MEMS Oscillator Research Articles

Mini-review on periodic properties of MEMS oscillators

This paper features a survey of the periodic property of micro-electro-mechanical systems by the homotopy perturbation method, the variational iteration method, the variational theory, He’s frequency formulation, and Taylor series method. Fractal MEMS systems are also introduced, and future prospective is elucidated. The emphasis of this min-review article is put mainly on the developments in last decade, so the references, therefore, are not exhaustive.

Synchronization bandwidth enhancement induced by a parametrically excited oscillator

The synchronization phenomenon in nature has been utilized in sensing and timekeeping fields due to its numerous advantages, including amplitude and frequency stabilization, noise reduction, and sensitivity improvement. However, the limited synchronization bandwidth hinders its broader application, and few techniques have been explored to enhance this aspect. In this paper, we conducted theoretical and experimental studies on the unidirectional synchronization characteristics of a resonator with phase lock loop oscillation. A novel enhancement method for the synchronization bandwidth using a parametrically excited MEMS oscillator is proposed, which achieves a remarkably large synchronization bandwidth of 8.85 kHz, covering more than 94% of the hysteresis interval. Importantly, the proposed method exhibits significant potential for high-order synchronization and frequency stabilization compared to the conventional directly excited oscillator. These findings present an effective approach for expanding the synchronization bandwidth, which has promising applications in nonlinear sensing, fully mechanical frequency dividers, and high-precision time references.

Electrothermal Tunable MEMS Oscillators for MEMS-Based Reservoir Computing

Electrothermal Tunable MEMS Oscillators for MEMS-Based Reservoir Computing

Adaptive frequency-stabilization of MEMS oscillators using mode coupling

Microelectromechanical systems (MEMS) oscillators with high frequency stability hold significant potential for a myriad of applications across diverse fields. This letter delves into an adaptive frequency stabilization system designed to significantly improve the performance of MEMS oscillators. Our approach leverages the concept of mode coupling to dynamically adjust the oscillator’s frequency based on phase control, ensuring optimal stability under varying operating conditions. The MEMS oscillator comprises a nonlinear low-frequency resonator and a linear high-frequency resonator. Through mode coupling and phase control, the nonlinear resonator is harnessed to regulate the oscillation frequency of the linear resonator. Experimental results prove that by applying the proposed approach, the frequency stability of the MEMS oscillator is enhanced by nearly 700 times for long-term stability at 1000 s. Additionally, in the scenario with varying temperature, the system also effectively improves the frequency stability by over 1000 times at 802 s.

MEMS Huygens Clock Based on Synchronized Micromechanical Resonators

With the continuous miniaturization of electronic devices, microelectromechanical system (MEMS) oscillators that can be combined with integrated circuits have attracted increasing attention. This study reports a MEMS Huygens clock based on the synchronization principle, comprising two synchronized MEMS oscillators and a frequency compensation system. The MEMS Huygens clock improved short-time stability, improving the Allan deviation by a factor of 3.73 from 19.3 to 5.17 ppb at 1 s. A frequency compensation system based on the MEMS oscillator’s temperature-frequency characteristics was developed to compensate for the frequency shift of the MEMS Huygens clock by controlling the resonator current. This effectively improved the long-term stability of the oscillator, with the Allan deviation improving by 1.6343 × 105 times to 30.9 ppt at 6000 s. The power consumption for compensating both oscillators simultaneously is only 2.85 mW∙°C−1. Our comprehensive solution scheme provides a novel and precise engineering solution for achieving high-precision MEMS oscillators and extends synchronization applications in MEMS.

A Low Phase Jitter MEMS Oscillator with Centrally-Anchored Piezoelectric Resonator for Wide Temperature Range Real Time Clock Applications.

This paper describes prototype temperature compensated piezoelectric MEMS oscillators operating in the wide temperature range of -40 °C to 85 °C for RTC applications. The AlN-on-Si resonator is centrally anchored at one point and designed for low power operation with a wide frequency tuning range of 5000 ppm. The oscillators exhibit a stable sinusoidal output at about 497 kHz frequency for time keeping applications with an integrated phase jitter being 10× better than the best commercially available MEMS RTC oscillators for supplementary use in portable devices for clocking audio circuits. The measured oscillator performance remains relatively unchanged when comparing the wafer level packaged capped MEMS resonator with the uncapped one, showing great potential for a high performance low-power RTC oscillator.

