Microelectromechanical Systems Resonators Research Articles

Five Low-Noise Stable Oscillators Referenced to the Same Multimode AlN/Si MEMS Resonator.

We report on the first experimental demonstration of five self-sustaining feedback oscillators referenced to a single multimode resonator, using piezoelectric aluminum nitride on silicon (AlN/Si) microelectromechanical systems (MEMS) technology. Integrated piezoelectric transduction enables efficient readout of five resonance modes of the same AlN/Si MEMS resonator, at 10MHz, 30MHz, 65MHz, 95MHz, and 233MHz with quality (Q) factors of 18600, 4350, 4230, 2630, and 2138, respectively. Five stable self-sustaining oscillators are built, each referenced to one of these high-Q modes, and their mode-dependent phase noise and frequency stability (Allan deviation) are measured and analyzed. The 10, 30, 65, 95 and 233MHz oscillators exhibit low phase noise of -116, -100, -105, -106 and -92dBc/Hz at 1kHz offset frequency, respectively. The 65MHz oscillator yields Allan deviation of 4×10-9 and 2×10-7 at 1s and 1000s averaging time, respectively. The 10MHz oscillator's low phase noise holds strong promise for clock and timing applications. The five oscillators' overall promising performance also suggests suitability for multimode resonant sensing and tracking. This work also elucidates mode dependency in oscillator noise and stability, one of the key attributes of mode-engineerable resonators.

A Micro-Oven Controlled Dual-Mode Piezoelectric MEMS Resonator With ± 190 ppb Stability Over −40 to 105 °C Temperature Range

This letter presents a dual-mode piezoelectric microelectromechanical system (MEMS) resonator with an in-chip micro-oven for resonator temperature control. The piezoelectric MEMS resonator simultaneously operates in width-extensional (WE) mode with a high temperature turnover point, and torsion-bending (TB) mode with a large temperature coefficient of frequency (TCF) based on a phase-locked loop based system. Exploiting the difference in frequency-temperature characteristics of these two modes, accurate temperature sensing and precise close-loop micro-oven heating control are achieved by phase locking the resonator at its turnover point temperature of WE mode. Measured real-time frequency stability of the reported micro-oven controlled MEMS resonator is ±190 ppb over an extended industrial temperature range of -40 °C to 105 °C, indicating potential applications in high-end timing field, such as macro base stations and instrumentations.

Terahertz Detectors Using Microelectromechanical System Resonators.

The doubly clamped microelectromechanical system (MEMS) beam resonators exhibit extremely high sensitivity to tiny changes in the resonance frequency owing to their high quality (Q-) factors, even at room temperature. Such a sensitive frequency-shift scheme is very attractive for fast and highly sensitive terahertz (THz) detection. The MEMS resonator absorbs THz radiation and induces a temperature rise, leading to a shift in its resonance frequency. This frequency shift is proportional to the amount of THz radiation absorbed by the resonator and can be detected and quantified, thereby allowing the THz radiation to be measured. In this review, we present an overview of the THz bolometer based on the doubly clamped MEMS beam resonators in the aspects of working principle, readout, detection speed, sensitivity, and attempts at improving the performance. This allows one to have a comprehensive view of such a novel THz detector.

Effects of Gamma Ray Radiation on the Performance of Microelectromechanical Resonators

While much radiation test data are available for metal‐oxide‐semiconductor (MOS) devices, research into the effects of radiation on microelectromechanical systems (MEMS) is in its relative infancy. Piezoelectrically transduced MEMS resonators have broad applications in signal processing, environmental monitoring, and navigation. Aluminum nitride (AlN), in particular, is an attractive piezoelectric because of its favorable fabrication characteristics and ease of integration into the complementary MOS (CMOS) manufacturing process. The utility of these devices in space and nuclear systems necessitates research into their performance in radiation environments. Resiliency and an established relationship between radiation dose and device behavior provide a critical tool for engineers in their design process. Multiple AlN‐based MEMS resonator designs are created and exposed the devices to 1 Mrad(Si) gamma irradiation from a Cobalt‐60 source while measuring scattering (S‐) parameters in situ. The experimental data are matched to a theoretical model to describe the change in frequency as a function of radiation‐induced displacement damage. It is demonstrated that the AlN‐based resonators are resilient against radiation‐induced charge‐trapping effects. Furthermore, a new method is presented of permanent frequency trimming MEMS resonators up to 30% of their bandwidth without modifying quality factor or motional resistance.

