Search

Quartz crystal resonators are widely used as reference frequency sources in modern electronic systems. However, their frequency often deviates from the nominal value due to the significant change in the ambient temperature. Therefore, it is of great value to develop an accurate dynamic frequency offset model regarding temperature changes. In this article, a novel feature-weighted echo state network (FWESN) method is presented to capture the dynamic frequency–temperature (${f}$ – ${T}$) characteristic of quartz crystal resonators. Different from the traditional echo state network (ESN), which simply takes the temperature measurement signal as a single model input variable, the proposed method mines the feature information hidden in the temperature measurement series to construct the model input vector. Specifically, five dynamic features are designed to substitute for the original temperature signal by investigating the influence mechanism of temperature versus frequency. Furthermore, considering the difference in these features’ importance, two feature weighting strategies, including the Pearson’s correlation coefficient (PCC)-based and particle swarm optimization (PSO)-based, are proposed to assign the different weights to the five features. Finally, the weighted features are fed into the ESN model to implement the dynamic frequency offset estimation. The application results on the real experiment datasets demonstrate that the presented FWESN method can estimate the frequency offset more precisely than the basic ESN method. [ABSTRACT FROM AUTHOR]

This article describes the first-order perturbation analysis of nonlinear responses in surface acoustic wave (SAW) resonators on the LiTaO3/SiO2/Si structure, where bulk wave radiation is negligible near the main resonance while the longitudinal resonances are not. The coupling-of-modes (COMs) theory is employed as the platform for both the linear and nonlinear response analyses. Stress and dielectric flux are assumed to be generated by nonlinear mixture of linear strain and electric fields proportional to the SAW displacement and applied voltage, respectively, and they are newly introduced to the extended COM equations as excitation sources. The simulated third harmonic (H3) responses agree well with the experimental ones including that caused by longitudinal resonances, and effectiveness of the present method is demonstrated. Furthermore, this theory is applied to the infinitely long interdigital transducer (IDT) to highlight the impact of longitudinal resonances. [ABSTRACT FROM AUTHOR]

This article presents the lamb wave contour mode resonators (CMRs) based on 22% aluminum scandium nitride (AlScN) thin film with $\lambda $ of 12–24 $\mu \text{m}$ , and operating in $\text{S}_{{0}}$ mode. We report the design, fabrication, and characterization of 500 nm-thick AlScN CMRs, which take advantage of optimized stress control of co-sputtered AlScN thin films and vertical inductively coupled plasma (ICP) etching profile. The experimental results are compared to theoretical predictions by finite element analysis (FEA). All Al $_{{0.78}}$ Sc $_{{0.22}}\text{N}$ devices show excellent agreement with simulations in piezoelectric coupling using modified AlScN film parameters. The best Al $_{{0.78}}$ Sc $_{{0.22}}\text{N}$ CMR has achieved an electromechanical coupling coefficient (${k}_{t}^{{2}}{)}$ of 5.24% and loaded quality factor (${Q}$) of 1219 with an operating frequency at approximately 300 MHz, which exhibits a high Figure-of-Merit (FoM) of 63.88 in piezoelectric microelectromechanical system (MEMS) lamb wave CMR. This article also presents the co-sputtering characteristics of the AlScN thin films under $\text{N}_{{2}}$ gas to achieve low-stress and high-quality piezoelectric materials, and the etching optimization of high concentration Sc doping aluminum nitride (AlN) thin films under Cl2/BCl3/Ar chemistry to obtain record profile angle of 77°, high selectivity of 1:1 with SiO2 hard mask. [ABSTRACT FROM AUTHOR]

The accurate calculation of vibration frequency is essential in design of circular quartz crystal resonators which are the core elements of high-precision microbalances used for testing and measurement. Currently, the prediction of thermal effects on frequency through an analytical analysis is still in its developmental stage, mainly due to the complexity of solving the 3-D equations with the consideration of asymmetric structure of resonators and electrodes along with material anisotropy. By using a scalar differential equation for vibrations with the eigen-displacement of thickness mode, the eigen-frequency of a plano-convex AT-cut circular quartz crystal plate with asymmetric electrodes is determined. Furthermore, the temperature effect in the scalar differential equation is successfully obtained by incorporating the incremental thermal field theory into the 1-D analysis. The theoretical results agree well with the experimental data. The combination of the thermal field and the thickness model for circular quartz crystal resonators can realize a full analysis of thermal properties in vital applications such as high-sensitivity microbalance sensors. [ABSTRACT FROM AUTHOR]

This article presents shear horizontal surface acoustic wave (SH-SAW) devices with excellent temperature stability and low loss on ultrathin Y42-cut lithium tantalate film on sapphire substrate (LiTaO3-on-sapphire, LTOS). The demonstrated resonators exhibit scalable resonances from 1.76 to 3.17 GHz, effective electromechanical coupling coefficients between 5.1% and 7.6%, and quality factors (Bode-Q) between 419 and 3019. The filter with a center frequency of 3.26 GHz features a suppressed spurious passband, a 3-dB fractional bandwidth (FBW) of 3%, and a minimum insertion loss (IL) of 2.39 dB. In addition, coplanar waveguides (CPWs) and SH-SAW resonators built on LTOS and LiTaO3-on-insulator (LTOI) substrates were compared over a temperature range of 25 °C–150 °C. Due to the extremely high resistivity of the sapphire and the excellent thermal stability of the LiTaO3/sapphire interface, the IL of the CPW and the impedance ratio (in addition to Bode-Q) of the SH-SAW on the LTOS are maintained well even at 150 °C, while those on the LTOI seriously deteriorate. Of these, the impedance attenuation of LTOS-SAW at the antiresonant frequency is only 3.7 dB at 150 °C, whereas that of LTOI-SAW reaches 9.6 dB, demonstrating excellent temperature stability of the LTOS substrate’s radio frequency (RF) performance. Overall, the SAW devices on LTOS substrates show great potential for temperature-sensitive and low-loss applications in RF wireless communications. [ABSTRACT FROM AUTHOR]