A Low-Noise Piezoelectric MEMS Oscillator Based on a Flexural Mode Membrane Resonator Array Toward In-Air Resonant Sensors

A Low-Noise Piezoelectric MEMS Oscillator Based on a Flexural Mode Membrane Resonator Array Toward In-Air Resonant Sensors

The Oven-Controlled MEMS Oscillators in Timing and Sensing Applications: A Review

The Oven-Controlled MEMS Oscillators in Timing and Sensing Applications: A Review

A Wide-Dynamic Range (-40 °C to 180 °C) Active Wireless MEMS Temperature Sensor With 7m °C Sensitivity

We demonstrate a highly-accurate active wireless microelectromechanical (MEMS) temperature sensor with the largest reported dynamic range (-40°C to 180°C) among active MEMS temperature sensors. The sensor uses a 27.2 MHz high quality factor (Q > 3,200) AlN-on-Si thin-film piezoelectric-on-silicon (TPoS) MEMS resonator to enable highly accurate temperature sensing, with minimum sensitivity (S), better than 0.011 °C across this wide temperature range. The wireless sensor uses an innovative frequency shift keying (FSK) 900 MHz direct up-conversion transmitter. The transmitter uses frequency multipliers for up-conversion, obviating the need for a temperature-stable frequency reference clock, thereby preserving the temperature coefficient of frequency (TCF) of the resonator, and consequently the sensitivity of the sensor. The experimental results show a very high correlation (<0.03% error) between the TCF of the MEMS oscillator and that of the transmitter output signal, demonstrating the viability of the proposed direct up-conversion technique. A detailed analysis of the Allan variance for MEMS temperature sensors which can be used to design for a given minimum sensitivity, is also presented in the paper.

Self-excited MEMS Oscillator using an Electrostatic Cantilever

In this paper, we propose a new use of an electrostatic MEMS cantilever structure as a voltage-controlled oscillator (VCO). A cantilever made of plated gold is accompanied with a drive electrode to turn on the contact switch upon voltage application. The electrical interconnection is arranged to discharge the cantilever when it is brought into contact with the switch, thereby promptly losing the electrostatic force and opening the contact switch again. As a result, the electrostatic cantilever spontaneously repeats the electrostatic pull-in and release at a frequency determined by the DC level of the applied voltage. A metallic cantilever of 500 μm long, 8 μm wide, and 12 μm thick is experimentally confirmed to work as an VCO in the frequency range between 8.4 kHz and 10.7 kHz controlled by the DC voltage between 160V and 180V.

Performance Analysis of MEMS Based Oscillator for High Frequency Wireless Communication Systems

The frequency oscillator is a basic component found in many electrical, electronic, and communications circuits and systems. Oscillators come in a variety of shapes and sizes, depending on the frequency range employed in a given application. Some applications need oscillators that generate low frequencies and other applications need oscillators that generate extremely high and high frequencies. As a result of the expansion and speed of modern technologies, new oscillators appeared that operating at extremely high frequencies. Most wireless communication systems are constrained in their performance by the accuracy and stability of the reference frequency. Because of its compatibility with silicon, micro-electro-mechanical system (MEMS) is the preferred technology for circuit integration and power reduction. MEMS are a rapidly evolving area of advanced microelectronics. The integration of electrical and mechanical components at the micro size is referred to as a MEMS. MEMS based oscillators have demonstrated tremendous high frequency application potential in recent years. This is owing to their great characteristics such as small size, integration of CMOS IC technology, high frequency-quality factor product, low power consumption, and cheap batch manufacturing cost. This paper's primary objective is to describe the performance of MEMS oscillator technology in high-frequency applications, as well as to discuss the challenges of developing a new MEMS oscillator capable of operating at gigahertz frequencies.

Multi-State Reliability Analysis Based on General Wiener Degradation Process and Random Shock

A multi-state reliability analysis model suffering from a dependent competing failure process is developed in this study, where the soft failure is described by general nonlinearity random effect. Wiener degradation process with measurement error and the hard failure is caused by random shock. Considering that the shock process not only may cause abrupt damage but also can accelerate degradation, there are some correlations between soft failure and hard failure. Based on the proposed new model, the multi-state functions are obtained under the cumulative shock model and the extreme shock model, and the system state probabilities are given under the different degradation state points. The fatigue cracks growth data example and MEMS oscillator example are given to demonstrate the proposed new model. At last, some sensitivity analyses are given to illustrate the influence of parameters on the state probability and the system reliability.