Effect of defects on Q factors of single-crystal diamond MEMS resonators

A resonator with a high Q factor is generally pursued in the single-crystal diamond (SCD) microelectromechanical system (MEMS) for high-performance sensors. In this report, we investigate the oxygen etching effect of SCD on the Q factors of the SCD resonators by using the Raman spectroscopy spatial mapping. We aim to establish the etch pit effect on the Q factors of the SCD MEMS resonators. The 2D Raman imaging technique discloses the dislocations and the local stress in the SCD MEMS resonators in microscale. It is observed that the full width half maximum (FWHM) of the Raman spectra of the SCD resonators has marked relationship with the Q factors of the SCD resonators. The etch pits resulted from the dislocations have weak influence on the Q factors of the SCD resonators.

Mechanically Coupled Single-Crystal Silicon MEMS Resonators for TCF Manipulation

This paper presents mechanically coupled single-crystal silicon (SCS) microelectromechanical system (MEMS) resonators for temperature coefficient of frequency (TCF) manipulation. The reported mechanically coupled square extensional (SE) mode resonator consists of two square plates coupled with a beam or a third square plate purposely vibrating in another bulk mode. The SE mode resonators and the coupled structure can be considered as two kinds of individual resonators with different TCFs. Within the specific dimensions of the coupled resonator, the resonant frequencies of the two components are assumed to be equal. Hence, the TCF of the mechanically coupled resonator could be manipulated by adjusting the sizes of the coupling parts. The design and fabrication of coupled resonators have been completed in a degenerate-doped (100) SCS wafer. Measurement results illustrate that the TCFs of the coupled resonators can be purposely manipulated by adjusting the volume and equivalent spring constant ratios of the individual resonators. The minimal measured frequency shift is roughly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm$</tex-math> </inline-formula> 10 ppm for an 18 MHz coupled SE mode resonator, over the entire industrial temperature range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$-$</tex-math> </inline-formula> 40 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> C to 85 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> C. This work highlights a novel and effective way to manipulate the TCFs of MEMS resonators via mechanical coupling. 2022-0197

A Micro-Acoustic Enhanced Low-Impedance Antenna System for IoT Wake-Up Receivers

In this work, we propose a passive radio frequency (RF) front-end tailored for wake-up receivers (WuRx) to be deployed in cellular IoT devices and wearables networks, featuring a low radiation resistance antenna and a high-Q matching network implemented with microacoustic resonators integrated to obtain a systematic higher node’s sensitivity at no cost in terms of power consumption. We show how these components can be co-designed to obtain high passive voltage gain, hardwarelevel blocker immunity, and increased resilience to integration parasitics, relaxing link budget for low-power IoT nodes. We report experimental validation of a PCB antenna with 2 dBi gain measured on an 11Ω input resistance at resonance, and an in-house fabricated Micro-Electro-Mechanical System (MEMS) thin-film aluminum nitride bulk acoustic resonator with a quality factor Q = 550 and a piezoelectric coupling coefficient k2 t =7%, hybridly integrated with a commercial off-the-shelf low-power WuRx circuit to benchmark the proposed RF front-end design at 850MHz. We demonstrate a passive voltage gain of 12 dB due to the MEMS resonator, and an additional 11 dB due to the proposed antenna design (for a total of an unprecedented 23 dB passive gain in this frequency range) leading to an over the air.61dBm minimum detectable input power and 23 dB blocker rejection.

