The performance of Lead Zirconate Titanate (PZT) and Scandium-doped Aluminum Nitride (ScAlN) Piezoelectric Micromachined Ultrasonic Transducers (pMUTs) and speakers is heavily influenced by residual stresses from thin-film fabrication. In cantilever-based designs, these stresses induce significant out-of-plane deflection, causing the membrane to vibrate around a biased offset. This displacement creates structural gaps that facilitate air leakage, leading to substantial acoustic loss and degraded Sound Pressure Level (SPL). Due to the residual stress variation of a piezoelectric layer in a wafer, this offset deflection is one of the bottlenecks for the high yield manufacturing. To address this problem, this study demonstrates that applying a DC bias effectively counteracts residual stress, flattening the membrane and restoring acoustic performance. To validate this, we fabricated Sc0.3Al0.7N triangular cantilever-type speakers exhibiting high tensile residual stress. This stress resulted in upward tip deflections of 68–100 µm across the wafer, creating leakage paths. We show that a DC bias (-125 V to -175 V) can compensate for this stress, flattening the membrane at a rate of 0.5 µm/V. Experimental results confirm that optimal DC bias tuning achieves a 2× increase in tip displacement and ~12 dBSPL sound pressure increases under 2Vpp AC excitation at resonance. While DC bias significantly enhances the sound pressure and allows for frequency tuning from 13.8 kHz to 12.6 kHz, we observe that polar directivity remains largely unaffected due to diffraction at the sharp cantilever tips. This study provides a comprehensive wafer-level analysis essential for improving the manufacturability and acoustic reliability of PiezoMEMS speakers.

This paper reports, for the first time, bistability in a bimorph Piezoelectric Micromachined Ultrasonic Transducer (PMUT) composed of $\text{Sc}_{0.3} \text{Al}_{0.7}\ \mathrm{N}$ layers, with a total device thickness of $1.65 \mu\ \mathrm{m}$. The device exhibits large switching displacement exceeding $11 \mu\ \mathrm{m}$ and peak-to-peak velocity of $16\ \mathrm{m} / \mathrm{s}$ under bipolar square-wave excitation. The switching process excites a higher-order $(0,3)$-like mode that dominates the dynamic response. Sound pressure level (SPL) of 74 dB at 88 kHz was measured at 5 cm. Across the $20-100 \text{kHz}$ input frequency range, the total SPL is maintained above 75 dB. The normalized SPL when compared with state-of-the-art PMUT results, demonstrates strong acoustic transmission capability of thin bistable bimorph PMUTs.

This work presents a zero-power acoustic wake-up device that achieves high receive (Rx) sensitivity without an amplifier, using series-connected Sc0.3Al0.7N transducers to enhance broadband acoustic signal response. In the 500 Hz-5 kHz range, the 4-transducer series-connected array exhibited a 2.6-fold improvement in Rx sensitivity compared to the single-element configuration, and a 2.1-fold improvement over the 2-element series array. Similarly, in the 5 kHz-10 kHz range, the 4-element array demonstrated a 2-fold improvement over the single element and a 1.4-fold improvement compared to the 2-element array. These results confirm that scaling through series-connected arrays is an effective strategy for substantially enhancing broadband acoustic sensitivity in zero-power receiver systems

This paper introduces a novel approach for evaluating residual stress of layers in PVD Lead Zirconate Titanate (PZT) Piezoelectric Micromachined Ultrasonic Transducers (PMUTs). The method automatically finds the residual stress of the layers of PMUTs cross a wafer by matching a finite element (FE) analysis to an optical profilometry topology of PMUT membranes using an Iterative Newton-Raphson (N-R) convergence script, enabling efficient, automated wafer-level residual stress extraction in the epi-Silicon, PVD PZT, and passivation layers, which are key thin films in unimorph pMUTs. This method allows us to extract the actual stress of PMUTs, which might differ in stress levels compared to a blanket deposited film. The results show compressive stress in the PVD PZT, ranging from -130 MPa to -184 MPa, which is approximately -40 MPa lower than the film stress of a non-patterned blanket-deposited PVD PZT wafer. The epi-Silicon and passivation layers also exhibit compressive stress, ranging from -0.6 MPa to -0.9 MPa and -71.8 MPa to -114.6 MPa, respectively.

