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

Flexural-Mode Piezoelectric Resonators: Structure, Performance, and Emerging Applications in Physical Sensing Technology, Micropower Systems, and Biomedicine

Piezoelectric material-based devices have garnered considerable attention from scientists and engineers due to their unique physical characteristics, resulting in numerous intriguing and practical applications. Among these, flexural-mode piezoelectric resonators (FMPRs) are progressively gaining prominence due to their compact, precise, and efficient performance in diverse applications. FMPRs, resonators that utilize one- or two-dimensional piezoelectric materials as their resonant structure, vibrate in a flexural mode. The resonant properties of the resonator directly influence its performance, making in-depth research into the resonant characteristics of FMPRs practically significant for optimizing their design and enhancing their performance. With the swift advancement of micro-nano electronic technology, the application range of FMPRs continues to broaden. These resonators, representing a domain of piezoelectric material application in micro-nanoelectromechanical systems, have found extensive use in the field of physical sensing and are starting to be used in micropower systems and biomedicine. This paper reviews the structure, working principle, resonance characteristics, applications, and future prospects of FMPRs.

Ultrahigh-quality-factor micro- and nanomechanical resonators using dissipation dilution

Mechanical resonators are widely used in sensors, transducers and optomechanical systems, where mechanical dissipation sets the ultimate limit to performance. Over the past 15 years, the quality factors in strained mechanical resonators have increased by four orders of magnitude, surpassing the previous state of the art achieved in bulk crystalline resonators at room temperature and liquid helium temperatures. In this Review, we describe how these advances were made by leveraging 'dissipation dilution'-where dissipation is reduced through a combination of static tensile strain and geometric nonlinearity in dynamic strain. We then review the state of the art in strained nanomechanical resonators and discuss the potential for even higher quality factors in crystalline materials. Finally, we detail current and future applications of dissipation-diluted mechanical resonators.

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.

Nonconventional Tether Structure for Quality Factor Enhancement of Thin-Film-Piezoelectric-on-Si MEMS Resonator

This article presents a new design of supporting tethers through the concept of force distribution. The transmitted force applied on tethers will be distributed on the new tether design area, resulting in low acoustic energy transferred to anchor boundaries and stored energy enhancement. This technique achieves an anchor quality factor of 175,000 compared to 58,000 obtained from the conventional tether design, representing a three-fold enhancement. Furthermore, the unloaded quality factor of the proposed design improved from 23,750 to 27,442, representing a 1.2-fold improvement.

Investigation on Quasi-Lamb Wave Modes in AlN-on-Si MEMS Resonators

Aluminum nitride (AlN)-on-Si MEMS resonators operating in Lamb wave modes have found wide applications for physical sensing and frequency generation. Due to the inherent layered structure, the strain distributions of Lamb wave modes become distorted in certain cases, which could benefit its potential application for surface physical sensing. This article investigates the strain distributions of fundamental and 1st-order Lamb wave modes (i.e., S0, A0, S1 , and A1 modes) associated with their piezoelectric transductions in a group of AlN-on-Si resonators. The devices were designed with notable changes in normalized wavenumber resulting in resonant frequencies ranging from 50 to 500 MHz. It is shown that the strain distributions of four Lamb wave modes vary quite differently as normalized wavenumber changes. In particular, it is found that the strain energy of the A1 -mode resonator tends to concentrate on the top surface of the acoustic cavity as the normalized wavenumber increases, while that of the S0 -mode device becomes more confined in the central area. By electrically characterizing the designed devices in four Lamb wave modes, the effects of vibration mode distortion on resonant frequency and piezoelectric transduction were analyzed and compared. It is shown that designing A1 -mode AlN-on-Si resonator with identical acoustic wavelength and device thickness benefits its surface strain concentration as well as piezoelectric transduction, which are both demanded for surface physical sensing. We herein demonstrate a 500-MHz A1 -mode AlN-on-Si resonator with a decent unloaded quality factor ( [Formula: see text]) and low motional resistance ( [Formula: see text]) at atmospheric pressure.

A GHz Silicon-Based Width Extensional Mode MEMS Resonator with Q over 10,000

This work presents a silicon-based capacitively transduced width extensional mode (WEM) MEMS rectangular plate resonator with quality factor (Q) of over 10,000 at a frequency of greater than 1 GHz. The Q value, determined by various loss mechanisms, was analyzed and quantified via numerical calculation and simulation. The energy loss of high order WEMs is dominated by anchor loss and phonon-phonon interaction dissipation (PPID). High-order resonators possess high effective stiffness, resulting in large motional impedance. To suppress anchor loss and reduce motional impedance, a novel combined tether was designed and comprehensively optimized. The resonators were batch fabricated based on a reliable and simple silicon-on-insulator (SOI)-based fabrication process. The combined tether experimentally contributes to low anchor loss and motional impedance. Especially in the 4th WEM, the resonator with a resonance frequency of 1.1 GHz and a Q of 10,920 was demonstrated, corresponding to the promising f × Q product of 1.2 × 10¹³. By using combined tether, the motional impedance decreases by 33% and 20% in 3rd and 4th modes, respectively. The WEM resonator proposed in this work has potential application for high-frequency wireless communication systems.

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.

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.

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 Novel Extensional Bulk Mode Resonator with Low Bias Voltages

This paper presents a novel Π-shaped bulk acoustic resonator (ΠBAR) with low bias voltages. Concave flanges were coupled with straight beams to effectively enlarge the transduction area. A silicon-on-insulator(SOI)-based fabrication process was developed to produce nanoscale spacing gaps. The tether designs were optimized to minimize the anchor loss. With a substantially improved electromechanical coupling coefficient, the high-stiffness ΠBAR can be driven into vibrations with low bias voltages down to 3 V. The resonator, vibrating at 20 MHz, implements Q values of 3600 and 4950 in air and vacuum, respectively. Strategies to further improve the resonator performance and robustness were investigated. The resonator has promising IC compatibility and could have potential for the development of high-performance timing reference devices.

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.

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.