Micromachined Resonators: A Review

Miniaturized Multi-Cantilever MEMS Resonators with Low Motional Impedance

Microelectromechanical system (MEMS) cantilever resonators suffer from high motional impedance (Rm). This paper investigates the use of mechanically coupled multi-cantilever piezoelectric MEMS resonators in the resolution of this issue. A double-sided actuating design, which utilizes a resonator with a 2.5 μm thick AlN film as the passive layer, is employed to reduce Rm. The results of experimental and finite element analysis (FEA) show agreement regarding single- to sextuple-cantilever resonators. Compared with a standalone cantilever resonator, the multi-cantilever resonator significantly reduces Rm; meanwhile, the high quality factor (Q) and effective electromechanical coupling coefficient (Kteff2) are maintained. The 30 μm wide quadruple-cantilever resonator achieves a resonance frequency (fs) of 55.8 kHz, a Q value of 10,300, and a series impedance (Rs) as low as 28.6 kΩ at a pressure of 0.02 Pa; meanwhile, the smaller size of this resonator compared to the existing multi-cantilever resonators is preserved. This represents a significant advancement in MEMS resonators for miniaturized ultra-low-power oscillator applications.

Feedthrough effect in MEMS gyroscopes and fully differential feedthrough cancellation method

In the operation of MEMS gyroscopes, the feedthrough signal is inevitably introduced through the feedthrough capacitance and significantly affects the performance of MEMS gyroscopes. The common feedthrough cancellation methods highly depend on the microfabrication process and the structural symmetry of MEMS gyroscopes, which cannot effectively eliminate the feedthrough signal. In order to solve this problem, a new feedthrough cancellation method based on a fully differential configuration is proposed in this paper. The influence of the feedthrough effect is analyzed by establishing an equivalent circuit model including the feedthrough capacitance and described by the admittance diagram. Different drive and detection configurations are compared for the problem of feedthrough mismatch on different paths. Based on the theoretical analysis, a fully differential feedthrough cancellation scheme combined with two inverse feedthrough cancellation circuits is proposed. The deviation of feedthrough signal caused by the asymmetry of two differential paths can be adjusted by the two inverse feedthrough cancellation circuits. The fully differential configuration can further increase the drive force and suppress the common mode errors. The experimental results indicate that the feedthrough signal is suppressed in a large degree by the designed feedthrough cancellation method. The feedthrough level is reduced by 50.53 dB, and the amplitude of the effective signal increases from 4.10 to 9.46 dB. The signal-to-noise ratio has an improvement of 212.48% than that before feedthrough cancellation. The proposed feedthrough cancellation method can significantly reduce the interference of feedthrough signals on the effective signal, effectively improving the signal quality of MEMS gyroscopes.

Multi-Material Radial Phononic Crystals to Improve the Quality Factor of Piezoelectric MEMS Resonators

In this paper, a multi-material radial phononic crystal (M-RPC) structure is proposed to reduce the anchor-point loss of piezoelectric micro-electro-mechanical system (MEMS) resonators and improve their quality factor. Compared with single-material phononic crystal structures, an M-RPC structure can reduce the strength damage at the anchor point of a resonator due to the etching of the substrate. The dispersion curve and frequency transmission response of the M-RPC structure were calculated by applying the finite element method, and it was shown that the M-RPC structure was more likely to produce a band-gap range with strong attenuation compared with a single-material radial phononic crystal (S-RPC) structure. Then, the effects of different metal-silicon combinations on the band gap of the M-RPC structures were studied, and we found that the largest band-gap range was produced by a Pt and Si combination, and the range was 84.1-118.3 MHz. Finally, the M-RPC structure was applied to a piezoelectric MEMS resonator. The results showed that the anchor quality factor of the M-RPC resonator was increased by 33.5 times compared with a conventional resonator, and the insertion loss was reduced by 53.6%. In addition, the loaded and unloaded quality factors of the M-RPC resonator were improved by 75.7% and 235.0%, respectively, and at the same time, there was no effect on the electromechanical coupling coefficient.

MEMS Electrostatically Driven Coupled Beam Filter Banks

MEMS bandpass filters based on electrostatically driven, mechanically coupled beams with in-plane motion have been demonstrated up to the VHF band. Filters higher than second order with parallel plate drives have inherent tuning difficulties, which may be resolved by adding mass-loaded beams to the ends of the array. These beams deflect for DC voltages, and thus allow synchronized electrostatic tuning, but do not respond to in-band AC voltages and hence do not interfere with dynamic synchronization. Additional out-of-band responses may be damped, leaving the desired response. The principle is extended here to close-packed banks of filters, with adjacent arrays sharing mass-loaded beams that localize modes to sub-arrays. The operating principles are explained using a lumped element model (LEM) of the equations of motion in terms of resonant modes and the reflection of acoustic waves at discontinuities. Performance is simulated using the LEM and verified using the more realistic stiffness matrix method (SMM) for banks of up to eight filters. Similar or dissimilar filters may be combined in a compact arrangement, and the method may be extended to higher order resonances and alternative coupled resonator systems.

A Review of Eigenmode and Frequency Control in Piezoelectric MEMS Resonators

Piezoelectric microelectromechanical systems (MEMS) resonators possess favorable properties, such as strong electromechanical coupling, high Q , and polarized linear transduction, making them ideal for various applications, including timing, sensing, and RF communication. However, due to process nonidealities and temperature variations, these resonators characteristics may deviate from their designed frequency and resonant eigenmode, requiring careful compensation for stable and precise operation. Furthermore, certain devices, such as gyroscopic resonators, have two eigenmodes that need to be adjusted for frequency proximity and cross-mode coupling. Therefore, mode-shape manipulation can also be important in piezoelectric resonators and will be another focus of this article. Techniques for frequency and eigenmode control are classified into device- or system-level tuning, trimming, and compensation. This article will compare and discuss the effectiveness of these techniques in specific applications to provide a comprehensive understanding of frequency and eigenmode control in piezoelectric MEMS resonators, aiding the development of advanced MEMS devices for diverse applications.