This article presents the first two-port lateral-extensional mode zinc oxide (ZnO) piezoelectric resonator with a reconfigurable bottom electrode that is enabled by embedding a vanadium dioxide (VO2) thin film. The insulator-to-metal phase transition of VO2 is triggered by substrate heating that translates to abrupt changes in electric field patterns and piezoelectrically transduced modal vibrations, thus allowing mode-switching of piezoelectric resonators at specific frequencies. Finite element method (FEM) analysis was used to model the broadband frequency response, while frequency characteristics of the corresponding two-port resonator were measured over a temperature range between 20 °C and 95 °C with a specific focus on two resonances at 88 and 148 MHz. By leveraging the hysteretic behavior of VO2 thin film during a heating/cooling cycle, a change in both the capacitive feedthrough and resonance signal levels was observed, due to the abrupt change in the conductivity of VO2 during its phase transition. The unique switch- ON behavior of the resonance at 88 MHz starts at 70 °C during the heating cycle, while the switch- OFF transition begins at 60 °C during the cooling cycle. On the other hand, when the temperature is increased from 20 °C to 60 °C, a decrease in the insertion loss and resonance frequency of 12 dB and 0.28 MHz, respectively, were observed for the resonance at 148 MHz. Meanwhile, a resonance frequency increase of 0.42 MHz was observed during a temperature increase from 60 °C to 95 °C, which can be ascribed to VO2 phase transition from monoclinic to rutile phase. The hysteresis loops for insertion loss and resonance frequency indicate a different critical temperature for phase transition from the monoclinic (insulator) phase and rutile (metallic) phase and vice versa. The substantial variation in the temperature coefficient of frequency can be largely ascribed to electrode reconfiguration enabled by VO2 phase transition. [ABSTRACT FROM AUTHOR]

In this article, a new high quality factor (${Q}$) inductor with piezoacoustic plate acoustic wave (PAW) resonators is presented. As indicated by the investigation of the acoustic wave propagation characteristics and transducer materials, the coupling coefficient (${k}^{{2}}$) of the shear-horizontal plate (SH0) mode that propagates in the LiNbO3 plate increases to 55.7%, which leads to a wide inductive bandwidth of 29%. The longitudinal and transversal spurious modes are inhibited through novel edge reflector design and transducer engineering. The peak inductor quality factor (${Q}_{L \text {,peak}}$) of the acoustic resonator–inductor is obtained as 347, and a large range of inductance values are achieved to be up to 49 nH by regulating the interdigital transducer (IDT) number of fingers (NF). It is noteworthy that a larger inductance is realized in a more miniaturized device. Furthermore, the wavelength-scaling-induced physics is investigated for frequency tuning in 1–5 GHz, which reveals the multifrequency ability on a single chip of the SH0 acoustic resonator–inductor. [ABSTRACT FROM AUTHOR]

Multilayered structures extensively studied as a novel type of substrates for surface acoustic wave (SAW) devices are characterized by an asymmetry of wave propagation: acoustic wave characteristics generally change with inversion of propagation direction or interchange of top/bottom surfaces in one of the layers, though separately each material is symmetric for such inversions. In this article, the matrix formalism known as an effective tool for theoretical and numerical investigation of acoustic wave propagation in multilayered structures is applied to explain the existence of asymmetry and analyze its relation to the symmetry and orientations of combined materials. This phenomenon is illustrated by the examples of layered structures combining LiTaO3 (LT) plate with quartz or Si, previously reported as potential substrates for SAW devices with improved performance. Asymmetry arises from anisotropy of combined materials and occurs even when one of these materials is non-piezoelectric. It was estimated numerically as a variation of SAW resonator characteristics with substrate or plate inversion and was analyzed as a function of plate or substrate orientation. In particular, it was shown that “polarity inverted” structure enabling alternative resonator performance for the same material layers can be obtained either by an interchange of top/bottom surfaces of a piezoelectric plate or by inversion of propagation direction in a substrate. Asymmetry decreases with the introduction of an isotropic layer at the plate-substrate interface. [ABSTRACT FROM AUTHOR]

The motivation of this work is to analyze the in-band intermodulation distortion (IMD) occurring in surface acoustic wave (SAW) devices, using a recently developed fast method based on the input–output equivalent sources (IOES). The method calculates the equivalent current sources of a given harmonic (H) or IMD, which when applied at the boundaries of any uniform nonlinear region produce the same nonlinearities as the full distributed circuit. The accuracy of the method is validated with a very simplified SAW resonator with ten digits, which is modeled by a discretized Mason-based circuit. The IOES method provides equal results to the ones obtained through harmonic balance (HB) simulations, performed by means of commercial software, being the first 1000 times faster. Once the accuracy of the method is guaranteed, it is used to analyze the measured in-band IMD3 of several lithium tantalite 42° cut leaky SAW (LSAW) resonators with different pitches and duty factors at the B66 long term evolution (LTE) frequency band. Those resonators are comprised of 100 and 20 electrode pairs for the active region and each of the reflectors, respectively, which implies the analysis of a very large distributed nonlinear problem with thousands of nonlinear local sources. The IOES method takes 35.4 s in simulating 51 frequency points, whereas this simulation is not possible using a commercial HB simulator on a general-purpose computer. [ABSTRACT FROM AUTHOR]

This work studies the influence of substrate loss on the performance of acoustic resonators and on-chip inductors and investigates the effective substrate resistivity of seven commonly used substrates in silicon-based devices. The substrates include X-cut lithium niobate (LiNbO3) film with two different thicknesses (400 nm and 1.6 $\mu \text{m}$) on high-resistivity Si (HR-Si) and amorphous Si wafers, SiO2 film with two different thicknesses on HR-Si, and bare HR-Si. The effective resistivities of these substrates are extracted using coplanar waveguides (CPWs) over a frequency range from 1 to 40 GHz. Using the effective resistivity approach, the efficiency of two substrate loss reduction techniques—Si wafer removal and amorphous Si—in reducing substrate loss is quantified. Comparison of the extracted substrate resistivities of the suspended and un-suspended dielectric-on-Si structures and comparison of LiNbO3 on HR-Si and amorphous Si are carried out. Substrate loss reduction techniques are more advantageous for a thinner dielectric film and at a lower frequency range due to the higher filling factor of the electric field in the Si wafer. Finally, by comparison of the effective substrate resistivity of SiO2 film on an HR-Si with bare HR-Si, thick plasma-enhanced chemical vapor deposition (PECVD) SiO2 film is found to be a good insulation layer to reduce substrate loss. [ABSTRACT FROM AUTHOR]