This article introduces curved-beam (CB) and curved-cantilever (CC) piezoelectric micromachined ultrasonic transducers (PMUTs) using 30% scandium-doped aluminum nitride (ScAlN), comparing their performance with conventional (C-PMUT) in the 45-75-kHz range. The CC-PMUT and CB-PMUT designs incorporate 2 mu m edge slits to achieve piston-mode vibration, significantly enhancing the effective vibration area to 65% and 60%, respectively, compared to 33% for C-PMUT. This structural design improves linearity, with CC-PMUT demonstrating minimal frequency sensitivity to dc bias (+/- 40 V) at 2.5 Hz/V, and CB-PMUT (7.5 Hz/V) both outperforming C-PMUT (100 Hz/V). Under increasing ac voltage excitation, CC-PMUT exhibits exceptional linearity with minimal resonance variation, while C-PMUTs and CB-PMUTs show nonlinear behavior with increasing frequency and stiffening effects. C-PMUT displays the highest nonlinearity, with a Duffing coefficient 2.5 times larger than CB-PMUT. The CB-PMUT exhibits the highest displacement sensitivity (1025 nm/V) compared to C-PMUT (825 nm/V) and CC-PMUT (610 nm/V). Despite its fourfold smaller area, the CB-PMUT generates comparable absolute pressure to the C-PMUT. Its exceptional normalized transmission pressure sensitivity of 77 dB SPL/V/mm2 surpasses both C-PMUT (65 dB) and CC-PMUT (67 dB), making it the highest reported among lead zirconate titanate (PZT) and ScAlN counterparts. C-PMUT demonstrates the highest receive sensitivity at 8.7 mV/Pa, followed by CB-PMUT at 4.2 mV/Pa and CC-PMUT at 3.3 mV/Pa. In pitch-catch experiments, CB-PMUT and C-PMUT detect signals up to 3.8 and 4 m, respectively, while CC-PMUT reaches 2.7 m (10 V-pp, 12-dB SNR threshold), demonstrating their potential for ultrasonic range-finding.

This research introduces a novel curved cantilever-based edge-actuated Piezoelectric Micromachined Ultrasonic Transducer (PMUT) utilizing a 30% Scandium-doped Aluminum Nitride (ScAlN) thin film. The cantilever-actuated PMUT achieves a linear piston-mode operation, with 75% of the membrane area vibrating in the vertical direction. In contrast to traditional PMUTs, this design operates at 63 kHz and features a flat vibrating membrane that remains frequency insensitive to DC voltage variation. It effectively maintains linear displacement and pressure response, even at driving voltages exceeding 50 V. At similar operating frequencies, the cantilever-actuated PMUT exhibits a displacement sensitivity of 700 nm/V, comparable to the 900 nm/V of the conventional PMUT. Additionally, the edge-actuated PMUT offers improved linearity and a Figure of Merit (FOM) of 65 mPa/V/mm 2 in transmission, which is 1.5 times larger than that of the conventional clamped PMUT.

This report presents a fully coupled method to extract the temperature coefficients (TCs) of transverse elastic properties for 15% scandium (Sc)-doped aluminum nitride (AlN) thin film from resonant test structures. The ScAlN thin film here is only 0.3 mu m-thick, grown on pre-formed cavities embedded below 2 mu m-thick silicon (Si) membranes with a 0.2 mu m-thick molybdenum (Mo) electrode over ScAlN. The intended parameters are extracted by interacting between finite element model methods and electrical measurement data of fabricated resonators. The proposed method allows extraction of first and second order TCs for transverse elastic properties. By extracting elastic properties at each temperature point, we directly obtain individual elastic property dependence on temperature without having any prior assumptions on the polynomial order of this dependence. This study marks one of the first reports on TCs for transverse elastic properties of ScAlN thin film: in-plane Young's modulus, in-plane shear modulus and in-plane Poisson's ratio.