Reem-Shape Phononic Crystal for Q Anchor Enhancement of Thin-Film-Piezoelectric-on-Si MEMS Resonator

This paper proposes a reem-shaped phononic crystal for the performance enhancement of TPoS resonators. The proposed phononic crystal offers an ultra-wide acoustic band gap that prevents energy leakage through the supporting substrate upon its placement at the anchoring boundary, resulting in significant improvements in the resonator quality factor. Simulated results show reem-shape phononic crystals generate a band gap up to 175 MHz with a BG of 90% and enhance the anchor quality factor from 180,000 to 6,000,000 and the unloaded quality factor from 133,000 to 160,000, representing 33.3-fold and 1.2-fold improvements, respectively.

Lab-on-a-chip systems for cancer biomarker diagnosis

Lab-on-a-chip (LOC) or micro total analysis system is one of the microfluidic technologies defined as the adaptation, miniaturization, integration, and automation of analytical laboratory procedures into a single instrument or "chip". In this article, we review developments over the past five years in the application of LOC biosensors for the detection of different types of cancer. Microfluidics encompasses chemistry and biotechnology skills and has revolutionized healthcare diagnosis. Superior to traditional cell culture or animal models, microfluidic technology has made it possible to reconstruct functional units of organs on chips to study human diseases such as cancer. LOCs have found numerous biomedical applications over the past five years, including integrated bioassays, cell analysis, metabolomics, drug discovery and delivery systems, tissue and organ physiology and disease modeling, and personalized medicine. This review provides an overview of the latest developments in microfluidic-based cancer research, with pros, cons, and prospects.

Self-Excited Microcantilever with Higher Mode Using Band-Pass Filter

Microresonators have a variety of scientific and industrial applications. The measurement methods based on the natural frequency shift of a resonator have been studied for a wide range of applications, including the detection of the microscopic mass and measurements of viscosity and stiffness. A higher natural frequency of the resonator realizes an increase in the sensitivity and a higher-frequency response of the sensors. In the present study, by utilizing the resonance of a higher mode, we propose a method to produce the self-excited oscillation with a higher natural frequency without downsizing the resonator. We establish the feedback control signal for the self-excited oscillation using the band-pass filter so that the signal consists of only the frequency corresponding to the desired excitation mode. It results that careful position setting of the sensor for constructing a feedback signal, which is needed in the method based on the mode shape, is not necessary. By the theoretical analysis of the equations governing the dynamics of the resonator coupled with the band-pass filter, it is clarified that the self-excited oscillation is produced with the second mode. Furthermore, the validity of the proposed method is experimentally confirmed by an apparatus using a microcantilever.

Study of the Performance Enhancement of Sc-Doped AlN Super High Frequency Cross-Sectional Lamé Mode Resonators

The increasing use of mobile broadband requires new acoustic filtering technologies that can operate efficiently at frequencies above 6 GHz. Previous research has shown that AlN Super High Frequency (SHF) Cross-Sectional Lamé Mode resonators (CLMRs) can address this challenge, but their performance is limited by the piezoelectric strength of AlN. In this work, we explore the use of substitutional doping of Al in AlN with Sc to enhance the kt2 values of SHF CLMRs. Our results showed that the measured kt2·Qm product of Al72Sc28N CLMRs was four times greater than that of AlN CLMRs operating at the same frequency. Additionally, the measured fractional bandwidth (FWB) of Al72Sc28N 2nd order ladder filters was 4.13%, a fourfold improvement over AlN filters with the same design. We also discuss other aspects of the technology, such as power handling, losses, and spurious mode suppression, and identify potential areas for future research.

H-Shaped Radial Phononic Crystal for High-Quality Factor on Lamb Wave Resonators

In this paper, a novel H-shaped radial phononic crystal (H-RPC) structure is proposed to suppress the anchor loss of a Lamb wave resonator (LWR), which has an ultra-high frequency (UHF) and ultra-wideband gap characteristics. Compared to previous studies on phononic crystal (PC) structures aimed at suppressing anchor loss, the radial phononic crystal (RPC) structure is more suitable for suppressing the anchor loss of the LWR. By using the finite element method, through the research and analysis of the complex energy band and frequency response, it is found that the elastic wave can generate an ultra-wideband gap with a relative bandwidth of up to 80.2% in the UHF range when propagating in the H-RPC structure. Furthermore, the influence of geometric parameters on the ultra-wideband gap is analyzed. Then, the H-RPC structure is introduced into the LWR. Through the analysis of the resonant frequency, it is found that the LWR formed by the H-RPC structure can effectively reduce the vibration energy radiated by the anchor point. The anchor quality factor was increased by 505,560.4% compared with the conventional LWR. In addition, the analysis of the LWR under load shows that the LWR with the H-RPC structure can increase the load quality factor by 249.9% and reduce the insertion loss by 93.1%, while the electromechanical coupling coefficient is less affected.

Quality Factor Enhancement of Piezoelectric MEMS Resonator Using a Small Cross-Section Connection Phononic Crystal

Anchor loss is usually the most significant energy loss factor in Micro-Electro-Mechanical Systems (MEMS) resonators, which seriously hinders the application of MEMS resonators in wireless communication. This paper proposes a cross-section connection phononic crystal (SCC-PnC), which can be used for MEMS resonators of various overtone modes. First, using the finite element method to study the frequency characteristics and delay line of the SCC-PnC band, the SCC-PnC has an ultra-wide bandgap of 56.6-269.6 MHz. Next, the effects of the height h and the position h₁ of the structural parameters of the small cross-connected plate on the band gap are studied, and it is found that h is more sensitive to the width of the band gap. Further, the SCC-PnC was implanted into the piezoelectric MEMS resonator, and the admittance and insertion loss curves were obtained. The results show that when the arrangement of 4 × 7 SCC-PnC plates is adopted, the anchor quality factors of the third-order overtone, fifth-order overtone, and seventh-order overtone MEMS resonators are increased by 1656 times, 2027 times, and 16 times, respectively.

