Microelectromechanical Systems Resonators Research Articles

Microelectromechanical System Resonant Devices: A Guide for Design, Modeling and Testing

Microelectromechanical systems (MEMSs) are attracting increasing interest from the scientific community for the large variety of possible applications and for the continuous request from the market to improve performances, while keeping small dimensions and reduced costs. To be able to simulate a priori and in real time the dynamic response of resonant devices is then crucial to guide the mechanical design and to support the MEMSs industry. In this work, we propose a simplified modeling procedure able to reproduce the nonlinear dynamics of MEMS resonant devices of arbitrary geometry. We validate it through the fabrication and testing of a cantilever beam resonator functioning in the nonlinear regime and we employ it to design a ring resonator working in the linear regime. Despite the uncertainties of a fabrication process available in the university facility, we demonstrate the predictability of the model and the effectiveness of the proposed design procedure. The satisfactory agreement between numerical predictions and experimental data proves indeed the proposed a priori design tool based on reduced-order numerical models and opens the way to its practical applications in the MEMS industry.

Optical mode localized sensing in on-chip coupled microring resonators.

Mode localization, predicted in solid-state physics, has attracted great attention in coupled micro-electro-mechanical system (MEMS) resonators for ultrasensitive sensing. Compared to MEMS resonators, optical microresonators can achieve high-quality factors without the need for vacuum conditions. In this work, we extended the mode localization effect to integrated optical microresonators, and experimentally demonstrated, for the first time, mode localized sensing in coupled optical microresonators. The optical mode-localization sensor consists of two coupled microring resonators. Strong coupling results in the appearance of symmetric (S) and antisymmetric (AS) resonances. When external perturbations, like thermal perturbations, are applied to one microring, optical energy will be unevenly distributed in the two microrings, giving rise to changes in the extinction ratios (ERs) of the two resonances. The phenomenon is called optical mode localization. By changing the local thermal perturbation, the ERs of the S and AS resonance can be changed by 26.67 dB and 21.24 dB, respectively. Mode localized sensing with high sensitivity can be achieved by evaluating the variation of resonances' transmitted power. It is demonstrated that the variations of transmitted power at the AS and S resonances can be three orders of magnitude greater than the corresponding variation in the resonant wavelength for an induced perturbation in temperature. The experimental results agree well with the theoretical calculation. This work demonstrates the feasibility of achieving mode-localized sensing in integrated optical microresonators and has great potential to significantly expand the scope of mode-localized sensing applications.

A Hybrid Mechanism and Data‐Driven Approach for Predicting Fatigue Life of MEMS Devices by Physics‐Informed Neural Networks

ABSTRACTOur research group has focused on the long‐term performance degradation of micro‐electro‐mechanical systems (MEMS) devices under mechanical, thermal, and electrical stresses. We previously used physics‐based models for performance prediction, but the diverse materials, structures, and environmental conditions of MEMS devices affect their long‐term stability. Traditional physics‐based models struggle to account for these factors, limiting practical application. To address this, we employ data‐driven methods to include more variables. This paper introduces a hybrid approach combining physical principles with data‐driven techniques, specifically physics‐informed neural networks (PINN), to model and analyze performance degradation in MEMS resonators. We compare this method with previous physics‐based and data‐driven approaches (support vector machine and random forest) under identical conditions. The hybrid method not only provides accurate predictions but also considers more operating conditions, enhancing practical application.

Piezoelectrically and Capacitively Transduced Hybrid MEMS Resonator with Superior RF Performance and Enhanced Parasitic Mitigation by Low-Temperature Batch Fabrication

