ethanol flow from source to drain randomly, while EDX result shows that the channel between the electrodes was well etched and clear.

An Experimental Study of Residual Stress Induced Modulation of Vibration Characteristics in 1-D MEMS Resonators

Abstract We experimentally study test structures of more than 100 microelectromechanical systems (MEMS) beam resonators with clamped ends and residual stresses varying from highly tensile to compressive loads beyond buckling and provide experimental verification of some key theoretical results reported in the literature. We compare the theoretically predicted natural frequencies over a large range of residual stresses that make the one-dimensional micro-mechanical resonators behave like beams or strings, depending on the relative magnitude of the effective axial load and the flexural stiffness. In particular, we measure the natural frequencies of the first four modes of buckled beams to show the drastically different behavior of beams under post critical buckling load from those under tension and, for the first time, present experimental evidence of invariance of even modes to compressive residual stresses in microscale beams. We then derive the sensitivity of these modes to residual stresses and discuss the consequences of such sensitivity on sensing applications along with recommendations on how to engineer the required level of residual stresses.

Reducing intrinsic energy dissipation in diamond-on-diamond mechanical resonators toward one million quality factor

This paper reports a batch fabrication of ultrahigh quality-factor single-crystal diamond microelectromechanical system resonators on diamond by using a smart-cut method and atomic scale etching of the defects within the resonators. As a result, the intrinsic energy dissipation induced by bulk defects is markedly reduced and quality factors over one million are realized, which can lead to the fabrication of highly sensitive physical and chemical sensors with high reliability.

Chaotic Behavior and Adaptive Control of the Arch MEMS Resonator With State Constraint and Sector Input

This paper mainly investigates adaptive control problem of the arch micro-electro-mechanical system (MEMS) resonator. To facilitate controller design, the power spectrum and bifurcation diagram are provided to judge whether the arch MEMS resonator is in chaotic oscillation or not under distributed electrostatic actuation. In the process of creating the controller, the Nussbaum function is employed to solve the issue of unknown control direction from the sector nonlinear input, and the barrier Lyapunov function is utilized to prevent constraint violation when the arch MEMS resonator faces physical limitations. Meanwhile a first-order filter is introduced to prevent repeated computation of the virtual control signal, and a Chebyshev neural network by merging an adaptive law is adopted to learn the behavior of unknown dynamics. Furthermore, an extended state observer which lifts the constraint against physical sensors is developed to estimate immeasurable states. Then, an adaptive control scheme fused with the Nussbaum function, filter and observer is created in the framework of backstepping without imposing any conditions on state variables and control direction of sector input. It is proved that all signals in the closed-loop system are bounded by selecting parameters appropriately. Finally, simulation verifications are presented to show the feasibility of the proposed method.

Vibration Identification of Folded-MEMS Comb Drive Resonators.

Natural frequency and frequency response are two important indicators for the performances of resonant microelectromechanical systems (MEMS) devices. This paper analytically and numerically investigates the vibration identification of the primary resonance of one type of folded-MEMS comb drive resonator. The governing equation of motion, considering structure and electrostatic nonlinearities, is firstly introduced. To overcome the shortcoming of frequency assumption in the literature, an improved theoretical solution procedure combined with the method of multiple scales and the homotopy concept is applied for primary resonance solutions in which frequency shift due to DC voltage is thoroughly considered. Through theoretical predictions and numerical results via the finite difference method and fourth-order Runge-Kutta simulation, we find that the primary frequency response actually includes low and high-energy branches when AC excitation is small enough. As AC excitation increases to a certain value, both branches intersect with each other. Then, based on the variation properties of frequency response branches, hardening and softening bending, and the ideal estimation of dynamic pull-in instability, a zoning diagram depicting extreme vibration amplitude versus DC voltage is then obtained that separates the dynamic response into five regions. Excellent agreements between the theoretical predictions and simulation results illustrate the effectiveness of the analyses.