A Novel Fault-Tolerant Super-Twisting Control Technique for Chaos Stabilization in Fractional-Order Arch MEMS Resonators

With the increasing demand for high-performance controllers in micro- and nano-systems, it is crucial to account for the effects of unexpected faults in control inputs during the design process. To tackle this challenge, we present a new approach that leverages an estimator-based super-twisting control technique that is capable of regulating chaos in fractional-order arch micro-electro-mechanical system (MEMS) resonators. We begin by studying the governing equation of a fractional-order arch MEMS resonator, followed by a thorough exploration of its chaotic properties. We then outline the design process for our novel control technique. The proposed technique takes into consideration the effects of uncertainty and faults in the control input by utilizing a finite time estimator and a super-twisting algorithm. The proposed technique addresses important challenges in the control of MEMS in real-world applications by providing fault tolerance, which enables the controller to withstand unexpected faults in the control input. We apply our controller to the fractional-order arch MEMS resonator, conducting numerical simulations. The numerical findings reveal that our proposed control technique is capable of stabilizing the system’s dynamics, even in the presence of a time-evolving fault in the control actuator. These results provide compelling evidence of the efficacy of our approach to control, despite the presence of an evolving fault.

Automatic Pico Laser Trimming System for Silicon MEMS Resonant Devices Based on Image Recognition

Laser trimming promises an increasing yield in microfabrication for the high performance Micro Electro-Mechanical Systems (MEMS) resonant devices by overcoming manufacturing tolerances and tuning sensors or actuators for certain operating conditions. How to achieve a high precision and efficiency trimming at low cost is the critical issue that the technical communities are most concerned. In this paper, we proposed an automatic laser trimming system for silicon MEMS devices based on a picosecond laser source and image recognition technique (IRT). Through the design of laser focusing optical path and coaxial imaging optical path, the observation of laser machining process is realized. A set of picosecond laser trimming parameters is determined by experiments, which enables a 4um width trench on the silicon resonator. Compared with the femtosecond laser trimming systems, the cost of the pico-laser system is reduced by more than 60%. The shape matching algorithm based on OpenCV and the chord-to-point distance accumulation (CPDA) algorithm for MEMS resonators image measurement solve the problem of inefficiency of manual trimming for complex resonators. A dual-mass tuning fork resonator is used to demonstrate the feasibility of the trimming approach. It is shown that the system realizes a fine-tuning (< 0.3Hz) of the resonant frequencies. The trimming time of a single device using the automatic trimming method is reduced from more than 1 hour manual trimming to less than 1 minute. Finally, the structural stiffness imbalance of tuning fork resonator caused by the manufacturing error is eliminated, which verifies the feasibility of the system.

A 0.82 μVrms ultralow 1/f noise bandgap reference for a MEMS gyroscope

High-precision microelectromechanical system (MEMS) gyroscopes are significant in many applications. Bias instability (BI) is an important parameter that indicates the performance of a MEMS gyroscope and is affected by the 1/f noise of the MEMS resonator and readout circuit. Since the bandgap reference (BGR) is an important block in the readout circuit, reducing its 1/f noise is key to improving a gyroscope’s BI. In a traditional BGR, the error amplifier is applied to provide a virtual short-circuit point, but it introduces the main low-frequency noise sources. This paper proposes an ultralow 1/f noise BGR by removing the error amplifier and applying an optimized circuit topology. In addition, a simplified but accurate noise model of the proposed BGR is obtained to optimize the BGR’s output noise performance. To verify this design, the proposed BGR has been implemented in a 180 nm CMOS process with a chip area of 545 × 423 μm. The experimental results show that the BGR’s output integrated noise from 0.1 to 10 Hz is 0.82 μV and the thermal noise is 35 nV/√Hz. Furthermore, bias stability tests of the MEMS gyroscope fabricated in our laboratory with the proposed BGR and some commercial BGRs are carried out. Statistical results show that reducing the BGR’s 1/f noise can nearly linearly improve the gyroscope’s BI.