This study investigates a hybrid microelectromechanical system (MEMS) acoustic resonator through a hybrid approach to combine capacitive and piezoelectric transduction mechanisms, thus harnessing the advantages of both transducer technologies within a single device. By seamlessly integrating both piezoelectric and capacitive transducers, the newly designed hybrid resonators mitigate the limitations of capacitive and piezoelectric resonators. The unique hybrid configuration holds promise to significantly enhance overall device performance, particularly in terms of quality factor (Q-factor), insertion loss, and motional impedance. Moreover, the dual-transduction approach improves the signal-to-noise ratio and reduces feedthrough noise levels at higher frequencies. In this paper, the detailed design, complex fabrication processes, and thorough experimental validation are presented, demonstrating substantial performance enhancement potentials. A hybrid disk resonator with a single side-supporting anchor achieved an outstanding loaded Q-factor higher than 28,000 when operating under a capacitive drive and piezoelectric sense configuration. This is comparably higher than the measured Q-factor of 7600 for another disk resonator with two side-supporting anchors. The hybrid resonator exhibits a high Q-factor at its resonance frequency at 20 MHz, representing 2-fold improvement over the highest reported Q-factor for similar MEMS resonators in the literature. Also, the dual-transduction approach resulted in a more than 30 dB improvement in feedthrough suppression for devices with a 500 nm-thick ZnO layer, while hybrid resonators with a thicker piezoelectric layer of 1300 nm realized an even greater feedthrough suppression of more than 50 dB. The hybrid resonator integration strategy discussed offers an innovative solution for current and future advanced RF front-end applications, providing a versatile platform for future innovations in on-chip resonator technology. This work has the potential to lead to advancements in MEMS resonator technology, facilitating some significant improvements in multi-frequency and frequency agile RF applications through the original designs equipped with integrated capacitive and piezoelectric transduction mechanisms. The hybrid design also results in remarkable performance metrics, making it an ideal candidate for integrating next-generation wireless communication devices where size, cost, and energy efficiency are critical.

True Random Number Generator Based on Chaotic Oscillation of a Tunable Double-Well MEMS Resonator.

Chaotic systems have aroused interest across various scientific disciplines such as physics, biology, chemistry, and meteorology. The deterministic but unpredictable nature of a chaotic system is an ideal feature for random number generation. Microelectromechanical systems (MEMS) are a promising technology that effectively harnesses chaos, offering advantages such as a compact footprint, scalability, and low power consumption. This paper presents a true random number generator (TRNG) based on a double-well MEMS resonator integrated with an actuator and position sensor. The potential energy landscape of the proposed MEMS resonator is actively tunable with a direct current voltage. Experimental demonstrations of tunable bistability and chaotic resonance are reported in this paper. A chaotic time sequence is generated through piezoresistive sensing of the position of the MEMS resonator once it is driven into the chaotic regime. Subsequently, the randomness of the bit sequence, achieved by applying the exclusive or function to a digital chaotic sequence and its delayed differential is confirmed to meet the National Institute of Standards and Technology specifications. Moreover, the throughput and energy efficiency of the proposed MEMS-based TRNG can be adjusted from 50 kb s-1 and 0.44 pJ per bit at a low energy barrier to 167 kb s-1 and 6.74 pJ per bit at a high energy barrier by changing the MEMS device's potential well. The tunability of the proposed double-well MEMS resonator not only offers continuous adjustments in the energy efficiency of TNRG but also unveils vast and diverse research opportunities in analog computing, encryption, and secure communications.

Q-enhancement of piezoelectric micro-oven-controlled MEMS resonators using honeycomb lattice phononic crystals

In this paper, a two-dimensional (2-D) honeycomb lattice phononic crystal (PnC) based micro-oven with large bandgap is introduced to be integrated with piezoelectric microelectromechanical systems (MEMS) resonator to reduce anchor loss for timing applications. Finite element method (FEM) analysis and experimental measurement were performed to verify that the proposed PnC micro-oven design gives advantage in quality factor (Q). The measurement results demonstrate that the resonator with 2-D honeycomb lattice PnC micro-oven shows a repeatable 1.7 times improvement of average Q compared with the bare one. The resonator with micro-oven control was further measured for frequency stability. The proposed piezoelectric micro-oven controlled MEMS resonator achieves a frequency stability of less than ±10 ppb in a stable environment, which indicates promising potential for application in high-end timing field.

Resonant MEMS Accelerometer with Low Cross-Axis Sensitivity-Optimized Based on BP and NSGA-II Algorithms.

This article proposes a low cross-axis sensitivity resonant MEMS(Micro-Electro-Mechanical Systems) accelerometer that is optimized based on the BP and NSGA-II algorithms. When resonant accelerometers are used in seismic monitoring, automotive safety systems, and navigation applications, high immunity and low cross-axis sensitivity are required. To improve the high immunity of the accelerometer, a coupling structure is introduced. This structure effectively separates the symmetric and antisymmetric mode frequencies of the DETF resonator and prevents mode coupling. To obtain higher detection accuracy and low cross-axis sensitivity, a decoupling structure is introduced. To find the optimal dimensional parameters of the decoupled structure, the BP and NSGA-II algorithms are used to optimize the dimensional parameters of the decoupled structure. The optimized decoupled structure has an axial stiffness of 6032.21 N/m and a transverse stiffness of 6.29 N/m. The finite element analysis results show that the sensitivity of the accelerometer is 59.1 Hz/g (Y-axis) and 59 Hz/g (X-axis). Cross-axis sensitivity is 0.508% (Y-axis) and 0.339% (X-axis), which is significantly lower than most resonant accelerometers. The coupling structure and optimization method proposed in this paper provide a new solution for designing resonant accelerometers with high interference immunity and low cross-axis sensitivity.