Imaging resonant micro-cantilever movement with ultrafast scanning electron microscopy

Here, we demonstrate ultrafast scanning electron microscopy (SEM) for making ultrafast movies of mechanical oscillators at resonance with nanoscale spatiotemporal resolution. Locking the laser excitation pulse sequence to the electron probe pulses allows for video framerates over 50 MHz, well above the detector bandwidth, while maintaining the electron beam resolution and depth of focus. The pulsed laser excitation is tuned to the oscillator resonance with a pulse frequency modulation scheme. We use an atomic force microscope cantilever as a model resonator, for which we show ultrafast real-space imaging of the first and even the 2 MHz second harmonic oscillation as well as verification of power and frequency response via the ultrafast movies series. We detect oscillation amplitudes as small as 20 nm and as large as 9 μm. Our implementation of ultrafast SEM for visualizing nanoscale oscillatory dynamics adds temporal resolution to the domain of SEM, providing new avenues for the characterization and development of devices based on micro- and nanoscale resonant motion.

Highly Sensitive Temperature Sensor Based on Coupled-Beam AlN-on-Si MEMS Resonators Operating in Out-of-Plane Flexural Vibration Modes

This paper reports a type of highly sensitive temperature sensor utilizing AlN-on-Si resonators with coupled-beam structures of double- and triple-ended-tuning-fork (D/TETF). For both resonators, the out-of-plane flexural mode is adopted as it favors the effect of thermal mismatch between the composite layers inherent to the AlN-on-Si structure and thus helps attain a large temperature coefficient of resonant frequency (TCF). The analytical model to calculate TCF values of D/TETF AlN-on-Si resonators is provided, which agrees well with the finite-element simulation and experimental results. The resonant temperature sensor is built by closing the loop of the AlN-on-Si resonator, a transimpedance amplifier, a low-pass filter, and a phase shifter to form an oscillator, the output frequency of which shifts proportionally to the ambient temperature. The measured sensitivities of the temperature sensors using D/TETF resonators are better than -1000 ppm/°C in the temperature range of 25°C~60°C, showing great potential to fulfill the on-chip temperature compensation scheme for cofabricated sensors.

Q-Factor Enhancement of Coupling Bragg and Local Resonance Band Gaps in Single-Phase Phononic Crystals for TPOS MEMS Resonator

This paper presents a type of single-phase double “I” hole phononic crystal (DIH-PnC) structure, which is formed by vertically intersecting double “I” holes. By using the finite element method, the complex energy band curve, special point mode shapes, and different delay lines were calculated. Numerical results showed that DIH-PnC yielded ultra-wide band gaps with strong attenuation. The formation mechanism is attributed to the Bragg-coupled local resonance mechanism. The effects of the pore width in DIH-PnC on the band gaps were further explored numerically. Significantly, as the pore width variable, the position of the local resonance natural frequency could be modulated, and this enabled the coupling between the local resonance and the Bragg mechanism. Subsequently, we introduced this DIH-PnC into the thin-film piezoelectric-on-silicon (TPOS) resonator. The results illustrated that the anchor loss quality factor (Qanc) of the DIH-PnC resonator was 20,425.1% higher than that of the conventional resonator and 3762.3% higher than the Qanc of the cross-like holey PnC resonator. In addition, the effect of periodic array numbers on Qanc was researched. When the Qanc reached 1.12 × 10⁶, the number of the period array in DIH-PnC only needed to be 1/6 compared with cross-like holey PnC. Adopting the PnC based on the coupling Bragg and local resonance band gaps had a good effect on improving the Qanc of the resonator.

A Review on Coupled Bulk Acoustic Wave MEMS Resonators

With the introduction of the working principle of coupled resonators, the coupled bulk acoustic wave (BAW) Micro-Electro-Mechanical System (MEMS) resonators have been attracting much attention. In this paper, coupled BAW MEMS resonators are discussed, including the coupling theory, the actuation and sensing theory, the transduction mechanism, and the applications. BAW MEMS resonators normally exhibit two types of vibration modes: lateral (in-plane) modes and flexural (out-of-plane) modes. Compared to flexural modes, lateral modes exhibit a higher stiffness with a higher operating frequency, resulting in a lower internal loss. Also, the lateral mode has a higher Q factor, as the fluid damping imposes less influence on the in-plane motion. The coupled BAW MEMS resonators in these two vibration modes are investigated in this work and their applications for sensing, timing, and frequency reference are also presented.

Research Progress of Graphene Nano-Electromechanical Resonant Sensors—A Review

Graphene nano-electromechanical resonant sensors have wide application in areas such as seawater desalination, new energy, biotechnology, and aerospace due to their small size, light weight, and high sensitivity and resolution. This review first introduces the physical and chemical properties of graphene and the research progress of four preparation processes of graphene. Next, the principle prototype of graphene resonators is analyzed, and three main methods for analyzing the vibration characteristics of a graphene resonant sheet are described: molecular structural mechanics, non-local elastic theory and molecular dynamics. Then, this paper reviews research on graphene resonator preparation, discussing the working mechanism and research status of the development of graphene resonant mass sensors, pressure sensors and inertial sensors. Finally, the difficulties in developing graphene nano-electromechanical resonant sensors are outlined and the future trend of these sensors is described.

Electrostatic-Fluid-Structure 3D Numerical Simulation of a MEMS Electrostatic Comb Resonator

The reliability and stability of MEMS electrostatic comb resonators have become bottlenecks in practical applications. However, there are few studies that comprehensively consider the nonlinear dynamic behavior characteristics of MEMS systems and devices in a coupled field so that the related simulation accuracy is low and cannot meet the needs of design applications. In this paper, to avoid the computational complexity and the uncertainty of the results of three-field direct coupling and take into the damping nonlinearity caused by coupled fields, a novel electrostatic-fluid-structure three-field indirect coupling method is proposed. Taking an actual microcomb resonant electric field sensor as an example, an electrostatic-fluid-structure multiphysics coupling 3D finite element simulation model is established. After considering the influence of nonlinear damping concerning the large displacement of the structure and the microscale effect, multifield coupling dynamics research is carried out using COMSOL software. The multiorder eigenmodes, resonant frequency, vibration amplitude, and the distribution of fluid load of the microresonator are calculated and analyzed. The simulated data of resonance frequency and displacement amplitude are compared with the measured data. The results show that the fluid load distribution of the microelectrostatic comb resonator along the thickness direction is high in the middle and low on both sides. The viscous damping of the sensor under atmospheric pressure is mainly composed of the incompressible flow damping of the comb teeth, which is an order of magnitude larger than those of other parts. Compared with the measured data, it can be concluded that the amplitude and resonance frequency of the microresonator considering the nonlinear damping force and residual thermal stress are close to the experimental values (amplitude error: 15.47%, resonance frequency error: 12.48%). This article provides a reference for studies on the dynamic characteristics of electrostatically driven MEMS devices.