Ultra-Tuning of nonlinear drumhead MEMS resonators by Electro-Thermoelastic buckling

Nonlinear micro-electro-mechanical systems (MEMS) resonators open new opportunities in sensing and signal manipulation compared to their linear counterparts by enabling frequency tuning and increased bandwidth. Here, we design, fabricate and study drumhead resonators exhibiting strongly nonlinear dynamics and develop a reduced order model (ROM) to capture their response accurately. The resonators undergo electrostatically-mediated thermoelastic buckling, which tunes their natural frequency from 4.7 to 11.3 MHz, a factor of 2.4× tunability. Moreover, the imposed buckling switches the nonlinearity of the resonators between purely stiffening, purely softening, and even softening-to-stiffening. Accessing these exotic dynamics requires precise control of the temperature and the DC electrostatic forces near the resonator’s critical-buckling point. To explain the observed tunability, we develop a one-dimensional physics-based ROM that predicts the linear and nonlinear response of the fundamental bending mode of these drumhead resonators. The ROM captures the dynamic effects of the internal stresses resulting from three sources: The residual stresses from the fabrication process, the mismatch in thermal expansion between the constituent layers, and lastly, the applied electrostatic forces. The novel ROM developed in this article not only replicates the observed tunability of linear (within 5.5 % error) and nonlinear responses even near the states of critical buckling but also provides insightful intuition on the interplay among the softening and stiffening, which is invaluable for the precise design of similar devices. This remarkable nonlinear and large tunability of the natural frequency are valuable features for on-chip acoustic devices in broad applications such as signal manipulation, filtering, and MEMS waveguides.

On‐chip Diamond MEMS Magnetic Sensing through Multifunctionalized Magnetostrictive Thin Film

AbstractElectrically integrable, high‐sensitivity, and high‐reliability magnetic sensors are not yet realized at high temperatures (500 °C). In this study, an integrated on‐chip single‐crystal diamond (SCD) micro‐electromechanical system (MEMS) magnetic transducer is demonstrated by coupling SCD with a large magnetostrictive FeGa film. The FeGa film is multifunctionalized to actuate the resonator, self‐sense the external magnetic field, and electrically readout the resonance signal. The on‐chip SCD MEMS transducer shows a high sensitivity of 3.2 Hz mT−1 from room temperature to 500 °C and a low noise level of 9.45 nT Hz−1/2 up to 300 °C. The minimum fluctuation of the resonance frequency is 1.9 × 10−6 at room temperature and 2.3 × 10−6 at 300 °C. An SCD MEMS resonator array with parallel electric readout is subsequently achieved, thus providing a basis for the development of magnetic image sensors. The present study facilitates the development of highly integrated on‐chip MEMS resonator transducers with high performance and high thermal stability.

A piezoelectric mechanically coupled Lamé mode resonator with ultra-high Q

A piezoelectrically actuated high quality factor (Q) mechanically coupled Lamé mode resonator based on a thin-film piezoelectric-on-silicon (TPoS) platform is demonstrated. The reported coupled resonator consists of two identical square plates of single-crystal silicon (SCS) coupled with a SCS beam having thin-film piezoelectric stacked layers on top. The coupled resonator is piezoelectrically driven into resonance, and the two square plates are excited into vibrations in a coupled Lamé mode through mechanical coupling. An impressive passive Q-enhancement is obtained by such a scheme based on mechanical coupling of two SCS square plates with a piezoelectrically transduced beam. A fabricated mechanically coupled Lamé mode resonator exhibits an ultra-high Q of 309 894 while still maintaining a moderate impedance (Rm) of 6652 Ω at its resonant frequency of 18.2838 MHz, corresponding to the record highest f-Q product of 5.67 × 1012 for TPoS resonators. The reported high Q microelectromechanical system (MEMS) resonator overcomes the inherent low-Q nature of piezoelectric MEMS resonators, indicating an application for providing a high-performance timing solution in a MEMS timing field.

