Microelectromechanical Systems Resonators Research Articles

Linear Modeling and Control of Comb-Actuated Resonant MEMS Mirror With Nonlinear Dynamics

This article presents a novel method to derive and identify an accurate small perturbation model of a comb-actuated resonant microelectromechanical system (MEMS) mirror with highly nonlinear dynamics. Besides the nonlinear stiffness and damping, the comb-drives add nonlinearities due to their electrostatic nature and their effect on the dynamic mirror amplitude over frequency behavior. The proposed model is based on a period to period energy conservation and applies for most nonlinearities present in an oscillator such as MEMS mirrors. It is shown that for specific nominal operation points with square wave excitation, the small perturbation model is linear for a wide range. The full dynamics of the derived linear model are parametrized by three constants, that can be estimated by the phase locked loop (PLL), performing a proposed identification method only based on phase measurements. An analysis of control laws usually applied in a PLL provides important information for the proper design of controllers to meet the desired behavior for individual applications.

Comparison between Linear and Branched Polyethylenimine and Reduced Graphene Oxide Coatings as a Capture Layer for Micro Resonant CO2 Gas Concentration Sensors.

The comparison between potential coatings for the measurement of CO2 concentration through the frequency shift in micro-resonators is presented. The polymers evaluated are linear polyethylenimine, branched polyethylenimine and reduced graphene oxide (rGO) by microwave reduction with polyethylenimine. The characterization of the coatings was made by using 6 MHz gold-plated quartz crystals, and a proof-of-concept sensor is shown with a diaphragm electrostatic microelectromechanical systems (MEMS) resonator. The methods of producing the solutions of the polymers deposited onto the quartz crystals are presented. A CO2 concentration range from 0.05% to 1% was dissolved in air and humidity level were controlled and evaluated. Linear polyethylenimine showed superior performance with a reaction time obtained for stabilization after the concentration increase of 345 s, while the time for recovery was of 126 s, with a maximum frequency deviation of 33.6 Hz for an in-air CO2 concentration of 0.1%.

Ultra-low-noise TIA topology for MEMS gyroscope readout

This paper proposes a TIA topology that can be used in accelerometer and gyroscope systems. The proposed TIA topology considerably relaxes the trade-off among the transimpedance gain, bandwidth, and input referred current noise without increasing the power consumption. Furthermore, this paper presents a model for gyroscope microelectromechanical systems (MEMS) resonator that enables us, unlike prior works, to predict the resolution of the gyroscope system at the early stage of the design. In this model, the noise arising from driving loop blocks is compared with the noise of sense channel blocks. It has been illuminated that the noise of sense transimpedance amplifier (TIA) is the most influential in the resolution of the gyroscope system. To improve the resolution, the proposed TIA is employed in the sense channel of the gyroscope system. It enhances the resolution by about 57% compared with the conventional TIA employed in the sense channel. Measurement results of a discrete-element prototype also verify the performance improvement of the proposed TIA topology.

Design of Perforated Membrane for Low-Noise Capacitive MEMS Accelerometers

We propose a design method for a thick membrane with several thousand perforations suitable for low-noise capacitive micro-electro-mechanical systems (MEMS) accelerometers. Although we have already reported that a membrane with two-step perforations shows good noise performance, it is difficult to simulate mechanical noise using a conventional method because the large number of perforations complicates the membrane structure. In this work, we assumed that the number of perforations is infinite and that there are symmetric planes between them. This assumption greatly reduces computational complexity because the simulation model is simplified in the region around a perforation. We fabricated MEMS resonators with a two-step perforated membrane and evaluated the accuracy of the simulation results. The measured Q values of the fabricated resonators were in good agreement with the calculated results. Using this design method, we optimized the structure of a membrane with two-step perforations and fabricated capacitive MEMS accelerometers that showed excellent low-noise performance (less than 15 ng/Hz1/2) and low-power consumption (20 mW).