Dynamical analysis and event-triggered adaptive finite-time prescribed performance control of the FO coupled MEMS resonators

This paper explores the dynamic behaviors and control method of weakly coupled micro-electro-mechanical system (MEMS) resonators with fractional-order (FO) dynamics. In the dynamics analysis session, Lyapunov exponents, bifurcation theory, and phase diagrams are used to analyze the effects of system parameters, coupling stiffness, and FO on the complex dynamical behaviors such as periodicity, pseudo-periodicity, and chaos oscillations. To suppress chaotic oscillations, a dynamic event-triggered finite-time prescribed performance controller is proposed. The unknown nonlinear functions are approximated through the interval type-3 fuzzy system (IT3FS) with an adaptive law. A novel finite-time prescribed performance function (finite-time PPF) is constructed to establish constrained boundaries for tracking errors. Compared with the existing PPFs, the proposed approach allows for more flexible setting of the convergence boundary before reaching steady-state. Subsequently, the constrained tracking errors are mapped to an unconstrained form using a nonlinear transformation function, whether the error constraint is symmetric or asymmetric. To circumvent the “explosion of complexity” arising from backstepping design process, a tracking differentiator (TD) is utilized. Additionally, to alleviate strain on communication resources, an event-triggered mechanism is devised to update control signals. The trigger threshold of the control signals can be adaptively adjusted based on the values of the Lyapunov function and the dynamic auxiliary variables. This control method guarantees finite-time convergence for all signals of the system. Finally, extensive simulations are performed to verify the effectiveness of the proposed algorithm.

Dependence of frequency-temperature stability on support tethers in dual-beam piezoresistive sensing MEMS resonators

This paper investigates the dependence of frequency stability over temperature on support tethers in dual-beam piezoresistive length-extensional (LE) mode microelectromechanical systems (MEMS) resonators. The designed dual-beam resonator consists of two identical single-crystal silicon beams, which are mechanically coupled and excited into vibrating in opposite phase to eliminate the inherent capacitive feedthrough signals. Both straight and folded beams are adopted as the support tethers for the reported dual-beam piezoresistive resonators. Quality factor (Q) and temperature distribution across the resonators with various support tethers are investigated by finite element method (FEM) analysis. It is found that folded beam tethers can reduce the support loss and hence improve the Q for the designed dual-beam resonator, while it comes with a tradeoff of high temperature rise on resonator body. The reported dual-beam resonator with straight beam tethers has low temperature rise on the resonator body, which is less sensitive to environmental temperature fluctuations, compared to its counterpart with folded beam tethers. Experimental results show that the fabricated dual-beam piezoresistive resonator with four straight beam tethers achieves a 0.5 ppm frequency shifts in the temperature-control chamber, which is nearly four times better than those with folded beam tethers.

Short-wavelength infrared light sensing using an electrostatic MEMS resonator integrated with a plasmonic optical absorber

Near-infrared light detectors are employed in various fields such as food inspection for spectroscopic measurements. Despite the fact that photodiodes made of compound semiconductors are used in conjunction with optical filters or monochromators for highly sensitive and wavelength-selective detection of near-infrared light, improvements in device size and cost are necessary for widespread application. Therefore, we propose the use of silicon microelectromechanical systems (MEMS) sensors. This study proposes a single-crystalline Si electrostatic MEMS resonator sensor that is integrated with a gold nanostructure near-infrared light absorber. The device utilizes the resonance frequency shift that occurs due to the thermal stress caused by the heat generated by the near-infrared light on the resonator. A gold nanostructure absorber is mounted on the resonator to enhance photothermal conversion efficiency, enabling the detection of near-infrared light with wavelength selectivity. We fabricated an Au nanostructure-mounted electrostatic transducer and evaluated its performance by measuring its resonance under near-infrared light irradiation. In a light intensity detection experiment, it was found that the relative resonant frequency shift increased linearly with the input in the range below 100 μW, which is consistent with the trend against the input heat. The minimum detection resolution of the light intensity was approximately 5 nW, and the minimum detectable intensity was 3.8 nW. The linear relationship between the optical absorption coefficient and the relative resonance frequency shift was clarified. An array of the devices with different absorption wavelength bands can be used to realize an ultra-compact spectroscopic analysis device without the need for traditional optical filters or monochromators.