Multilayered flexible piezoelectric energy harvesting devices (FPEDs) are a new future harvesting technology which are highly flexible and lightweight than familiar cantilever piezoelectric energy harvesters. This mechanical vibration driven FPED is a strongly coupled multiphysics phenomena that involve complex natural three-way interaction among the composite piezoelectric structure, the electric charge accumulated in the piezoelectric material, and a controlling electrical circuit attached to it. Efficient and accurate computational solution approaches are essential for analyzing these mechanical vibration-driven FPEDs to capture the main physical aspect of the coupled phenomena and to accurately predict the output voltage. While there are some numerical models for simple familiar cantilever type piezoelectric energy harvester reported in the literature, a fully three-dimensional strongly coupled model for complex material distributed, complex geometry, and multilayered FPED involving strong coupling of structure, piezoelectricity, and circuit phenomena has not yet been developed. A partitioned iterative algorithm is developed using a hierarchical decomposition approach wherein the coupled three fields are solved separately and coupled through loop union integration techniques that provide an efficient and accurate simulation of FPEDs. The simulation results matched the experiment results very well. This study provides a basis for the natural extension of partitioned iterative finite element coupled algorithm to simulate the future piezoelectric energy harvesting technologies involving a strong coupling of structure, piezoelectricity, and circuit phenomenon.

Aluminum Nitride (AlN) offers a CMOS-compatible, stable, and lead-free solution for piezoelectric micromachined ultrasonic transducers (pMUTs), if not for its limited e(31,f) piezoelectric coefficient. Even though increasing scandium (Sc) doping content in ScAlN is known to enhance the electromechanical coupling factor (K-t(2)) and overall acoustic performance, the outcome is highly dependent on the stress of the ScAlN film especially for air-coupled pMUTs. This study aims to compare pMUT performance (in terms of K-t(2)) due to increasing Sc content from 20% to 30% in relation to stress and considering its effects on frequency and static deformation of the membrane. Results show that 30% Sc devices achieved an average K-t(2) >6% at -50 MPa, on par with PZT-based pMUTs. Compared to 20% Sc, the 30% Sc-doped pMUTs demonstrated a 50% increase in transmit pressure sensitivity and overall 6 dB increase in two-way sensitivity.

In this work, we demonstrate that the performance of ScAIN pMUTs can be enhanced by adjusting DC bias voltages. DC biases up to 80 V on ScAIN pMUTs contribute to film stress alleviation and enhance pMUT performance. Laser Doppler Vibrometry characterization was performed to evaluate an improvement in displacement transfer according to the DC bias, as well as to investigate the ferroelectric effect of 15% scandium-doped AIN film. As a result, both transmission sensitivity and receive sensitivity are improved by 11 % and 50%, respectively, at 80V bias compared to 0V. Additionally, a 55% enlargement in the -3dB bandwidth (BW) has been achieved.

We propose the use of a thickness extensional (TE) mode in a piezoelectric-on-silicon resonator to accurately extract the elastic stiffness constant (c11) of a degenerately doped 2μm-thin silicon (Si) membrane with the piezoelectric stack in place. The frequency of this mode is discriminately sensitive to the Si membrane thickness and c11 of Si alone over the other layers in the stack. This presents a methodology to extract the properties of the elastic layer of a piezoelectrically transduced device with little influence from the other layers. The vertical stack of the TE mode resonator here is composed of 15% scandium doped aluminum nitride (ScAlN: ~0.3μm), molybdenum (~0.2μm) and thin passivation piezoelectric (~50nm) on the doped Si membrane formed by silicon migration. The methodology and test structure are validated by the close agreement of the extracted Young’s modulus to literature values. We use Si as a well-studied material to validate the method, demonstrating that the method could be extended to other materials.