Fully-Differential TPoS Resonators Based on Dual Interdigital Electrodes for Feedthrough Suppression

As one of the core components of MEMS (i.e., micro-electro-mechanical systems), thin-film piezoelectric-on-silicon (TPoS) resonators experienced a blooming development in the past decades due to unique features such as a remarkable capability of integration for attractive applications of system-on-chip integrated timing references. However, the parasitic capacitive feedthrough poses a great challenge to electrical detection of resonance in a microscale silicon-based mechanical resonator. Herein, a fully-differential configuration of a TPoS MEMS resonator based on a novel structural design of dual interdigital electrodes is proposed to eliminate the negative effect of feedthrough. The fundamental principle of feedthrough suppression was comprehensively investigated by using FEA (i.e., finite-element analysis) modeling and electrical measurements of fabricated devices. It was shown that with the help of fully-differential configuration, the key parameter of SBR (i.e., signal-to-background ratio) was significantly enhanced by greatly suppressing the in-phase signal. The S-parameter measurement results further verified the effectiveness of this novel feedthrough suppression strategy, and the insertion loss and SBR of proposed TPoS resonators were improved to 4.27 dB and 42.47 dB, respectively.

Validating the Critical Point of Spontaneous Parametric Downconversion for Over 600 Scanning MEMS Micromirrors on Wafer Level

Sensors and actuators based on resonant micro-electro-mechanical systems (MEMS), such as scanning micro mirrors, are well-established in automotive and consumer products. As the areas of application broaden, the requirements for the MEMS are increasing. Devices outside of the performance specifications have to be rejected which is costly due to the high processing times of MEMS technologies. In particular, nonlinear system behavior is often found to cause unexpected device failure or performance issues. Thus, accurate simulation or rather system models which account for nonlinear sensor dynamics can not only increase process yield, but more importantly, lead to a comprehensive understanding of the underlying physics and to improved MEMS design. We have studied [1] the possibility of a rather drastic device failure induced by nonlinearities on the example of a resonant scanning MEMS micro mirror. On the level of a few selected chips, we have carefully measured the complex nonlinear system behavior and modeled it by a nonlinear mode-coupling phenomenon known as spontaneous parametric down-conversion (SPDC). The most intriguing feature of SPDC is the sudden change from a rather linear to a nonlinear system behavior at the critical oscillation amplitude. However, the threshold only lies within the range of the mirror's operational amplitude, if certain frequency resonance conditions regarding the mechanical modes are met. Thus, the critical amplitude strongly depends on the frequency spectrum of the MEMS design which in turn is largely influenced by fabrication imperfections. We validate the dependence of the critical amplitude on the resonance condition by measuring it for over 600 micro mirrors on wafer-level. Our work does not only validate the theory of SPDC with measurements on such a large scale, but also demonstrates modeling strategies which are essential for MEMS product design.

A 10 MHz thin-film piezoelectric-on-silicon MEMS resonator with T-shaped tethers for Q enhancement

Thin-film piezoelectric-on-silicon (TPoS) MEMS (i.e. micro-electro-mechanical system) resonators have attracted much attention due to its unique features, such as CMOS-compatible fabrication process, however, its applications require, in particular, the enhancement of quality factor (Q). Herein, a 10 MHz TPoS MEMS resonator with T-shaped tethers coupled with reflecting blocks was proposed. Finite-element analysis was employed for modeling the proposed TPoS resonators to investigate the underlying mechanism of Q enhancement by the introduction of T-shaped tethers and reflecting blocks. It was figured out that the combination of T-shaped tethers and reflecting blocks can significantly reduce the energy leakage through the anchor substrate by reflecting mechanical waves and trapping the energy. The measured results of fabricated TPoS resonators further verified the effectiveness of Q enhancement by the as-presented new design, and the insertion loss and the Q were improved to 3.27 dB and 1903, respectively.