Dual-Resonator-Based (DRB) and Multiple-Resonator-Based (MRB) MEMS Sensors: A Review

Single-resonator-based (SRB) sensors have thrived in many sensing applications. However, they cannot meet the high-sensitivity requirement of future high-end markets such as ultra-small mass sensors and ultra-low accelerometers, and are vulnerable to environmental influences. It is fortunate that the integration of dual or multiple resonators into a sensor has become an effective way to solve such issues. Studies have shown that dual-resonator-based (DRB) and multiple-resonator-based (MRB) MEMS sensors have the ability to reject environmental influences, and their sensitivity is tens or hundreds of times that of SRB sensors. Hence, it is worth understanding the state-of-the-art technology behind DRB and MRB MEMS sensors to promote their application in future high-end markets.

Inertial and viscous flywheel sensing of nanoparticles

Rotational dynamics often challenge physical intuition while enabling unique realizations, from the rotor of a gyroscope that maintains its orientation regardless of the outer gimbals, to a tennis racket that rotates around its handle when tossed face-up in the air. In the context of inertial sensing, which can measure mass with atomic precision, rotational dynamics are normally considered a complication hindering measurement interpretation. Here, we exploit the rotational dynamics of a microfluidic device to develop a modality in inertial sensing. Combining theory with experiments, we show that this modality measures the volume of a rigid particle while normally being insensitive to its density. Paradoxically, particle density only emerges when fluid viscosity becomes dominant over inertia. We explain this paradox via a viscosity-driven, hydrodynamic coupling between the fluid and the particle that activates the rotational inertia of the particle, converting it into a ‘viscous flywheel’. This modality now enables the simultaneous measurement of particle volume and mass in fluid, using a single, high-throughput measurement.

Balances for nanoparticles such as resonating fluid-filled cantilevers usually probe only mass through changes in oscillation frequency. Katsikis and Collis et al. tap information from previously ignored rotational motion to simultaneously measure particle mass and volume.

A Semi-Linear Elliptic Model for a Circular Membrane MEMS Device Considering the Effect of the Fringing Field

In this study, an accurate analytic semi-linear elliptic differential model for a circular membrane MEMS device, which considers the effect of the fringing field on the membrane curvature recovering, is presented. A novel algebraic condition, related to the membrane electromechanical properties, able to govern the uniqueness of the solution, is also demonstrated. Numerical results for the membrane profile, obtained by using the Shooting techniques, the Keller-Box scheme, and the III/IV Stage Lobatto IIIa formulas, have been carried out, and their performances have been compared. The convergence conditions, and the possible presence of ghost solutions, have been evaluated and discussed. Finally, a practical criterion for choosing the membrane material as a function of the MEMS specific application is presented.

A Real-Time Circuit Phase Delay Correction System for MEMS Vibratory Gyroscopes

With the development of the designing and manufacturing level for micro-electromechanical system (MEMS) gyroscopes, the control circuit system has become a key point to determine their internal performance. Nevertheless, the phase delay of electronic components may result in some serious hazards. This study described a real-time circuit phase delay correction system for MEMS vibratory gyroscopes. A detailed theoretical analysis was provided to clarify the influence of circuit phase delay on the in-phase and quadrature (IQ) coupling characteristics and the zero-rate output (ZRO) utilizing a force-to-rebalance (FTR) closed-loop detection and quadrature correction system. By deducing the relationship between the amplitude-frequency, the phase-frequency of the MEMS gyroscope, and the phase relationship of the whole control loop, a real-time correction system was proposed to automatically adjust the phase reference value of the phase-locked loop (PLL) and thus compensate for the real-time circuit phase delay. The experimental results showed that the correction system can accurately measure and compensate the circuit phase delay in real time. Furthermore, the unwanted IQ coupling can be eliminated and the ZRO was decreased by 755% to 0.095°/s. This correction system realized a small angle random walk of 0.978°/√h and a low bias instability of 9.458°/h together with a scale factor nonlinearity of 255 ppm at room temperature. The thermal drift of the ZRO was reduced to 0.0034°/s/°C at a temperature range from -20 to 70 °C.

Microcantilever: Dynamical Response for Mass Sensing and Fluid Characterization

A microcantilever is a suspended micro-scale beam structure supported at one end which can bend and/or vibrate when subjected to a load. Microcantilevers are one of the most fundamental miniaturized devices used in microelectromechanical systems and are ubiquitous in sensing, imaging, time reference, and biological/biomedical applications. They are typically built using micro and nanofabrication techniques derived from the microelectronics industry and can involve microelectronics-related materials, polymeric materials, and biological materials. This work presents a comprehensive review of the rich dynamical response of a microcantilever and how it has been used for measuring the mass and rheological properties of Newtonian/non-Newtonian fluids in real time, in ever-decreasing space and time scales, and with unprecedented resolution.

Q-Factor Enhancement of Thin-Film Piezoelectric-on-Silicon MEMS Resonator by Phononic Crystal-Reflector Composite Structure

Thin-film piezoelectric-on-silicon (TPoS) microelectromechanical (MEMS) resonators are required to have high Q-factor to offer satisfactory results in their application areas, such as oscillator, filter, and sensors. This paper proposed a phononic crystal (PnC)-reflector composite structure to improve the Q factor of TPoS resonators. A one-dimensional phononic crystal is designed and deployed on the tether aiming to suppress the acoustic leakage loss as the acoustic wave with frequency in the range of the PnC is not able to propagate through it, and a reflector is fixed on the anchoring boundaries to reflect the acoustic wave that lefts from the effect of the PnC. Several 10 MHz TPoS resonators are fabricated and tested from which the Q-factor of the proposed 10 MHz TPoS resonator which has PnC-reflector composite structure on the tether and anchoring boundaries achieved offers a loaded Q-factor of 4682 which is about a threefold improvement compared to that of the conventional resonator which is about 1570.