In this article, a methodology for increasing the displacement of the membrane in nonlinear transducers is presented. This methodology that relies on pulse shaping is based on the frequency modulation of the excitation signal which in turn results in an amplitude modulation of the displacement of the resonator. The benefits of pulse shaping include the increase of the displacement of the membrane of the resonator, the ability to leverage two mechanisms to dynamically tune the resonant frequency of the device and a relative control of the decay time of the resonator. These properties have been verified using simulations and experimental results. The experimental results are performed using two nonlinear resonators with a frequency of 3.9 and 7.9 kHz. With a constant amplitude of the excitation voltage, experimental results show that the use of pulse shaping allows a velocity increase of the membrane of a piezoelectric microelectromechanical systems (MEMS) resonator of up to 191% for a softening type resonator (STR), and 348% for a hardening type resonator (HTR). The frequency tuning mechanism allowed the operation of the STR and of the HTR over a bandwidth of 280 and 115 Hz, respectively, while providing higher velocity than with the non-optimized excitation signal. The resulting pulse shaping methodology can be applied to other nonlinear resonators as shown using simulation and experimental results. Therefore, this work should lead to an increase of the use of nonlinear resonators for various applications. [ABSTRACT FROM AUTHOR]

In this work, a compact model is presented for a 14-nm CMOS-based fin resonant body transistor (fRBT) operating at a frequency of 11.8 GHz and targeting radio frequency (RF) generation/filtering for next-generation radio communication, clocking, and sensing applications. Analysis of the phononic dispersion characteristics of the device, which informs the model development, shows the presence of displacement component coupling due to the periodic nature of the back-end-of-line (BEOL) metal phononic crystal (PnC). An eigenfrequency-based extraction process, applicable to resonators based on electrostatic force transduction, has been used to model the resonance cavity. Augmented forms of the Berkeley short channel IGFET model (BSIM)-common multigate (CMG) model for FinFETs are used to model the drive and sense transistors in the fRBT. This model framework allows easy integration with the foundry-supplied process design kits (PDKs) and circuit simulators while being flexible toward change in transduction mechanisms and device architecture. Ultimately, the behavior is validated against RF measured data for the fabricated fRBT device under different operating conditions, leading to the demonstration of the first complete model for this class of resonant device integrated seamlessly in the CMOS stack. [ABSTRACT FROM AUTHOR]

Surface acoustic wave (SAW) cavities have been widely applied as electronic bandpass filters, sensors, microfluidic tweezers, and, in recent years, as devices for coupling with quantum systems. Here we propose a novel method of analyzing acoustic Fabry–Pérot spectra, by analogy with optical cavities, to determine the free surface velocity and attenuation of SAW waves, as well as the reflection of interdigital transducers (IDTs), all of which are crucial design parameters. In our experiment, two-port SAW resonators, consisting of two IDTs laterally separated by a free surface cavity length, are used to generate SAWs on 128° Y-X lithium niobate that are trapped between the two IDTs which also act as Bragg reflectors. Resonant cavity peaks can be observed through the electrical ${S}_{{11}}$ (reflection) spectrum measured on one IDT. The free spectral range and linewidths of cavity peaks are then measured to obtain the free surface SAW velocity, SAW propagation attenuation coefficient, and IDT reflection phase and amplitude. Our method of analyzing Fabry–Pérot spectra provides an intuitive approach for determining key characteristics of SAW waves and cavities. [ABSTRACT FROM AUTHOR]

High-temperature (HT) properties of a thickness-shear mode (TSM) langasite resonator with Ru–Ti electrodes are reported for the first time. Resonators with 300 nm Ru and 15 nm Ti films as the primary and adhesive electrode layers, respectively, were investigated and compared against those with Au–Cr and Au–Ti electrodes. HT stability of the fabricated samples under continuous excitation were examined up to 750 °C by monitoring their morphological changes, sheet resistance, resonance parameters, and their equivalent circuit elements. Results indicate that for Ru–Ti electrodes, a polycrystalline RuO2 cover layer was formed on the surface of Ru, which protected the underlying layer from further oxidation. Consequently, the electrical and motional resistances of the Ru–Ti sample experienced the least change post-annealing, which was also reflected in its ability to retain the highest ${Q}$ -factor after heat treatment. Ru–Ti-based resonator also exhibited comparable performance to other samples in terms of resonant frequency shifts and second-order temperature coefficients, further strengthening the position of Ru as a suitable alternative to other electrode materials. [ABSTRACT FROM AUTHOR]

The effect of the difference in the thickness ratio of the double-layered thickness-shear resonator on the temperature characteristics of the resonance frequency was investigated using a Ca3TaGa3Si2O14 (CTGS) single crystal. Three specimens with thickness ratios of ${x} =0.25$ , 0.33, and 0.50 were prepared using $122^{\circ } ~{Y}$ - and $171^{\circ }~{Y}$ -cut CTGS substrates. For the specimens with ${x} =0.25$ and 0.33, the temperature characteristics varied depending on the order of the resonance mode. For the specimen with ${x} =0.50$ , on the other hand, almost the same temperature characteristics were observed regardless of the order of the resonance mode. To interpret this phenomenon, a new equation for predicting the temperature characteristics of the fundamental mode (first mode) for the double-layered resonator was created using the electric flux density ratio generated in the two substrates. The expected values using this equation were in good agreement with the result of the first mode temperature characteristics. [ABSTRACT FROM AUTHOR]

This article deals with 2-D modeling of coupled vibrations of finite piezoelectric resonators. A general solution for all the physical quantities in the Cartesian and cylindrical coordinate systems is deduced from the governing equations by expansion in series summation of trigonometric functions of thickness coordinate and trigonometric or Bessel functions of the lateral one. The essential difference between this model and the earlier ones is that instead of expressing mainly in the thickness coordinate and integration through the thickness, the solutions are expressed in the form of double Fourier series augmented by single Fourier or Fourier–Bessel series, which contributes to better satisfy the mechanical and electrical boundary conditions. The dynamic stiffness matrix of the system is developed. Electrical impedances of a typical piezoelectric parallelepiped under stress-free and symmetrical loading conditions and its frequency spectrum for different width-to-thickness ratios are calculated using our model as well as by the finite element method. A comparison shows an excellent agreement. Finally, theoretical and measured electrical impedances of a piezoelectric parallelepiped and a piezoelectric disk are compared and discussed. The 2-D theoretical model proposed here is shown to be accurate and efficient for coupled vibration analysis of piezoelectric resonators and is applicable for any set of finite dimensions and crystal symmetry. [ABSTRACT FROM AUTHOR]