Piezoelectric MEMS resonator with magnetic tip mass for energy harvesting from ultra-low intensity magnetic fields

This article addresses the limitation in the implementation of the Internet of Things (IoT) due to its energy dependence on batteries. The central focus of this work is the development and characterization of a magnetoelectric (ME) energy generator for IoT, which combines a piezoelectric microelectromechanical system (MEMS) with a magnetic mass to interact with ambient magnetic fields (MFs). The device's efficiency is validated through finite element modeling (FEM) simulations and electrical characterization. Its applicability in environments with residual magnetic fields, such as near common household appliances, highlights its viability. Specific results, such as a maximum generated power of 0.55 µW, corresponding to a power density of 9.19 µW/cm³, for a magnetic field strength of 5 µT, emphasize its ability to address energy challenges and promote the sustainable autonomy of IoT.

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.

Geometrically engineered mass sensing CMOS-MEMS resonators for temperature compensation via folded anchors

We present, for the first time, a single-layer plate resonator with specific folded anchors capable of reducing the temperature coefficient of frequency (TCF) by two orders of magnitude compared to straight beams. Folded anchors provide differential strain through either compressive or tensile thermal stress depending on the anchor design and, in turn, allow for positive and negative temperature-induced frequency change components. With a nominal 2 MHz frequency, we experimentally report a frequency shift of 2500 ppm over a temperature span from 0ºC to 90ºC using an optimal anchor folding aspect ratio. The frequency-temperature curve exhibits a turnover point at 27ºC granting a unique opportunity to, in a future application, complement this passive strategy with an active micro-oven for negligible TCF. The proposed approach main advantage relies on its mechanical design-level implementation exploiting a geometrical engineering strategy than can be directly extended to other topologies. This technique reveals as particularly suited for ultra-sensitive mass sensing applications based on microelectromechanical systems (MEMS) resonators where single-layer resonators are optimal thanks to their minimum footprint, attaining minimum mass structures. Results demonstrate that adoption of the proposed folded anchors strategy decreases effectively the thermally induced frequency fluctuations within the system intrinsic noise level.

Electrical actuation of single-crystal diamond MEMS resonators at high temperatures

Achieving efficient low-voltage actuation of microelectromechanical system (MEMS) resonators in high-temperature environments poses a difficult topic due to the thermal interference and the risk of high-temperature failure. In this work, the single-crystal diamond (SCD) resonators fabricated through the ion implantation-assisted lift-off (IAL) technique exhibit a SCD-on-SCD cantilever structure. We propose an electrical actuation system based on the electrostatic effect specifically designed for SCD MEMS resonators with a low radio-frequency amplitude of ∼ 100 mV. The SCD resonators demonstrate stable and efficient actuation across a wide temperature range, from room temperature to 500 °C. Importantly, the actuation voltage exhibits little impact on the resonance frequency and the Q factor of the resonator. The SCD resonator showcases exceptional thermal stability in resonance frequency, with a low temperature coefficient of frequency (TCF) below −12 ppm/°C up to 500 °C. The developed actuation scheme holds tremendous potential as a robust platform for realizing SCD MEMS devices, particularly in applications requiring high integration at high temperatures.

Theoretical modeling and experimental investigation of in-phase resonant MEMS mirrors with cascaded structures

This paper proposes an efficient nonlinear one-dimensional (1D) compact mass-damper-spring model to predict the dynamic response of electrostatic resonant micro-electro-mechanical system (MEMS) mirrors with cascaded structures. The time-dependent damping moment due to viscous shear and pressure drag is computed using semi-empirical analytical equations for comb-drive structures and device frames. Nonlinear electrostatic force induced by the comb drives is efficiently acquired based on the hybrid method. The optimized device is fabricated using MEMS fabrication processes based on a 4-inch silicon-on-insulator wafer. The proposed compact model with the measured key parameters from the fabricated device shows excellent capability to accurately predict nonlinear dynamic responses of the fabricated device, including parametric excitation and hysteretic frequency response, with an average error of less than 5%. In particular, our 1D model is three orders of magnitude faster than the conventional finite element method model (0.8 s versus 1 h), enabling efficient system-level optimization of the critical design parameters. Based on the parametric study, electrode gap distance and torsion spring width are found to be two critical design parameters and dimensional analysis is conducted for design optimization with scan angle enhancing from 16.8° to 24° compared with the first design.