Characterization of Nano-Gravimetric-Detector Response and Application to Petroleum Fluids up to C34

A nano-gravimetric detector (NGD) for gas chromatography is based on a nanoelectromechanical array of adsorbent-coated resonating double clamped beams. NGD is a concentration-sensitive detector and its sensitivity is analyte-dependent based on the affinity of the analyte with the porous layer coated on the NEMS surface. This affinity is also strongly related to the NGD temperature (NGD working temperature can be dynamically set up from 40 to 220 °C), so the sensitivity can be tuned through temperature detector control. An adsorption-desorption model was set up to characterize the NGD response on a large set of n-alkanes from C₁₀ to C₂₂ at different NGD temperatures. For fast identification of petroleum mixture based on chromatogram fingerprint, a general strategy for NGD temperature program design was developed leading to a constant relative response factor between 0.96 and 1.03 for all the alkanes, and then chromatograms are very similar to those obtained with a flame ionization detector (FID). The analysis of a real petroleum fluid was also performed and compared to FID results: quantitative results obtained for all the analytes were satisfactory according to precision (<5%) and accuracy (average relative error = 4.3%). Based on such temperature control strategy, NGD sensitivity and the dynamic linear range can be adjusted and detection limits at a picogram level can be easily achieved for all n-alkanes.

Dominant Loss Mechanisms of Whispering Gallery Mode RF-MEMS Resonators with Wide Frequency Coverage

This work investigates the dominant energy dissipations of the multi-frequency whispering gallery mode (WGM) resonators to provide an insight into the loss mechanisms of the devices. An extensive theory for each loss source was established and experimentally testified. The squeezed film damping (SFD) is a major loss for all the WGMs at atmosphere, which is distinguished from traditional bulk acoustic wave (BAW) resonators where the high-order modes suffer less from the air damping. In vacuum, the SFD is negligible, and the frequency-dependent Akhiezer damping (AKE) has significant effects on different order modes. For low-order WGMs, the AKE is limited, and the anchor loss behaves as the dominant loss. For high-order modes with an extended nodal region, the anchor loss is reduced, and the AKE determines the Q values. Substantial Q enhancements over four times and an excellent f × Q product up to 6.36 × 1013 at 7 K were achieved.

Dissipation Analysis Methods and Q-Enhancement Strategies in Piezoelectric MEMS Laterally Vibrating Resonators: A Review

Over the last two decades, piezoelectric resonant sensors based on micro-electromechanical systems (MEMS) technologies have been extensively studied as such sensors offer several unique benefits, such as small form factor, high sensitivity, low noise performance and fabrication compatibility with mainstream integrated circuit technologies. One key challenge for piezoelectric MEMS resonant sensors is enhancing their quality factors (Qs) to improve the resolution of these resonant sensors. Apart from sensing applications, large values of Qs are also demanded when using piezoelectric MEMS resonators to build high-frequency oscillators and radio frequency (RF) filters due to the fact that high-Q MEMS resonators favor lowering close-to-carrier phase noise in oscillators and sharpening roll-off characteristics in RF filters. Pursuant to boosting Q, it is essential to elucidate the dominant dissipation mechanisms that set the Q of the resonator. Based upon these insights on dissipation, Q-enhancement strategies can then be designed to target and suppress the identified dominant losses. This paper provides a comprehensive review of the substantial progress that has been made during the last two decades for dissipation analysis methods and Q-enhancement strategies of piezoelectric MEMS laterally vibrating resonators.

A Novel High Q Lamé-Mode Bulk Resonator with Low Bias Voltage

This work reports a novel silicon on insulator (SOI)-based high quality factor (Q factor) Lamé-mode bulk resonator which can be driven into vibration by a bias voltage as low as 3 V. A SOI-based fabrication process was developed to produce the resonators with 70 nm air gaps, which have a high resonance frequency of 51.3 MHz and high Q factors over 8000 in air and over 30,000 in vacuum. The high Q values, nano-scale air gaps, and large electrode area greatly improve the capacitive transduction efficiency, which decreases the bias voltage for the high-stiffness bulk mode resonators with high Q. The resonator showed the nonlinear behavior. The proposed resonator can be applied to construct a wireless communication system with low power consumption and integrated circuit (IC) integration.

Analysis of the Thermoelastic Damping Effect in Electrostatically Actuated MEMS Resonators

An important aspect that must be considered when designing micro-electro-mechanical systems (MEMS) for all domains, including robotics, is the thermoelastic damping which occurs when the MEMS material is subjected to cyclic stress. This paper is focused on a model for the thermoelastic damping developed based on the generalized thermoelastic theory with the non-Fourier thermal conduction equation. The model was implemented in MATLAB and several simulations were performed. The theoretical results show a decrease in the deflection amplitude with the increase in time. The deflection amplitude decrease was validated by the experimental investigations, consisting of measuring the loss in amplitude and velocity of oscillations as a function of time. Moreover, this paper also presents the influence of the geometric dimensions on the mentioned decrease, as well as on the initial and final values of the amplitude for several polysilicon resonators investigated in this paper.

Technique and Circuit for Contactless Readout of Piezoelectric MEMS Resonator Sensors

A technique and electronic circuit for contactless electromagnetic interrogation of piezoelectric micro-electromechanical system (MEMS) resonator sensors are proposed. The adopted resonator is an aluminum-nitride (AlN) thin-film piezoelectric-on-silicon (TPoS) disk vibrating in radial contour mode at about 6.3 MHz. The MEMS resonator is operated in one-port configuration and it is connected to a spiral coil, forming the sensor unit. A proximate electronic interrogation unit is electromagnetically coupled through a readout coil to the sensor unit. The proposed technique exploits interleaved excitation and detection phases of the MEMS resonator. A tailored electronic circuit manages the periodic switching between the excitation phase, where it generates the excitation signal driving the readout coil, and the detection phase, where it senses the transient decaying response of the resonator by measuring through a high-impedance amplifier the voltage induced back across the readout coil. This approach advantageously ensures that the readout frequency of the MEMS resonator is first order independent of the interrogation distance between the readout and sensor coils. The reported experimental results show successful contactless readout of the MEMS resonator independently from the interrogation distance over a range of 12 mm, and the application as a resonant sensor for ambient temperature and as a resonant acoustic-load sensor to detect and track the deposition and evaporation processes of water microdroplets on the MEMS resonator surface.