Highly-Linear Magnet-Free Microelectromechanical Circulators

This paper reports the first demonstration of a magnet-free, high performance microelectromechanical system (MEMS) based circulator. An innovative circuit based on the commutation of MEMS resonators with high quality (Q) factor using RF switches is designed and implemented. Thanks to the high Q factor, a much smaller modulation frequency can be achieved compared to the previous demonstrations, reducing the power consumption and enabling the use of high power-handling switches. Furthermore, the MEMS resonators greatly reduce the required inductance value, guaranteeing much smaller form factor compared to the previous LC demonstrations. The demonstrated circulator shows broad BW (15 dB-IX BW = 34.7 MHz for an operational frequency around 2.5 GHz), low IL (4 dB), high IX (30 dB), high linearity (P1dB = 28 dBm; IIP3 = 40 dBm) and at the same time low power consumption, addressing several of the current limitations hindering the full development of magnet-free circulators.

Fabrication, electrical characterization and sub-ng mass resolution of sub-μm air-gap bulk mode MEMS mass sensors for the detection of airborne particles

In this study, we propose to realize high-performance inertial Micro-Electro-Mechanical Systems (MEMS) mass sensors by the thick oxide as a mask layer fabrication technique. This method enables to reduce the air-gap to sub-μm in capacitively transduced MEMS with optical lithography and has been used to fabricate high aspect ratio sub-μm air-gap bulk mode MEMS mass sensors. MEMS devices have been designed and fabricated with the gap size as small as ~400 nm for ~38 μm thick SOI-based resonators (~95:1). Due to the conical characteristic of the gap, the mean air-gap has also been estimated as ~868 nm with 46 μm depth, which results in ~ 53:1 aspect ratio for the silicon test wafers that have been treated under the same conditions with the SOI-based devices. COMSOL simulation results and fabricated MEMS resonators coherently show that MEMS devices exhibit Lamé mode at 4.099 MHz resonance frequency with the estimated quality factor around 20,000, and extensional mode at 4.467 MHz with the estimated quality factors around 18,000 in the air. The motional resistance has been estimated as small as 27.28 Ω for the Lamé mode operating at 40 V. In this study, two different bulk modes have been considered as sensitive and uniform mass sensors for the detection of airborne particles. Then, minimum mass measurement capability of both modes has been experimentally estimated as 0.51 ng and 0.47 ng for Lamé and extensional modes, respectively. The latter, a proof-of-concept mass measurement has been conducted to deduce the resonance frequency shifts of both modes upon an added mass. This work demonstrates optimization of the thick oxide mask layer fabrication technique and realization of high aspect ratio bulk-mode MEMS mass sensors.

Multimode excitations for complex multifunctional logic device

The simplicity and prospect of energy efficiency of microelectromechanical systems (MEMS) resonator-based computing devices have captivated considerable research interest in recent years. Hence, they are being explored for ultra-low power computing machines, which are currently needed for internet-of-things (IoT) applications. Recently, there have been successful demonstrations of fundamental logic gates. However, the realization of complex multifunctional logic devices that involve multi-input and multi-output lines are facing challenges, such as the interconnections between multiple resonators and the limited controllability of the operating frequency. In this study, we demonstrate a 1:2 Demux combinational logic device with improved energy efficiency using the multi vibration modes of a single MEMS resonator. The MEMS device consists of three connected in-plane microbeams in the form of a U-shape structure. The actuation and modulation are based on electrostatic forces. The device shows actuation energy of 0.082 fJ and 0.91 fJ for output 1 and output 2, respectively, and switching energy per logic operation of 11.01 pJ for output 1 and 5.31 pJ for output 2. This indicates 75% decrease in switching energy per logic operation in comparison with the previously reported values for electrostatically actuated MEMS resonator-based computing devices.

Narrowband Impedance Transformer With Extremely High Transformation Ratio of 200

This letter presents a hybrid narrowband radio frequency (RF) impedance transformer using an aluminum nitride (AlN) microelectromechanical system (MEMS) resonator and lumped elements. The hybrid transformer consists of an AlN Lamb wave resonator, a parallel inductor, and a set of three lumped-element networks on a printed circuit board (PCB). The AlN resonator and the parallel inductor form the narrowband response while the lumped element networks fulfill the high impedance transformation. The transformer has been theoretically predicted and experimentally shown to achieve a narrow fractional bandwidth (FBW) of 2.2% and an extremely high impedance transformation ratio (ITR) of 200.

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.