This article proposes an innovative viscosity sensor based on the thickness-shear vibration of stress compensated (SC)-cut quartz resonator. The thickness-shear mode is first analyzed and further studied with fluid-structure interaction between the resonator and the viscous fluid loading. The characteristic equation is derived based on the 3-D linear piezoelectric equations and solved for sensitivity analysis. Then laboratory experiment is carried out to validate the theory. To conduct the viscosity measurement, the SC-cut quartz resonator is integrated with a U-tube test fixture, which is designed and fabricated for sensor housing to avoid the influence of the mass of the fluid. The resonator is tested with various viscosities by tuning the ratio of glycerol/water mixture. Experiment results show consistency with the analytical solution, which together present an improved sensitivity of viscosity measurement by using SC-cut quartz resonator comparing to other resonator-based viscosity sensors. The proposed viscosity sensor is sensitive, accurate, and portable, and therefore can be applied to real-time, on-site measurement or sampling of fluidic samples. [ABSTRACT FROM AUTHOR]

LiNbO3 (LN) or LiTaO3 (LT) thin plates bonded to quartz are novel types of layered substrates for temperature-compensated surface acoustic wave (TCSAW) devices. In SAW resonators with Al electrodes arranged on LT/quartz and LN/quartz substrates, improved temperature behavior due to opposite signs of temperature coefficients of frequency (TCF) in quartz substrates and LT or LN plates can be combined with high ${Q}$ -factors if the quartz orientation is optimized. The quartz orientation areas that enabled high ${Q}$ -factors were deduced from analyzing the quartz anisotropy and the characteristics of shear horizontally (SH) polarized waves were calculated in the optimal orientations as functions of the quartz cut angle and plate thickness. The simulation results illustrated by contour plots of the wave characteristics revealed the presence of zero lines on the plots demonstrating TCFs at resonant (TCFR) and antiresonant (TCFA) frequencies in both layered structures. The strong quartz anisotropy explained anomalous temperature behavior of SAW resonators and the existence of LT/quartz structures with TCFA = TCFR facilitating the design of SAW devices with improved thermal stability in the passband. In the LT/quartz structures, two TCFs vanished simultaneously at certain plate thickness and quartz orientation, while in the LN/quartz zero lines did not intersect but low TCF = −(10–20) ppm/°C combined with electromechanical coupling exceeding 18% were obtained numerically in some structures. The effect of inverting the propagation direction or cut angle in one of the combined materials on the wave characteristics was discussed and numerically estimated. [ABSTRACT FROM AUTHOR]

A solidly mounted resonator on flexible polyimide (PI) substrate with high-effective coupling coefficient (${K}_{t}^{{2}}$) of 14.06% is reported in this article. This high ${K}_{t}^{{2}}$ is resulting from the LiNbO3 (LN) single-crystalline film and [SiO2/Mo]3 Bragg reflector. The quality of LN film fabricated by the crystal-ion-slicing (CIS) technique using benzocyclobutene (BCB) bonding layer was close to the bulk crystalline LN. The interfaces of the Al/LN/Al/[SiO2/Mo]3 Bragg reflector/BCB/PI multilayer are sharp, and the thickness of each layer is consistent with its design value. The resonant frequency and ${K}_{t}^{{2}}$ keep stable when it is bent at different radii. These results demonstrate a feasible approach to realizing RF filters on flexible polymer substrates, which is an indispensable device for building integrated and multifunctional wireless flexible electronic systems. [ABSTRACT FROM AUTHOR]

This work presents an improved design that exploits dispersion matching to suppress the spurious modes in the lithium niobate first-order antisymmetric (A1) Lamb wave mode resonators. The dispersion matching in this work is achieved by micro-machining the lithium niobate thin film to balance the electrical and mechanical loadings of electrodes. In this article, the dispersion matchings of the A1 mode in lithium niobate based on different metals are analytically modeled and validated with finite-element analysis. The fabricated devices exhibit spurious-free responses with a quality factor of 692 and an electromechanical coupling coefficient of 28%. The demonstrated method herein could overcome a significant hurdle that is currently impeding the commercialization of A1 devices. [ABSTRACT FROM AUTHOR]

A dynamic model to analyze the thickness-shear vibration of a circular quartz crystal plate with multiple concentric ring electrodes on its upper and bottom surfaces is established with the aid of coordinate transformation. The theoretical solution is obtained, which can be written in a superposition form of Mathieu functions and modified Mathieu functions. The convergence of the solution is demonstrated, and the correctness is numerically validated via results from the finite element method (FEM). Subsequently, a systematic investigation is carried out to quantify the effect of the electrode size on the energy trapping phenomenon, i.e., the resonant frequency and mode shape, which reveals that the ring electrode has a great influence on the work performance of resonators. With the increase of the electrode inertia, i.e., the radius and mass ratio, new trapped modes emergence with the vibration mainly focused on the plate with partial electrodes. Besides, owing to the anisotropy, degenerated trapped modes have different resonant frequencies and the frequency discrepancy between them will become smaller for higher modes. Finally, the influence of multiple ring electrodes is investigated, and the qualitative analysis and quantitative results demonstrate that multiple ring electrodes will lead to a more uniform mass sensitivity compared with a single ring electrode. The outcome is widely applicable, which can provide theoretical guidance for the structural design and manufacturing of quartz resonators, as well as a thorough interpretation about the underlying physical mechanism. [ABSTRACT FROM AUTHOR]

This work presents a new method to analyze weak distributed nonlinear (NL) effects, with a focus on the generation of harmonics (H) and intermodulation products (IMD) in bulk acoustic wave (BAW) resonators and filters composed of them. The method consists of finding equivalent current sources [input–output equivalent sources (IOES)] at the H or IMD frequencies of interest that are applied to the boundary nodes of any layer that can contribute to the nonlinearities according to its local NL constitutive equations. The new methodology is compared with the harmonic balance (HB) analysis, by means of a commercial tool, of a discretized NL Mason model, which is the most used model for NL BAW resonators. While the computation time is drastically reduced, the results are fully identical. For the simulation of a seventh-order filter, the IOES method is around 700 times faster than the HB simulations. [ABSTRACT FROM AUTHOR]