Piezoelectric-structure interaction (PSI) and fluid-structure interaction (FSI) are multi-physics coupled systems. These interactions affect the vibration characteristics of coupled systems and thus such complex coupled systems must be controlled. This paper proposes computational control based on the finite element method for strongly coupled multi-physics analysis of the PSI of a thin flexible piezoelectric bimorph actuator. The vibration characteristics and the effect of direct velocity and displacement feedback (DVDFB) control in coupled systems are investigated. The displacement and velocity feedback gains are used together as well as separately. DVDFB control is extended to the FSI of stiff and soft structures to study vibration characteristics using active control and compare the stability of the two types of structure. The results of PSI show a reduction in actuator displacement amplitude and a shift in the resonance frequency due to DVDFB control. For FSI, the results for a stiff material show a reduction in displacement. The velocity feedback gain has no effect for a stiff material and leads to instability due to a large control force. The results for a soft material show a reduction in displacement and amplitude and more stability compared to the case for the stiff material.

This paper demonstrates the importance of three-dimensional (3-D) piezoelectric coupling in the electromechan-ical behavior of piezoelectric devices using three-dimensional finite element analyses based on weak and strong coupling models for a thin cantilevered piezoelectric bimorph actuator. It is found that there is a significant difference between the strong and weak coupling solutions given by coupling direct and inverse piezoelectric effects (i.e., piezoelectric coupling effect). In addition, there is significant longitudinal bending caused by the constraint of the inverse piezoelectric effect in the width direction at the fixed end (i.e., 3-D effect). Hence, modeling of these effects or 3-D piezoelectric coupling modeling is an electromechanical basis for the piezoelectric devices, which contributes to the accurate prediction of their behavior.

We present the first demonstration of our event-driven ultra-low power MEMS inertial switch for dry cabinet door lock monitoring. The MEMS inertial switch is integrated into a wireless sensing node (WSN) which houses a commercial accelerometer (ADXL355) and Bluetooth Low Energy (BLE) module to detect the door lock status. Upon the acceleration generated by unlocking of the dry cabinet, the MEMS inertial switch is turned on and wakes up the BLE module and the accelerometer sequentially. After wake-up, the BLE module streams the accelerometer data to a remote PC tracking the activities on the dry cabinet door. The inertial switch successfully detects the door unlock events and wakes up the WSN to stream the accelerometer data for 2 hours. The data signature of the accelerometer is able to classify the status of the opening, closure and locking of door.

We report preliminary wafer-level measurement results of air-coupled $\mathrm{S}\mathrm{c}_{0.15}\mathrm{A}\mathrm{l}_{0.85}\mathrm{N}$ pMUTs recently fabricated in our Lab-in-Fab 8-inch line. In this work, we show that the $\mathrm{K}_{\mathrm{t}}{}^{2}$ and mechanical performance of the devices are correlated to the resonant frequency in connection to film stress. At lower film stresses, the electromechanical coupling, $\mathrm{K}_{\mathrm{t}}{}^{2}$ , can reach typical values of 3%. While ScAlN-based pMUTs of similar levels of doping concentration have been reported previously, $\mathrm{K}_{\mathrm{t}}{}^{2}$ has been limited to approximately 2% [1]. In this work, the effects of varying tensile film stress have been recorded to show drastic changes to Kt 2 causing variations on the wafer-level from 0.5% to 3% in relation to the induced local stress. The effect on the resonant frequency of the device was also recorded, ranging from 157kHz to 215kHz. These effects were also validated mechanically under an LDV that show displacement transfer variations of 224 to 557nm/V, whereby the transfer is inversely proportional to the amount of tensile stress.

We report preliminary wafer-level measurement results of air-coupled phase vapor deposition (PVD) PZT pMUTs for ranging applications recently fabricated in our Lab-in-Fab 8-inch line. Dual-port PVD PZT pMUTs designed to resonate in the 100kHz range were fabricated based on a $\boldsymbol{2\mu} \mathbf{m}$ - thick PZT film on a $\boldsymbol{4\mu}\mathbf{m}$ -thick silicon diaphragm. The standard deviation of the PZT stack capacitance was <2% across the wafer. Despite the sensitivity of compliant diaphragms to film residual stress, the standard deviation of frequency was <5%. Out of 16 sites across wafer probed, all devices were verified to be in good working condition. Given the strong piezoelectric constant of the PZT film $(\mathbf{e}_{\boldsymbol{31,}\mathbf{f}}\boldsymbol{\sim 16}\mathbf{C}/\mathbf{m}^{\boldsymbol{2}})$ and compliance of the diaphragm designed for ranging applications, we demonstrate large tunability in frequency (120-210kHz), $\mathbf{K}_{\mathbf{t}}{}^{\boldsymbol{2}}$ (1-7.3%), and quality factor (50–100) for a bias voltage range of0-40V. Results have been obtained without poling of the PVD PZT film. No unresponsive devices were found.