Phase noise in a Duffing oscillator induced by quantum turbulence

We report a comprehensive investigation of the effects of quantum turbulence and quantized vorticity in superfluid $^{4}\mathrm{He}$ at ultralow temperatures on a nonlinear microelectromechanical systems (MEMS) resonator which is uniquely sensitive to fluctuations of quantum turbulence. We observe that the phase noise of the MEMS is significantly increased in the presence of turbulence, while the noise in the amplitude channel is negligible in comparison. We formulated a model based on a fluctuating number of vortices pinned on the device to explain the observed noise. We also present measurements of the noise statistics and power spectra, providing insight into the dissipation mechanism of vortices at the micrometer scale in the ultraquantum regime. The high degree of customizability of MEMS oscillators coupled with their sensitivity to a small number of vortices lays the foundation for a more complete understanding of the interaction between quantized vortices and oscillating structures, and also offers a window into the dynamics of single vortices and small-scale fluctuations of quantum turbulence.

Towards Portable MEMS Oscillators for Sensing Nanoparticles.

This paper reports on the design, and implementation of piezoelectric-on-silicon MEMS resonators installed within a portable experimental setup for sensing nanoparticles in a laboratory environment. MEMS oscillators with a center frequency of approximately 5.999 MHz are employed for sensing 50 nm size-selected silver nanoparticles generated in the laboratory. The same experimental setup is then assembled to sense indoor particles that are present in the laboratory environment. The challenges associated with particle deposition as a result of assembling the portable experimental setup is highlighted. Furthermore, the MEMS oscillators demonstrate that the total mass of silver nanoparticles deposited onto the MEMS resonator surface using the inertial impaction technique-based experimental setup is approximately 7.993 nanograms. The total indoor particle mass accumulated on the MEMS resonator surface is estimated to be approximately 1.732 nanograms and 26.9 picograms for two different runs. The frequency resolution of the MEMS oscillator is estimated to be approximately 32 ppb and, consequently, the minimum detectable particle mass is approximately 60 femtograms for a 9.2 s integration time.

High Resolution CMOS Frequency-to-digital Converter for a Fine Dust Sensor using a MEMS Resonator

A high resolution, low power CMOS oscillator and frequency-to-digital converter for a fine dust sensor using a MEMS resonator is proposed. The proposed frequency-to-digital converter is realized based on dual-loop hybrid delay-locked loop to distinguish fine frequency variations according to very small fine dust concentrations, and simultaneously applied binary and square search algorithms to obtain accurate digital codes indicating frequency changes. An oscillator and frequency-to-digital converter for a fine dust sensor is implemented using the 0.18-μm CMOS process. The core size of the fabricated MEMS oscillator and frequency-to-digital converter is 0.9 mm² and consumes about 16 mW of power at 1.8 V supply voltage. The proposed frequency-to-digital converter covers the input frequency range of 1.7 GHz to 2.3 GHz with 1 bit resolution of about 3 MHz.

Generalized Damping Model for MEMS Oscillators from Molecular to Viscous Flow Regime

In this study, we investigate the damping phenomena acting on piezoelectrically driven MEMS oscillators. Three different geometrical shapes of MEMS oscillators are presented, including cantilevers, bending oscillators, and paddle oscillators. An analytical model for their resonance frequencies is derived. The bending modes of these micro-oscillator structures are characterized regarding their resonance frequency and their quality factor as a function of the ambient pressure in a nitrogen atmosphere as well as the dependence on the distance to a neighboring plate representing a geometrical boundary (e.g., to the package or to the mounting). The investigations cover a pressure range from 10−3 mbar up to 900 mbar and a gap width from 150 µm to 3500 µm. Consequently, a Knudsen number range over six orders of magnitude from 100 to 10−4 is covered. The measurement data are evaluated with a generalized damping model consisting of four parts representing the individual damping mechanisms (intrinsic, molecular, transitional, and viscous). The evaluated parameters are analyzed as a function of the resonance frequency and the gap width. The data reveal an exponential growing saturation behavior, which is determined by two characteristic lengths, being correlated with the viscous and the thermal boundary layer thickness, respectively. This leads to an estimation of the strength and of the range of the damping effect just by calculating the boundary layer thicknesses given by the resonance frequency and the gas properties. From these results, we gain fundamental insights on the viscous and transitional damping mechanisms as well as on the intrinsic losses. In conclusion, a basic concept is provided to reduce the damping of micro-oscillator bending modes and thus increase the quality factor. Additionally, the results are supported by finite element simulations revealing the temperature and pressure distribution within the gap.