In this review article, we address two vital design considerations that govern the high-temperature operation of a thickness–shear mode langasite resonator: 1) electrode design and 2) electrode material. Optimal electrode designs to mitigate unwanted spurious modes and achieve a high Q-factor for fundamental and higher overtone modes have been discussed in great detail. Governing equations that determine the size, shape, and orientation of these electrodes have also been presented. In addition, the suitability of six platinum-group metals as electrode materials for high-temperature resonators have been assessed and summarized. Furthermore, the adhesion to the substrate, electrical conductivity, thermal stability, and various other temperature-dependent properties of these metals have been discussed. Finally, several combinations and operating ranges of these electrode materials have been thoroughly evaluated. [ABSTRACT FROM AUTHOR]

This article reports a new concept of surface-acoustic-wave (SAW) resonator, which uses shear horizontal (SH) wave confined in a thin LiTaO3 (LT) layer supported by a quartz (Qz) substrate. The LT layer is 35–50°YX LT, and the quartz substrate is 35–60°Y90°X Qz. A negative temperature coefficient of frequency (TCF) of the SH SAW in the LT layer is compensated by the quartz substrate, which shows a wide range of positive TCF depending on the crystalline orientation. Excellent TCFs of 2 and −10 ppm/°C were measured for the series and parallel resonance frequencies, respectively. The strong confinement of the SH SAW in the LT layer results in the best level of resonance characteristics ever reported. The measured impedance ratio reached 84 dB. On the other hand, spurious waves other than the SH SAW are not confined in the LT layer due to the unique properties of quartz, which results in spurious-free characteristics throughout a wide frequency range. [ABSTRACT FROM AUTHOR]

This article presents the design approach and the first demonstration of a wideband hybrid monolithic acoustic filter in the K-band, which exceeds the limitation of electromechanical coupling on the fractional bandwidth (FBW) of acoustic filters. The hybrid filter utilizes the codesign of electromagnetic (EM) and acoustic to attain wide bandwidth while keeping the advantages of small sizes and high Q in the acoustic domain. The performance trade space and design flow of the hybrid filter are also presented in this article, which allows this technology to be applied for filters with different center frequencies and FBWs. The hybrid filter is simulated by hybridizing the EM and acoustic finite element analysis, which are carried out separately and combined at a system level. The fabricated filter built with resonators having an electromechanical coupling of 0.7% based on the seventh-order antisymmetric Lamb wave mode (A7) has a 3-dB FBW of 2.4% at 19 GHz and a compact footprint of 1.4 mm2. [ABSTRACT FROM AUTHOR]

Structural and electrode material engineering methodology to attain quality factor enhancement in a support transducer enabled Wine-glass and Lamé mode resonator has been demonstrated in this work. To boost the quality factor, a series of short mechanical couplers is utilized to link the central resonant structure with the piezoelectric transducer arms. Two different top electrode materials are investigated, and the effect of metal loading on the performance of aluminum nitride (AlN)-on-Si-based resonator is investigated in detail. The new resonator design strategy improves the quality factor of the Wine-glass resonator from 9800 to 16 300 while still being able to maintain a spurious-free spectrum for a 200-MHz span, which is crucial for oscillator applications. An optimized oscillation system is realized using a commercially available low-noise amplifier. Careful positioning of the passive components is utilized to attain an ideal operating point for the resonator in the closed-loop condition. Using this scheme, Wine-glass and Lamé mode resonator-based high-performance oscillators with a low phase noise of −133.6 and −132.7dBc/Hz at 1-kHz offset and −153.7 and −150.4 dBc/Hz at 1-MHz offset, respectively, which satisfy that the Global System for Mobile (GSM) communication requirements are attained when normalized to a 13-MHz carrier frequency. [ABSTRACT FROM AUTHOR]

Miniaturized physical transducers based on weakly coupled resonators have previously demonstrated the twin benefits of high parametric sensitivity and the first-order common-mode rejection of environmental effects. Current approaches to sensing based on coupled resonator transducers employ strong coupling where the modal overlap of the responses is avoided. This strong coupling limits the sensitivity for such mode-localized sensors that utilize an amplitude ratio (AR) output metric as opposed to tracking resonant frequency shifts. In this article, this limitation is broken through by theoretically and experimentally demonstrating the operation of the weakly coupled resonators in the weak-coupling (modal overlap) regime. Especially, a prototype microelectromechanical systems (MEMS) sensor based on this principle is employed to detect shifts in stiffness, with a stiffness bias instability of 10.3 μN/m (9.5 ppb) and a corresponding noise floor of 7.1 μN/m/√Hz (6.8 ppb/√Hz). The linear dynamic range of such AR readout sensors is first explored and found to be defined by the dynamic range of the secondary resonator. The proposed method provides a promising approach for high-performance resonant force and inertial sensors. [ABSTRACT FROM AUTHOR]

Piezoelectric resonators have been extensively used as filters, actuator, and sensors. The effective electromechanical coupling coefficient (${k}_{\text {eff}}{)}$ is the most useful parameter to evaluate the electromechanical conversion efficiency of piezoelectric resonators. However, even for simple geometry piezoelectric resonators, such as disks, the coupling between different modes makes the resonant characteristics very complex. The coupling causes low electromechanical coupling efficiency of the intended mode. We propose a finite-element-based energy integration method to calculate ${k}_{\text {eff}}$ of piezoelectric resonators. This method is more accurate than the conventional resonance-antiresonance method and provides a powerful tool for the design optimization of pure mode resonators. A special case studied here is the fundamental thickness extensional (TE) mode of PZT-8 disks in the aspect ratio range of 2–20. Our results showed that multimode coupling near this mode can be greatly suppressed by modifying the edge surface of the disk to a convex shape. Such an optimized design could enhance ${k}_{\text {eff}}$ of the fundamental TE mode by as much as 10%–45% depending on the aspect ratio. [ABSTRACT FROM AUTHOR]