Oxygen-termination effect on the surface energy dissipation in diamond MEMS

Single-crystal diamond (SCD) microelectromechanical systems (MEMS) resonators with lower energy dissipation and higher quality (Q) factors have always been pursued for the development of high-sensitivity and high signal-to-noise ratio (SNR) MEMS sensors. The intrinsic loss such as the crystal quality and extrinsic loss of clamping loss have been examined to improve the Q factors of SCD MEMS resonators. Nevertheless, the surface termination induced energy dissipation has rarely been known due to the lack of high crystal quality diamond resonators and in-situ characterization. Here we examine the effect of oxygen-termination on the surface energy dissipation of SCD cantilevers by in-situ heating these cantilevers in a high vacuum chamber. After thermal treatment of the cantilevers at 933 K, the Q factor of the cantilever is improved from 2.8x105 to 3.3x105 (i.e. the 120 μm-long). The resonance frequency increase confirms the desorption of surface adsorbates. Compared to silicon, on which a native solid-state oxide exists, the surface oxygen-termination induced loss in diamond MEMS is much smaller. The non-existence of native oxides on diamond surface is an obvious merit toward ultra-high Q factor MEMS resonators.

Multi-harmonic phononic frequency comb generation in capacitive CMOS-MEMS resonators

Phononic frequency combs (PFCs) have emerged as a pivotal technology in precision measurements and advanced signal processing, harnessing the power of discrete, evenly spaced frequency lines. Their expansion into the realm of microelectromechanical systems (MEMS) presents potential opportunities for enhanced control in various applications, from telecommunications to quantum computing. This work presents an experimental study on the generation of PFCs at the fundamental frequency and its higher harmonics in a complementary metal oxide semiconductor based electrostatic MEMS resonator measured under an open-loop configuration. The phenomenon is attributed to nonlinear mode coupling and 1:2 internal resonance between two eigenmodes and their harmonics when the resonator operates in nonlinear resonance. The experimental approach employs a combination of optical and electrical characterization techniques. This study, primarily experimental in nature, provides crucial insights into the behavior of PFCs in MEMS resonators, suggesting possible multi-harmonic internal resonance as the underlying mechanism. These findings contribute significantly to the field of MEMS research, offering potential applications in high-precision frequency control for telecommunications, sensor technology, and quantum computing.

Nonparametric identification of a MEMS resonator actuated by levitation forces

This work presents nonparametric identification of a Micro-Electro-Mechanical Systems (MEMS) beam subjected to a non-classical nonlinear electrostatic (levitation) force. The approach is based on the Restoring Force Surface method and the Chebyshev polynomials. The study examines the main challenges associated with the used approach as applied to small-scale systems, such as the inability to measure the restoring force and acceleration. In this work, we use a mix of analytical techniques, experimental data, and Lagrange polynomial interpolation to estimate the restoring forces of the system and its nonlinearities. The extracted results are compared with the measurements, which show excellent agreement. Results are shown for several cases of forcing strength (voltage loads). The results reveal for some cases quadratic terms for the velocity indicating nonlinear damping, which cannot be revealed using parametric identification methods with a priori assumed forms. It is shown that the extracted nonlinear model is robust enough to predict the dynamical behavior of the beam even when the voltage load is increased to nearly 300 % more than the one used for model identification. The presented approach can be applied to other micro and nano systems to identify their characteristics and reveal their nonlinear stiffness and damping parameters.

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.

One-to-two internal resonance in a micro-mechanical resonator with strong Duffing nonlinearity

This paper investigates the implementation of 1:2 internal resonance (InRes) in a clamped–clamped stepped beam resonator with a strong Duffing effect, focusing on its potential for frequency stabilization in micro-electro-mechanical systems (MEMS) resonators. InRes can arise in a nonlinear system of which mode frequencies are close to an integer ratio, facilitating the internal exchange of energy from an externally driven mode to an undriven mode. The presence of 1:2 InRes and Duffing hardening nonlinearity can result in frequency saturation phenomena, leading to a flat amplitude-frequency response range, which forms the basis for frequency stabilization. The stepped beam resonator design, combined with thermal frequency tuning, enables precise alteration of the frequency ratio between the second and third flexural modes required to achieve the desired 1:2 ratio for InRes. Experimental characterization and theoretical analysis revealed that frequency mismatch plays a significant role, with larger mismatch conditions leading to stronger energy exchange and a wider range of drive force for frequency saturation. The study highlights the frequency saturation mechanism utilizing 1:2 InRes and emphasizes the advantage of Duffing nonlinearity and larger intermodal frequency mismatch for broader frequency stabilization, providing valuable insights for the design and optimization of MEMS resonators.