Nanoscale imaging of super-high-frequency microelectromechanical resonators with femtometer sensitivity

Implementing microelectromechanical system (MEMS) resonators calls for detailed microscopic understanding of the devices, such as energy dissipation channels, spurious modes, and imperfections from microfabrication. Here, we report the nanoscale imaging of a freestanding super-high-frequency (3 – 30 GHz) lateral overtone bulk acoustic resonator with unprecedented spatial resolution and displacement sensitivity. Using transmission-mode microwave impedance microscopy, we have visualized mode profiles of individual overtones and analyzed higher-order transverse spurious modes and anchor loss. The integrated TMIM signals are in good agreement with the stored mechanical energy in the resonator. Quantitative analysis with finite-element modeling shows that the noise floor is equivalent to an in-plane displacement of 10 fm/√Hz at room temperatures, which can be further improved under cryogenic environments. Our work contributes to the design and characterization of MEMS resonators with better performance for telecommunication, sensing, and quantum information science applications.

Stabilization of Nonlinear Vibration of a Fractional-Order Arch MEMS Resonator Using a New Disturbance-Observer-Based Finite-Time Sliding Mode Control

This paper deals with chaos control in an arch microelectromechanical system (MEMS) from the fractional calculus perspective. There is a growing need for effective controllers in various technological fields, and it is important to consider disruptions, uncertainties, and control input limitations when designing a practical controller. To address this problem, we propose a novel disturbance-observer-based terminal sliding mode control technique for stabilizing and controlling chaos in a fractional-order arch MEMS resonator. The design of this technique takes into account uncertainty, disturbances, and control input saturation in the fractional-order system. The proposed control technique is practical for real-world applications because it includes control input saturation. The equation for a fractional-order arch MEMS resonator is presented, and its nonlinear vibration and chaotic behavior are studied. The design process for the proposed control technique is then described. The Lyapunov stability theorem is used to prove the finite-time convergence of the proposed controller and disturbance observer. The proposed controller is applied to the arch MEMS resonator, and numerical simulations are used to demonstrate its effectiveness and robustness for uncertain nonlinear systems. The results of these simulations clearly show the effectiveness of the proposed control technique.

Design and Fabrication of a Flexible Gravimetric Sensor Based on a Thin-Film Bulk Acoustic Wave Resonator.

Sensing systems are becoming less and less invasive. In this context, flexible materials offer new opportunities that are impossible to achieve with bulky and rigid chips. Standard silicon sensors cannot be adapted to curved shapes and are susceptible to big deformations, thus discouraging their use in wearable applications. Another step forward toward minimising the impacts of the sensors can be to avoid the use of cables and connectors by exploiting wireless transmissions at ultra-high frequencies (UHFs). Thin-film bulk acoustic wave resonators (FBARs) represent the most promising choice among all of the piezoelectric microelectromechanical system (MEMS) resonators for the climbing of radio frequencies. Accordingly, the fabrication of FBARs on flexible and wearable substrates represents a strategic step toward obtaining a new generation of highly sensitive wireless sensors. In this work, we propose the design and fabrication of a flexible gravimetric sensor based on an FBAR on a polymeric substrate. The resonator presents one of the highest electromechanical coupling factors in the category of flexible AlN-based FBARs, equal to 6%. Moreover, thanks to the polymeric support layer, the presence of membranes can be avoided, which leads to a faster and cheaper fabrication process and higher robustness of the structure. The mass sensitivity of the device was evaluated, obtaining a promising value of 23.31 ppm/pg. We strongly believe that these results can pave the way to a new class of wearable MEMS sensors that exploit ultra-high-frequency (UHF) transmissions.

A Compact Reconfigurable Resonator-Based Direct Current Sensing System

A compact and reconfigurable current readout system is presented that is based on microelectromechanical system (MEMS) resonators. The proposed system generates analog and digital outputs by electrothermally tuning the microbeam resonant frequency according to variations in the input current signal. A single resonator is utilized to generate the analog output, while a resonator array operating at different frequencies is utilized to generate a digital one-hot output. Experiments showed that the frequency shift is linearly proportional to the square of the current. The single resonator has a detection limit of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.16 ~\mu \text{A}$ </tex-math></inline-formula> , and the resonator array offers good static linearity with a maximum differential/integral non-linearity of 0.55/0.23 least significant bits. The single resonator is suitable for applications requiring high-resolution measurements. The proposed resonator sensing system has a small footprint, is compatible with large-scale integration, and provides considerable flexibility for reconfiguration.