Vapor-cell devices based on microwave interrogation provide a stable frequency reference with a compact and robust setup. Further miniaturization must focus on optimizing the physics package, containing the microwave cavity and atomic reservoir. In this article, we present a compact cavity-cell assembly based on a dielectric-loaded cylindrical resonator. The loaded cavity resonating at 6.83 GHz has an external volume of only 35 cm3 and accommodates a vapor cell with 0.9-cm3 inner volume. The proposed design aims at strongly reducing the core of the atomic clock, maintaining, at the same time, high-performing short-term stability ($\sigma _{y}{(}\tau {)} \leq {5}\times {10}^{-{13}} \,\tau ^{-{1}/{2}}$ standard Allan deviation). The proposed structure is characterized in terms of microwave field uniformity and atom-field coupling with the aid of finite-element calculations. The thermal sensitivity is also analyzed and experimentally characterized. We present preliminary spectroscopy results by integrating the compact cavity within a rubidium clock setup based on the pulsed optically pumping technique. The obtained clock signals are compatible with the targeted performances. The loaded-cavity approach is, thus, a viable design option for miniaturized microwave clocks. [ABSTRACT FROM AUTHOR]

A 1-GHz full cryogenic oscillator is presented. The oscillator is based on a planar superconductor resonator featuring a loaded ${Q}$ factor of 200 000 at low microwave input power (unloaded ${Q}$ of 400 000) and on amplifying parts realized with SiGe bipolar transistors. The circuit is designed with a harmonic balance software and realized on an alumina substrate. A nonlinear model is extracted at low temperature both for the transistor and the resonator. This double nonlinearity increases the difficulty of the oscillator design and implies a strategy to limit the power inside the resonator. The vibrations of the cryogenerator are also a serious issue to get high performance. Finally, the oscillator features a phase noise of −112 dBc/Hz at 100-Hz offset frequency and a phase noise floor of −170 dBc/Hz (100-kHz offset) at a temperature of 65 K. [ABSTRACT FROM AUTHOR]

We have designed, fabricated, and characterized magnetostatic wave (MSW) resonators on a chip. The resonators are fabricated by patterning single-crystal yttrium iron garnet (YIG) film on a gadolinium gallium garnet (GGG) substrate and excited by loop-inductor transducers. We achieved this technology breakthrough by developing a YIG film etching process and fabricating thick aluminum coplanar waveguide (CPW) inductor loop around each resonator to individually address and excite MSWs. At 4.77 GHz, the 0.68-mm2 resonator achieves a quality factor (${Q}{)} > {5000}$ with a bias field of 987 Oe. We also demonstrate YIG resonator tuning by more than one octave from 3.63 to 7.63 GHz by applying an in-plane external magnetic field. The measured quality factor of the resonator is consistently over 3000 above 4 GHz. The micromachining technology enables the fabrication of multiple single- and two-port YIG resonators on the same chip with all resonators demonstrating octave tunability and high ${Q}$. [ABSTRACT FROM AUTHOR]

In this article, an electrothermal modeling approach of surface acoustic wave (SAW) resonators and filters is presented. The starting point for the model is a preliminary design that has to be assessed for thermal aspects. Due to the high geometrical complexity of SAW components, simplifications are elaborated and qualified on resonator and filter levels to prepare the design for thermal simulation. A thermal model is created and simulated in a finite-element method environment. The simulated behavior is exported as a thermal impedance and implemented in a circuit model of a SAW filter. The layout’s electromagnetic behavior is taken into account. Electrothermal models of the SAW resonators and the bus bars are developed. The interface to the thermal impedance is achieved by the use of electrothermal ports. The dynamic effect of the frequency shift is included. Verification is done by a comparison of the temperature increase of a resonator in a filter test structure to a corresponding simulation model. The filter is excited by a radio frequency large signal, and the temperature is detected by the use of a resistive temperature sensor. A simulation that shows the impact of mutual heating between the resonators in a filter environment is performed. [ABSTRACT FROM AUTHOR]

New ultrasound-mediated drug delivery systems, such as acoustic cluster therapy or combined imaging and therapy systems, require transducers that can operate beyond the bandwidth limitation (~100%) of conventional piezoceramic transducers. In this article, a dual-frequency coupled resonator transducer (CRT) comprised of a polymeric coupling layer with a low acoustic impedance (2–5 MRayl) sandwiched between two piezoceramic layers is investigated. Depending on the electrical configuration, the CRT exhibits two usable frequency bands. The resonance frequency of the high-frequency (HF) band can be tailored to be ~3–5 times higher than that of the low-frequency (LF) band using the stiffness in the coupling layer. The CRT’s LF band was analyzed analytically, and we obtained the closed-form expressions for the LF resonance frequency. A dual-frequency CRT was designed, manufactured, and characterized acoustically, and comparisons with theory showed good agreement. The HF band exhibited a center frequency of 2.5 MHz with a −3-dB bandwidth of 70% and is suited to manipulate microbubbles or for diagnostic imaging applications. The LF band exhibited a center frequency of 0.5 MHz with a −3-dB bandwidth of 13% and is suited to induce biological effects in tissue, therein manipulation of microbubbles. [ABSTRACT FROM AUTHOR]

The shear mode film bulk acoustic wave resonators (FBARs) have been developed rapidly in recent years due to the increased interest in biosensors. In this article, the mode coupling effects that are unavoidable in real devices are theoretically analyzed and discussed. Mindlin’s approximation method of expanding the displacement fields with power series along the plate thickness direction is employed, and a system of 2-D plate equations is obtained. The accuracy of the plate theory is validated through the comparison of dispersion curves with the results calculated by 3-D exact theory. Free coupling vibrations of the cross-sectional plane of finite-sized shear mode FBAR plates are further studied with the derived 2-D theory. The results in this article show that the presented plate theory is accurate and efficient for the structural analyses of shear mode FBARs. Besides, the selection of aspect ratios can be used to avoid strong mode couplings, which is helpful for device designs. [ABSTRACT FROM AUTHOR]