A partitioned iterative method based on hierarchical decomposition is proposed for providing numerical modeling and analysis of the piezoelectric energy harvester which is involved in coupled fluid-structure interaction, coupled electro-mechanical, and a controlling electrical circuit for piezoelectric structural applications in energy harvesting. This circuitintegrated piezoelectric structural application in energy harvesting surrounded by fluid media takes the form of natural four-way coupling of fluid flow, the structure, the electromechanical effect of the piezoelectric material, and the electrical circuit. This can be formulated exactly as a fluid-structure-piezoelectric-circuit interaction. These coupled four fields are hierarchically decomposed into the fluid-structure interaction, structure-piezoelectric interaction, and piezoelectric-circuit interaction interactions. Then these subsystems are decomposed into each field. The proposed finite element method enables to reuse of existing techniques because of its modularity. Furthermore, scalability to multiphysics and multisystem couplings is expected. There are some numerical approaches in particular monolithic coupling methods are studied which are computationally expensive and leads to an ill-conditioned coefficient matrix. Nevertheless, accurate modeling for predicting the characteristics of this four-way coupling using partitioned methods has not yet been developed. This method enables an investigation of piezoelectric structures in fluid with complex geometry, material composition, and attached electrical circuits to the harvester. A flexible piezoelectric bimorph harvester in the converging channel is analyzed to demonstrate the efficiency of the proposed method. The results indicate that the method captures the coupled effect accurately.

The key to the design of advanced micro electro-mechanical devices is an accurate evaluation of the circuit-integrated piezoelectric oscillator that accounts for its complicated configuration. Here, the direct numerical modeling of this oscillator leads to a general formulation as a structure-piezoelectric-circuit interaction. Hence, this study developed a strongly coupled partitioned iterative method for the structure-piezoelectric-circuit interaction. The proposed method was constructed using hierarchical decomposition, the partitioned iterative method for two coupled fields, and loop union. That is, the whole system of the coupled multiphysics is hierarchically decomposed into coupled two-field subsystems, partitioned iterative algorithms for two coupled fields are applied to these subsystems, and the coupling algorithms for these subsystems are reduced to a single coupling algorithm. In the proposed method, three distinct direct piezoelectric, inverse piezoelectric, and circuit solvers are strongly coupled with each other. The inverse piezoelectric solver uses shell finite elements to analyze the response of the thin oscillator efficiently, while the direct piezoelectric solver uses solid finite elements to accurately describe the three-dimensional distribution of the electric potential in the piezoelectric continuum. The proposed method can accurately analyze coupling phenomena in the RC circuit, piezoelectric shunt damping, and piezoelectric energy harvesting. (C) 2021 Elsevier Ltd. All rights reserved.

This paper presents an improved design of polymer micromachined transmission for flapping-wing Nano Air Vehicles (FWNAVs) in comparison with our last design. Design Improvement includes (1) reduction of the crack and fracture during microfabrication, and (2) performance improvement of the transmission. The novelty of our polymer micromachined transmission includes (1) the transmission mechanism based on the geometrical nonlinear bending deformation, and (2) the complete 2.5-dimensional structure that can be fabricated using standard microfabrication techniques including the etching, the photolithography, the deposition, and the curing process. The complete 2.5-dimensional structure requires no post-assembly and leads to further miniaturization without so much difficulty. Each wing of FWNAVs will be driven by the proposed transmission and actuator separately. The present transmission can produce around 40° stroke angle, which is about 50% higher than that of our previous work without considering the mass effect.