STUDIES ON PULL-IN INSTABILITY OF AN ELECTROSTATIC MEMS ACTUATOR: DYNAMICAL SYSTEM APPROACH

The pull-in instability of an electrostatic microstructures is a common undesirable phenomenon which implies the loss of reliability of microelectromechanical systems. It is important to better understand its mechanism and then to reduce the occurrence of such phenomenon. Our work is devoted to analyzing the pull-in instability of a typical electrostatic micro-electromechanical-system actuators with edge effects. The pull-in phenomenon and the dynamic threshold are examined via dynamical system approach and the qualitative theory of differential equations. Nonlinear interplays between the voltage and the initial positions are characterized, from which critical voltage values are identified. Those critical voltages play crucial roles in our analysis. Effects from other system parameters are also examined numerically. It turns out that most of the parameters involved in the MEMS oscillator have corresponding threshold values, beyond which the pull-in instability occurs.

A Simple Frequency Formulation for the Tangent Oscillator

The frequency of a nonlinear vibration system is nonlinearly related to its amplitude, and this relationship is critical in the design of a packaging system and a microelectromechanical system (MEMS). This paper proposes a straightforward frequency prediction method for nonlinear oscillators with arbitrary initial conditions. The tangent oscillator, the hyperbolic tangent oscillator, a singular oscillator, and a MEMS oscillator are chosen to elucidate the simple solving process. The results, when compared with those obtained by the homotopy perturbation method, exhibit a good agreement. This paper introduces a very convenient procedure for attaining quick and accurate insight into the vibration property of a nonlinear vibration system.

A 6.89-MHz 143-nW MEMS Oscillator Based on a 118-dBΩ Tunable Gain and Duty-Cycle CMOS TIA

This article presents a 6.89 MHz MEMS oscillator based on an ultra-low-power, low-noise, tunable gain/duty-cycle transimpedance amplifier (TIA) and a bulk Lamé-mode MEMS resonator that has a quality factor (Q) of 3.24 × 106. Self-cascoding and current-starving techniques are used in the TIA design to minimize the power consumption and tune the duty-cycle of the output signal. The TIA was designed and fabricated in TSMC 65 nm CMOS process technology. Its open-loop performance has been measured separately. It achieves a tunable gain between 107.9 dBΩ and 118.1 dBΩ while dissipating only 143 nW from a 1 V supply. The duty-cycle of the output waveform can be tuned from 23.25% to 79.03%. The TIA has been interfaced and wire bonded in a series-resonant oscillator configuration with the MEMS resonator and mounted in a small cavity standard package. The closed-loop performance of the whole oscillator has been experimentally measured. It exhibits a phase noise of −128.1 dBc/Hz and −133.7 dBc/Hz at 1 kHz and 1 MHz offsets, respectively.

A 5-pJ/Bit OOK Transmitter Using MEMS-Based RF Oscillator for IoT Application in 180-nm CMOS

An 800-MHz OOK transmitter for short-range Internet-of-Things (IoT) applications is presented in this letter. The OOK transmitter utilizes a microelectromechanical system (MEMS)-based RF oscillator for carrier frequency generation, leading to a hardware- and power-efficient architecture. The transmitter is implemented in a 180-nm CMOS process and delivers −12.4-dBm output power. The power consumption of the MEMS oscillator is only 0.24-mW with 126.3-dBc/Hz phase noise at 100-kHz offset and a figure-of-merit (FoM) of 210.5 dB due to the optimized high- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> aluminum nitride (AlN) piezoelectric MEMS resonator. The transmitter can provide a 120-Mb/s data rate of OOK modulation with an energy efficiency of 5 pJ/bit by directly switching ON/OFF the power amplifier (PA). The 175-ns startup time of the MEMS-based oscillator can support very heavy duty-cycle transmitter operation, leading to ultralow average power consumption of 50 nW.