A Microfluidic MEMS-Microbalance Platform With Minimized Acoustic Radiation in Liquid

In this article, the microfluidic channels that deliver liquid to a microscale thin-film piezoelectric-on-silicon (TPoS) gravimetric resonant sensor are incorporated into the backside of the silicon-on-insulator (SOI) wafer on which the resonator is fabricated. Specifically, a microwell is embedded at the bottom of the disk -shaped TPoS resonator, while a very thin layer of parylene covering the backside of the resonator and the microwell forms an isolation layer between the liquid and the top device-layer features. In this way, the liquid is in contact with the backside of the resonator, while the device-defining trenches and the electrical connections to the resonator stay clear, thus mitigating the acoustic energy loss and undesirable feedthroughs. The impact of the parylene layer thickness on a few symmetric ( S ) and antisymmetric ( A ) Lamb wave modes of the resonator is experimentally studied, and the performance of such modes in the liquid is characterized by filling the microwells through a PDMS-based microfluidic channel. The parylene layer, while marginally affecting the resonator in the air, is found to substantially enhance its performance in the liquid media. Strong resonance peaks with high quality factors ( Q ) are observed for the S modes, among which Q values above 400 are recorded for a specific mode named S (4, 2) (among the highest ever reported). This article can potentially facilitate the realization of highly stable and sensitive resonant mass sensors (i.e., microbalance) for real-time applications. Additionally, the effect of the acoustic energy radiation in the form of evanescent shear and longitudinal waves in liquid on the Q and resonance frequency of the disk resonators is experimentally validated.

AC/DC Fields Demodulation Methods of Resonant Electric Field Microsensor

Electric field microsensors have the advantages of a small size, a low power consumption, of avoiding wear, and of measuring both direct-current (DC) and alternating-current (AC) fields, which are especially suited to applications in power systems. However, previous reports were chiefly concerned with proposing new structures or improving the resolution, and there are no systematic studies on the signal characteristics of the microsensor output and the demodulation methods under different electric fields. In this paper, the use of an improved resonant microsensor with coplanar electrodes, and the signal characteristics under a DC field, power frequency field, and AC/DC hybrid fields were thoroughly analyzed respectively, and matching demodulation methods derived from synchronous detection were proposed. We theoretically obtained that the frequencies of the detectable electric fields should be less than half of the resonant frequency of the microsensor, and that the sensitivities of the microsensor were identical for AC/DC hybrid fields with different frequencies. Experiments were conducted to verify the proposed demodulation methods. Within electric field ranges of 0–667 kV/m, the uncertainties were 2.4% and 1.5% for the most common DC and 50 Hz power frequency fields, respectively. The frequency characteristic test results of the microsensor were in agreement with those of the theoretical analysis in the range of 0–1 kHz.

Oven-Controlled MEMS Oscillator with Integrated Micro-Evaporation Trimming

This study reports an oven-controlled microelectromechanical systems oscillator with integrated micro-evaporation trimming that achieves frequency stability over the industrial temperature range and permanent frequency trimming after vacuum packaging. The length-extensional-mode resonator is micro-oven controlled and doped degenerately with phosphorous to achieve a frequency instability of ±2.6 parts per million (ppm) in a temperature range of -40 to 85 °C. The micro-evaporators are bonded to the resonator, integrated face-to-face, and encapsulated in vacuum. During trimming, the micro-evaporators are heated electrically, and the aluminum layers on their surfaces are evaporated and deposited on the surface of the resonator that trims the resonant frequency of the resonator permanently. The impact of the frequency trimming on the temperature stability is very small. The temperature drift increases from ±2.6 ppm within the industrial temperature range before trimming to ±3.3 ppm after a permanent trimming of -426 ppm based on the local evaporation of Al. The trimming rate can be controlled by electric power. A resonator is coarse-trimmed by approximately -807 ppm with an evaporation power of 960 mW for 0.5 h, and fine-trimmed by approximately -815 ppm with an evaporation power of 456 mW for 1 h. Though the Q-factor decreases after trimming, a Q-factor of 304,240 is achieved after the trimming of -1442 ppm.

Non-Destructive Evaluation Device for Monitoring Fluid Viscosity

There is an increasing need for non-destructive, low-cost devices for real-time fluid viscosity monitoring. Therefore, in this study, a method based on structural health monitoring is adapted for monitoring fluid properties. A device is built such that an inexpensive and disposable viscosity probe be possible. The design incorporates a sensor/actuator pair using a piezoelectric material layered with copper/brass and capable of monitoring viscosity changes in low volume liquids (e.g., vacutainer vial). Experiments performed with the new device show a definite pattern of wave propagation in viscous solutions. A numerical model is built to investigate the wave propagation in the fluid. For experimental measurements, the sensor part of the device detects the generated pressure wave in fluid (e.g., air, water, glycerin) by the actuator part. The phase shift between the actuator and the sensor signals is then recorded and plotted for different concentrations of glycerin and water at room temperature. The results of this study show a direct correlation between the phase shift and varying viscosity in the ultrasonic frequency range from 6 to 9 MHz. The numerical simulation, performed utilizing acoustic modal and harmonic response analysis, results also demonstrate the same trend as the experimental results: a phase shift increases with the viscosity of the fluid.