Concepts and Key Technologies of Microelectromechanical Systems Resonators.

In this paper, the basic concepts of the equivalent model, vibration modes, and conduction mechanisms of MEMS resonators are described. By reviewing the existing representative results, the performance parameters and key technologies, such as quality factor, frequency accuracy, and temperature stability of MEMS resonators, are summarized. Finally, the development status, existing challenges and future trend of MEMS resonators are summarized. As a typical research field of vibration engineering, MEMS resonators have shown great potential to replace quartz resonators in timing, frequency, and resonant sensor applications. However, because of the limitations of practical applications, there are still many aspects of the MEMS resonators that could be improved. This paper aims to provide scientific and technical support for the improvement of MEMS resonators in timing, frequency, and resonant sensor applications.

Amplitude–frequency response of parametric resonance of electrostatically actuated MEMS clamped circular plate

This paper investigates the amplitude–frequency response of parametric resonance of a clamped elastic circular plate microelectromechanical system (MEMS) resonator above a parallel ground plate and under electrostatic actuation. Soft AC voltage with frequency near the first natural frequency of the plate is used. This results into parametric resonance. The system is assumed to be weakly nonlinear. Numerical and analytical methods are used to solve the reduced order models of the electrostatically actuated MEMS circular plate resonators in order to obtain the amplitude–frequency response of their parametric resonance. Seven Reduced Order Models (ROM) with one to seven modes of vibration (terms) have been developed and used in this investigation. ROM with one mode of vibration was solved using the Method of Multiple Scales (MMS) and predicted the existence of the resonance. ROMs with two to seven modes of vibration were solved using continuation and bifurcation software AUTO 07p to simulate and predict the amplitude–frequency response. These simulations showed that increasing the number of modes of vibration in the ROM produced better results. However, there is no significant difference between six and seven modes of vibration ROMs. Therefore, the ROM using seven modes of vibration was used in this research. This ROM was also numerically integrated to predict time responses of the MEMS plate. All methods showed an excellent agreement for amplitudes less than 0.5 of the gap. Only ROM using seven modes of vibrations had accurate predictions for all amplitudes, i.e. amplitudes between zero and the gap distance. The frequency response consists of two bifurcations, subcritical and supercritical. The effects of AC voltage and damping on the amplitude–frequency response are reported. Increasing the AC voltage results in shifting of the bifurcations to lower frequencies, subcritical significantly more than supercritical. Increasing the damping results in a narrower frequency range between the bifurcations.

Frequency combs in a MEMS resonator featuring 1:2 internal resonance: ab initio reduced order modelling and experimental validation

This paper is devoted to a detailed analysis of the appearance of frequency combs in the dynamics of a micro-electro-mechanical systems (MEMS) resonator featuring 1:2 internal resonance. To that purpose, both experiments and numerical predictions are reported and analysed to predict and follow the appearance of the phononic frequency comb arising as a quasi-periodic regime between two Neimark-Sacker bifurcations. Numerical predictions are based on a reduced-order model built thanks to an implicit condensation method, where both mechanical nonlinearities and electrostatic forces are taken into account. The reduced order model is able to predict a priori, i.e. without the need of experimental calibration of parameters, and in real time, i.e. by solving one or two degrees-of-freedom system of equations, the nonlinear behaviour of the MEMS resonator. Numerical predictions show a good agreement with experiments under different operating conditions, thus proving the great potentiality of the proposed simulation tool. In particular, the bifurcation points and frequency content of the frequency comb are carefully predicted by the model, and the main features of the periodic and quasi-periodic regimes are given with accuracy, underlining that the complex dynamics of such MEMS device is effectively driven by the characteristics of the 1:2 internal resonance.