Mode-switchable ferroelectric thin-film bulk acoustic resonators (FBARs) are presented. Such resonators operate based on a dynamic nonuniform effective piezoelectricity in composite multilayer ferroelectrics with large electrostriction coefficients, like barium strontium titanate (BST). Harmonic resonance modes ($\textit {nf}_{o}$) of a multilayer ferroelectric bulk acoustic wave (BAW) resonator can be selectively excited with an electromechanical coupling coefficient (${K}_{\mathrm {eff}}^{{{2}}}$) equal to the fundament mode, which is contrary to the trend ${K}_{\mathrm {eff}}^{{{2}}}\propto {1}/{n}^{{{2}}}$ exhibited by conventional piezoelectric BAW resonators. Such a device can selectively be set to resonate at its different resonance harmonics by generating a pattern of nonuniform piezoelectric coefficient proportional to the stress field of each mode with an application of a proper set of dc control voltages applied across the ferroelectric layers. Such a resonator allows for the design of a new class of band-switching filters. As an experimental validation, a mode-switchable FBAR and a band-switching ladder-type filter based on a bilayer ferroelectric BST structure are designed and fabricated for the first time. The bilayer BST FBARs not only can be switched ON or OFF but also by choosing different bias configurations, two resonance modes at 2 and 3.6 GHz can be selectively excited having ${K}_{\mathrm {eff}}^{{{2}}}$ of 8% and 7%, respectively. [ABSTRACT FROM AUTHOR]

This article reports on a design journey for ScxAl1 – N-based dual-mode hybrid quasi-surface and bulk acoustic wave (quasi-SAW/BAW) resonators. Four types of acoustic excitation configurations are proposed in these designs based on Scx Al1–xN/6H-SiC stack architectures. The influence of Scx Al1–xN materials, film thickness, and device configurations on the performance is investigated. After design optimization, the final dual-mode hybrid quasi-SAW/BAW resonators comprise of top electrode, partially etched Scx Al1–xN pillars, and bottom electrode, which are stacked on a 6H-SiC substrate. The coupled quasi-SAW and BAW excited in the hybrid resonators enhance the resonance for both quasi-Rayleigh and quasi-Sezawa modes which results in a high effective coupling coefficient (Keff2) and phase velocity (${v}$). Simulation results show that the optimized hybrid quasi-SAW/BAW resonator based on Mo/Sc0.4 Al0.6N/Mo/6H-SiC configuration with SiO2 filling the grooves has a remarkable Keff2 value of 14.55% and a high ${v}$ above 7500 m/s, which make this kind of dual-mode hybrid quasi-SAW/BAW resonators have great potential in wideband and high-frequency applications. [ABSTRACT FROM AUTHOR]

This article reports on the modeling, design, fabrication, and testing of high-performance X-cut lithium niobate (LN) laterally vibrating resonators (LVRs) operating around 50 MHz. The objective of this work is to exploit the high figure of merit (FoM)—product of quality factor at series resonance (${Q}_{s}$) and electromechanical coupling (${k}_{t}^{{2}}$)—to provide for large passive voltage amplification in the front end of emerging radio frequency (RF) applications, i.e., wake-up radio receivers (WuRx). Finite-element analysis (FEA) is performed to optimize the devices’ geometry and ensure simultaneous high ${Q}_{s}$ and ${k}_{t}^{{2}}$. Resonators exhibiting ${Q}_{s} >5300$ and ${k}_{t}^{{2}} >27$ % are demonstrated, with FoM >1650—the highest value recorded for resonators in the megahertz range to the best of our knowledge. Finally, passive voltage gains between 35 and 57 V/V are showcased for capacitive loads ranging from 400 fF to 1 pF. [ABSTRACT FROM AUTHOR]

This article describes derivation of an equivalent circuit for nonlinear responses in film bulk acoustic resonators from the first-order perturbation analysis using the piezoelectric constitutive equations with the ${h}$ -form. For simplicity, electrodes and piezoelectric layers are considered as mass and spring, respectively, in the derivation. Then, it is demonstrated that the second- and third-order harmonic responses can be simulated well by the circuit. In addition, nonlinearity in the Si substrate is also taken into account and its impact is discussed. It is also discussed how the frequency dependences vary with the nonlinearity mechanisms as a finding from the derived equivalent circuit. [ABSTRACT FROM AUTHOR]

Quartz-enhanced photoacoustic spectroscopy (QEPAS) gas sensors have been widely developed over the last decade. This technique takes the advantage of a high quality factor tuning fork to enable high-sensitivity and high-selectivity miniature gas sensors. Lock-in detection is classically used to measure the resonator amplitude, which is proportional to the gas concentration, but this technique is slow and leads to measurement drifts as it does not follow the resonator frequency drifts over temperature and pressure. This article presents a new QEPAS signal processing technique that allows faster and more stable measurements that will enable accurate and fast multigas sensors. [ABSTRACT FROM AUTHOR]

Reconfigurable bulk acoustic wave filters provide a number of advantages for wireless communication systems, including compact size, cost effectiveness, and less complexity. This article presents the design methodology of an intrinsically switchable and bandwidth reconfigurable film bulk acoustic resonator (FBAR) filter, employing the electrostriction in ferroelectric barium strontium titanate (BST). Two examples of ferroelectric BST-based filters are designed and fabricated as a proof of concept. Under the application of a dc bias voltage, the fabricated switchable filters exhibit a bandpass response with a fractional BW of 3%. By changing the state of the ferroelectric BST FBARs through applied dc bias voltages, the bandwidth of the filters is adjusted. Without any bias, the filters switch OFF to provide isolation between the input and output ports. BST-based bandwidth reconfigurable filters can potentially reduce the number of required filters and switches in future multiband RF front ends. [ABSTRACT FROM AUTHOR]

This study reports the design of a novel Butterfly Lamb wave resonator (LWR) employing the $S_{0}$ mode in the AlN plate, and for the first time, its ultrahigh parallel-resonance quality factor ($Q_{p}$) of 4,021 is demonstrated, indicating an ultralow acoustic loss. Although the series resonance quality factor ($Q_{s}$) is widely used for various loss comparisons, it is inconclusive since $Q_{s}$ is always dominated by the routing resistance ($R_{s}$), which is normally huge without the thick metal rewiring. Instead, $Q_{p}$ is a precise representation of the acoustic loss level for its independence of $R_{s}$ and as it is closer to $Q_{\max }$ of the Bode $Q$ -curve in the IDT-excited devices. A butterfly-shaped resonance cavity, theoretically predicted to reduce the anchor loss and suppress the transverse spurious mode, has been applied to the AlN LWR and experimentally shown to boost the $Q_{p}$ by 2.3 times. In addition, a directly measured Bode- $Q$ curve for the LWR is reported for the first time, showing superior $Q$ profile for the Butterfly-LWR than the conventional-LWR and good agreement with the 3 dB- $Q_{p}$ ’s. [ABSTRACT FROM AUTHOR]