Single particles as resonators for thermomechanical analysis

Thermal methods are indispensable for the characterization of most materials. However, the existing methods require bulk amounts for analysis and give an averaged response of a material. This can be especially challenging in a biomedical setting, where only very limited amounts of material are initially available. Nano- and microelectromechanical systems (NEMS/MEMS) offer the possibility of conducting thermal analysis on small amounts of materials in the nano-microgram range, but cleanroom fabricated resonators are required. Here, we report the use of single drug and collagen particles as micro mechanical resonators, thereby eliminating the need for cleanroom fabrication. Furthermore, the proposed method reveals additional thermal transitions that are undetected by standard thermal methods and provide the possibility of understanding fundamental changes in the mechanical properties of the materials during thermal cycling. This method is applicable to a variety of different materials and opens the door to fundamental mechanistic insights.

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.

Design and Development of a Disposable Lab-on-a-Chip for Prostate Cancer Detection

We have designed and fabricated a low-cost modular electrical and fluidic integration platform for microelectromechanical systems (MEMS) based biosensors, paving the way for a disposable, low-cost Lab-on-a-Chip. We demonstrate seamless integration using an additive manufacturing enabled "plug-and-play" platform that does not require permanent electronic or fluidic integration. This paper describes the fabrication steps and assembly of the method and highlights its advantages over the more traditional methods, such as `wire bonding' and `flip chip'. We also provide design guidelines for improved biosensing, taking transport and binding kinetics into consideration in the context of prostate cancer diagnosis. Our novel approach combined with the design guidelines, opens up new opportunities for low-cost disposable high-density MEMS-based lab-on-a-chips for biosensing applications.

Spider Web-Like Phononic Crystals for Piezoelectric MEMS Resonators to Reduce Acoustic Energy Dissipation

Phononic crystals (PnC) are a remarkable example of acoustic metamaterials with superior wave attenuation mechanisms for piezoelectric micro-electro-mechanical systems (MEMS) resonators to reduce the energy dissipation. Herein, a spider web-like PnC (SW-PnC) is proposed to sufficiently isolate the wave vibration. Finite-element analysis is performed to gain insight into the transmission property of finite PnC, and band characteristics by infinite periods. In comparison with the circle hole PnC at a similar bandgap, due to its already very lightweight PnC structure compared with previously reported PnCs, the proposed PnC offers a significantly lighter weight, smaller lattice constant, and greater energy leakage inhibition. More specifically, the resonator with the SW-PnC plate as the anchoring substrate exhibited a quality factor as high as 66569.7 at 75.82 MHz.

A Sub-mW 18-MHz MEMS Oscillator Based on a 98-dBΩ Adjustable Bandwidth Transimpedance Amplifier and a Lamé-Mode Resonator

This paper presents a microelectromechanical system (MEMS)-based oscillator based on a Lamé-mode capacitive micromachined resonator and a fully differential high-gain transimpedance amplifier (TIA). The proposed TIA is designed using TSMC 65 nm CMOS technology and consumes only 0.9 mA from a 1-V supply. The measured mid-band transimpedance gain is 98 dB Ω and the TIA features an adjustable bandwidth with a maximum bandwidth of 142 MHz for a parasitic capacitance C P of 4 pF. The measured input-referred current noise of the TIA at mid-band is below 15 pA/ Hz . The TIA is connected to a Lamé-mode resonator, and the oscillator performance in terms of phase noise and frequency stability is presented. The measured phase noise under vacuum is -120 dBc/Hz at a 1-kHz offset, while the phase noise floor reaches -127 dBc/Hz. The measured short-term stability of the MEMS-based oscillator is ±0.25 ppm.

Side-Supported Radial-Mode Thin-Film Piezoelectric-on-Silicon Disk Resonators

In this paper, anisotropy of single-crystalline silicon (SCS) is exploited to enable side-supported radial-mode thin-film piezoelectric-on-substrate (TPoS) disk resonators. In contrast to the case for isotropic material, it is demonstrated that the displacement of the disk periphery is not uniform for the radial-mode resonance in SCS disks. Specifically, for high-order harmonics, nodal points are formed on the edges, creating an opportunity for placing suspension tethers and enabling side-supported silicon disk resonators at the very high-frequency band with negligible anchor loss. In order to thoroughly study the effect of material properties and the tether location, anchor loss is simulated using a 3-D perfectly matched layer in COMSOL. Through modeling, it is shown that eighth-harmonic side-supported SCS disk resonators could potentially have orders of magnitude lower anchor loss in comparison to their nanocrystalline diamond (NCD) disk resonator counterparts given the tethers are aligned to the [100] crystalline plane of silicon. It is then experimentally demonstrated that in TPoS disk, resonators fabricated on an 8- [Formula: see text] silicon-on-insulator (SOI) wafer, unloaded quality factor improves from ~450 for the second-harmonic mode at 43 MHz to ~11500 for the eighth-harmonic mode at 196 MHz if tethers are aligned to [100] plane. The same trend is not observed for NCD disk resonators and SCS disk resonators with tethers aligned to [110] plane. Finally, the temperature coefficient of frequency is simulated and measured for the radial-mode disk resonators fabricated on the 8- [Formula: see text]-thick degenerately n-type doped SCS, and the TFC data are utilized to guarantee proper identification of the harmonic radial-mode resonance peaks among others.

Gas sensors based on mass-sensitive transducers part 1: transducers and receptors-basic understanding

The scientific interest in gas sensors is continuously increasing because of their environmental, medical, industrial, and domestic applications. This has resulted in an increasing number of investigations being reported in the literature and communicated at conferences. The present review, organized in two parts, addresses the peculiarities of gas sensors based on mass-sensitive transducers, starting with their structure and functionality and progressing to implementation and specific use. In this first part of the review, we discuss the constructional peculiarities and operation regions and the physical and chemical processes governing the reception and transduction functions and the way in which they influence the sensor sensing parameters/features. Scientific outcomes and trends in research into gas sensors based on mass sensitive transducers are also considered.

Utilization of 2:1 Internal Resonance in Microsystems

In this paper, the nonlinear mode coupling at 2:1 internal resonance has been studied both analytically and experimentally. A modified micro T-beam structure is proposed, and the equations of motion are developed using Lagrange's energy method. A two-variable expansion perturbation method is used to describe the nonlinear behavior of the system. It is shown that in a microresonator with 2:1 internal resonance, the low-frequency mode is autoparametrically excited after the excitation amplitude reaches a certain threshold. The effect of damping on the performance of the system is also investigated.

