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.

The MEMS microphone is a representative device among the MEMS family, which has attracted substantial research interest, and those tailored for human voice have earned distinct success in commercialization. Although sustained development persists, challenges such as residual stress, environmental noise, and structural innovation are posed. To collect and summarize the recent advances in this subject, this paper presents a concise review concerning the transduction mechanism, diverse mechanical structure topologies, and effective methods of noise reduction for high-performance MEMS microphones with a dynamic range akin to the audible spectrum, aiming to provide a comprehensive and adequate analysis of this scope.

This article presents a mass sensor based on a 3-degree-of-freedom (DoF) mode localized piezoelectric bulk acoustic wave (BAW) resonator system operating in the contour extensional mode. It features a quality factor of $\sim$ 4200 under atmospheric pressure at a resonance frequency of $\sim$ 6.36 MHz. More than three orders of magnitude enhancement ( $\sim$ 1700 times) of the normalized mass sensitivity based on the amplitude ratio (AR) change were achieved compared to that based on the frequency shift. The mass resolution thereof was obtained as 1.2 pg (for the AR change output) and 0.727 pg (for the frequency shift output), respectively. Compared with the previously reported mass sensor based on coupled BAW resonators, the presented device achieved an enhanced performance in terms of both quality factor ( $\sim$ 2.37 times higher), stability ( $\sim$ 100 and $\sim$ 3.5 times better for the AR change and frequency shift), and mass resolution ( $\sim$ 307 and $\sim$ 2.97 times better for the AR change and frequency shift). Moreover, the stability of the 3-DoF system with the AR change output was enhanced since there was only a $\sim$ 1.65-fold difference in the mass resolution in terms of the frequency shift and AR change, compared to $\sim$ 170-fold in the previous study. Furthermore, the novel device operated with a Q-factor of $\sim$ 305 in deionized (DI) water, demonstrating the considerable potential of such devices for future sensing applications in a liquid environment.

In this work, the relationship between nonlinear effects and the signal-to-noise ratio of a resonator is analyzed and the impact of reducing nonlinear effects of the resonator on the performance of a resonant accelerometer is investigated. A theoretical framework is formulated to evaluate the dynamic range of the double clamped-clamped resonator. A reduction of the mechanical nonlinearity is achieved through an external electrostatic force, resulting in an enhancement of the dynamic range from 93.8 dB to 132.6 dB. Experimental findings indicate the nonlinear coefficient is reduced to 2.2% compared to an approach without nonlinearity compensation. The nonlinearity compensation demonstrates a 12.8 dB improvement in the signal-to-noise ratio of the resonator, leading to a 5.5-fold increase in resolution of the accelerometer and an extension of the dynamic range by 15 dB. The proposed technique enables the performance of resonant sensors to be further optimized. 2024-0107

This article for the first time introduces the blue-sideband excitation (BSE) scheme to two types of 2-degree-of-freedom (2-DoF) weakly coupled electrostatic resonant sensors, i.e., a 2-DoF electrostatically coupled resonating system with parallel suspension beams (Device 1) and a 2-DoF coupled double-ended tuning fork (DETF) resonant device (Device 2), boosting the functionality of the mode localization phenomena and ultimately achieving distinct performance upgradation. The amplitude ratio (AR) is hence adopted as the readout metric for the sensitivity characterization with respect to different external stiffness perturbations introduced by the capacitive transduction. Three paradigms of AR were implemented in this subject, namely, intermodal AR (IM-AR), interresonator AR (IR-AR), and interresonator-IM-AR (IRIM-AR), owing to the feature of simultaneous multiple-mode excitation of BSE. A comparison regarding the coupled resonant devices subject to the conventional drive scheme and the BSE was conducted, where the experimental results indicated that more than two orders of magnitude enhancement in sensitivity were achieved with the BSE scheme, along with the possibility of a pronounced $\sim$17 times improvement in the noise floor, as well as the capability of simultaneous multiple parameter extraction across different resonators and vibration modes within the coupled system. This work further verified the feasibility and effectiveness of the BSE scheme, demonstrating the potential of such a technique for sensing applications based on mode-localized resonant sensors, fostering ultrahigh performance augmentation.

This paper reports on a gas sensor based on two bulk acoustic wave (BAW) resonators electrically coupled with a tuneable capacitor. The weak coupling strength was tuned to its optimal value (achieving maximum sensitivity) by varying the capacitance (without complex filtering, a control circuit as required in the state of the art). A gas sensor was developed based on the electrically coupled BAW resonators by functionalizing one of the resonators with zeolitic imidazolate framework-8 (ZIF-8). It featured a quality (Q) factor of ~2.2 k in air and a resonance frequency of ~6.32 MHz. Such a simple coupling mechanism can be tuned and further extended to coupled resonators in other domains.