An Analytical Temperature-Dependent Design Model for Contour-Mode MEMS Resonators and Oscillators Verified by Measurements

The importance of micro-electromechanical systems (MEMS) for radio-frequency (RF) applications is rapidly growing. In RF mobile-communication systems, MEMS-based circuits enable a compact implementation, low power consumption and high RF performance, e.g., bulk-acoustic wave filters with low insertion loss and low noise or fast and reliable MEMS switches. However, the cross-hierarchical modelling of micro-electronic and micro-electromechanical constituents together in one multi-physical design process is still not as established as the design of integrated micro-electronic circuits, such as operational amplifiers. To close the gap between micro-electronics and micro-electromechanics, this paper presents an analytical approach towards the linear top-down design of MEMS resonators, based on their electrical specification, by the solution of the mechanical wave equation. In view of the central importance of thermal effects for the performance and stability of MEMS-based RF circuits, the temperature dependence was included in the model; the aim was to study the variations of the RF parameters of the resonators and to enable a temperature dependent MEMS oscillator simulation. The variations of the resonator parameters with respect to the ambient temperature were then verified by RF measurements in a vacuum chamber at temperatures between −35 ∘C and 85 ∘C. The systematic body of data revealed temperature coefficients of the resonant frequency between −26 ppm/K and −20 ppm/K, which are in good agreement with other data from the literature. Based on the MEMS resonator model derived, a MEMS oscillator was designed, simulated, and measured in a vacuum chamber yielding a measured temperature coefficient of the oscillation frequency of −26.3 ppm/K. The difference of the temperature coefficients of frequency of oscillator and resonator turned out to be mainly influenced by the limited Q-factor of the MEMS device. In both studies, the analytical model and the measurement showed very good agreement in terms of temperature dependence and the prediction of fabrication results of the resonators designed. This analytical modelling approach serves therefore as an important step towards the design and simulation of micro-electronics and micro-electromechanics in one uniform design process. Furthermore, temperature dependences of MEMS oscillators can now be studied by simulations instead of time-consuming and complex measurements.

Acceleration Sensitivity in Bulk-Extensional Mode, Silicon-Based MEMS Oscillators

Acceleration sensitivity in silicon bulk-extensional mode oscillators is studied in this work, and a correlation between the resonator alignment to different crystalline planes of silicon and the observed acceleration sensitivity is established. It is shown that the oscillator sensitivity to the applied vibration is significantly lower when the silicon-based lateral-extensional mode resonator is aligned to the <110> plane compared to when the same resonator is aligned to <100>. A finite element model is developed that is capable of predicting the resonance frequency variation when a distributed load (i.e., acceleration) is applied to the resonator. Using this model, the orientation-dependent nature of acceleration sensitivity is confirmed, and the effect of material nonlinearity on the acceleration sensitivity is also verified. A thin-film piezoelectric-on-substrate platform is chosen for the implementation of resonators. Approximately, one order of magnitude higher acceleration sensitivity is measured for oscillators built with a resonator aligned to the <100> plane versus those with a resonator aligned to the <110> plane (an average of ~5.66 × 10-8 (1/g) vs. ~3.66 × 10-9 (1/g), respectively, for resonators on a degenerately n-type doped silicon layer).

A Novel Single-Axis MEMS Tilt Sensor with a High Sensitivity in the Measurement Range from 0∘ to 360∘

In this paper, a novel single-axis MEMS tilt sensor is presented. It contains a hexagonal proof mass, six micro-lever force amplifiers and three double-ended-tuning fork (DETF) resonant strain gauges. The proof mass is placed in the center with the micro-levers and the DETFs radially arrayed around. The variation of gravity acceleration applied on the proof mass will result in frequency shifts of the DETFs. Angular tilt can be got by analyzing the frequency outputs. The structural design of the tilt sensor is optimized by finite element simulation and the device is microfabricated using a silicon-on-insulator process, followed by open-loop and closed-loop characterizations. Results show that the scale factor of such sensor is at least 11.53 Hz/degree. Minimum Allan deviation of the DETF oscillator is 220 ppb (parts per billion) of the resonant frequency for an 5 s integration time. Resolution of the tilt sensor is 0.002 ∘ in the whole measurement range from 0 ∘ to 360 ∘ .

System Modeling of a MEMS Vibratory Gyroscope and Integration to Circuit Simulation

Recently, consumer applications have dramatically created the demand for low-cost and compact gyroscopes. Therefore, on the basis of microelectromechanical systems (MEMS) technology, many gyroscopes have been developed and successfully commercialized. A MEMS gyroscope consists of a MEMS device and an electrical circuit for self-oscillation and angular-rate detection. Since the MEMS device and circuit are interactively related, the entire system should be analyzed together to design or test the gyroscope. In this study, a MEMS vibratory gyroscope is analyzed based on the system dynamic modeling; thus, it can be mathematically expressed and integrated into a circuit simulator. A behavioral simulation of the entire system was conducted to prove the self-oscillation and angular-rate detection and to determine the circuit parameters to be optimized. From the simulation, the operating characteristic according to the vacuum pressure and scale factor was obtained, which indicated similar trends compared with those of the experimental results. The simulation method presented in this paper can be generalized to a wide range of MEMS devices.

Design and Fabrication of Capacitive Silicon Nanomechanical Resonators with Selective Vibration of a High-Order Mode

This paper reports the design and fabrication of capacitive silicon nanomechanical resonators with the selective vibration of a high-order mode. Fixed-fixed beam capacitive silicon resonators have been successfully produced by the use of electron beam lithography, photolithography, deep reactive ion etching, and anodic bonding methods. All resonators with different vibration modes are designed to have the same resonant frequency for performance comparison. Measurement results show that higher-order mode capacitive silicon resonators can achieve lower insertion loss compared to that of lower-order mode capacitive silicon resonators. The motional resistance of the fourth mode vibration resonator is improved by 83%, 90%, and 93% over the third, second, and first mode vibration resonators, respectively.