Nonlinearly coupled sets of piezoelectric field equations in the frequency domain were derived for the nonlinear propagation of finite-amplitude waves in piezoelectric bulk acoustic wave (BAW) and surface acoustic wave (SAW) devices. To verify their accuracy, we have embedded these sets of equations in the finite-element method (FEM) of COMSOL Multiphysics software and compared the FEM results with both the analytical and experimental results found in the published literature. The nonlinear frequency responses for both plano- and contoured-plate resonators of AT-cut quartz were investigated under various voltage drives, circuit resistances, and quality factors. The proposed equations with FEM have also been employed to study 33.3-MHz very-high-frequency (VHF) quartz resonators, showing that under different conditions of how well the third overtone mode (f3) matches the third harmonic (3f) and how the fractional frequency shift of the third overtone mode (f3) occurs as a function of the fundamental mode current. Furthermore, we have studied the nonlinear harmonic generation of an 840-MHz 128° Y-cut X-propagating (128° YX) LiNbO3 SAW resonator. The second-harmonic (H2) and third-harmonic (H3) modes were observed to occur, respectively, at two-time (2f) and three-time (3f) frequencies of fundamental frequency (f) when such resonators were driven with high power. The effects of substrate thickness, bottom surface conditions of the substrate, and different circuit connections on the H2 and H3 generations were simulated and compared with available measurements. Current proposed sets of equations are general and could be used for the study of nonlinear resonance, amplitude–frequency effect, and harmonic generation in any piezoelectric devices, provided that the necessary nonlinear material constants are known. [ABSTRACT FROM AUTHOR]

This study lays a foundation for the design of the SH0 plate acoustic wave (PAW) resonators based on LiNbO3 plate, and are applicable to the ultra-wideband filters and next-generation tunable filters. The coupling coefficient ($k^{2}$) of SH0 mode is optimized to as high as 55% and wideband spurious are well controlled by analyzing the propagation characteristics of plate modes in LiNbO3. The SH0 mode is demonstrated to be slowly dispersive and features the superiority of interdigital transducer (IDT)—defining frequency over most other plate modes. On the device level, the transducer types and electrode materials are investigated and compared. In addition, for edge-reflected SH0 resonators, stopband dispersion analysis is provided and the longitudinal ripples are suppressed. For edge-reflected SH0 resonators, a novel perfect edge reflector is proposed with elimination of longitudinal spurious ripples. [ABSTRACT FROM AUTHOR]

Thin-film bulk acoustic wave resonators (FBARs) are of significant interest for wireless applications due to their good performance. To achieve excellent characteristics, the frame-like FBARs were previously invented by researchers in this field to suppress the resonances of spurious lateral modes (or spurious modes). Another aspect that has an impact on the working performance of FBAR is the undesired coupling modes, which were rarely studied due to the lack of proper theoretical tools. In this article, we thoroughly investigate the coupling modes and spurious modes in frame-like FBARs by 2-D theory, which was already derived in our previous work. The widely used state-vector approach is applied here and both free and forced vibration problems are analyzed. Frequency spectra and mode shapes obtained from free vibration analysis show the coupling vibration characteristics in this structure. Moreover, the admittance resonance obtained from the forced vibration analysis shows the efficiency of the designed structure on the suppression of both undesired coupling and spurious modes. Results in this article provide a thorough understanding of the vibration in frame-like FBAR, and the method presented can work as an effective tool in engineering design process. [ABSTRACT FROM AUTHOR]

This theoretical work investigates the properties of nonlinearly operated weakly coupled resonators (WCRs) for resonant sensing applications. We propose an analysis framework for mutually injection-locked oscillators (MILOs) and mode-localized oscillators (MOLOs), subject to nonlinear restoring and damping forces. Under some simplifying assumptions, three sensor architectures are investigated and compared, highlighting several common features, such as: 1) the insensitivity of the amplitude ratio output metric to the A-f effect and 2) the instability of one oscillation state above a threshold amplitude. These results are illustrated and validated using transient simulations. Their range of validity is then discussed with finite perturbations, finite bandwidth, measurement noise, and nonlinear dissipation-fluctuation. [ABSTRACT FROM AUTHOR]

Acoustic wave devices utilizing plate waves in thin lithium tantalate (LiTaO3) have the potential of achieving high resonance frequency with a suitable electromechanical coupling factor and a relatively small temperature coefficient of frequency (TCF). The influence of Euler angle and plate thickness on the characteristics of plate waves has been investigated. High-frequency resonators using first antisymmetric Lamb wave mode (A1) in (0°, 42°, 0°) LiTaO3 thin plates have been fabricated and optimized. The resonance frequency is as high as 5 GHz, with a relative bandwidth of 7.3% and an impedance ratio of 72 dB. Finally, the TCF of (0°, 42°, 0°) LiTaO3 has been evaluated. Therefore, it is proved that A1 Lamb wave mode propagating in LiTaO3 at a Euler angle close to (0°, 42°, 0°) is suitable for high-frequency devices. [ABSTRACT FROM AUTHOR]

In this part of the paper, the numerical and experimental verification of the analytical design procedure is presented. Various waveguide-based test vehicles, implemented in single-crystal silicon and transduced by thin aluminum nitride films, are demonstrated. Silicon resonators with type-I and type-II dispersion characteristics are presented to experimentally verify the analytical mode synthesis technique for realization of high-quality-factor silicon guided wave resonators. [ABSTRACT FROM AUTHOR]

This paper presents an analytical approach for the implementation of high quality-factor ($Q$) resonators with arbitrary cross-sectional vibration mode shapes in anisotropic single-crystal substrates. A closed-form dispersion relation is analytically derived to characterize the dynamics of guided waves in rectangular waveguides. Three categories of waves with propagating, standing-evanescent, and propagating-evanescent dynamics are identified and used for energy localization of acoustic excitations with arbitrary cross-sectional vibration patterns. An analytical design procedure is presented for dispersion engineering of waveguides to realize high- $Q$ resonators without the need for geometrical suspension through narrow tethers or rigid anchors. The effectiveness of the dispersion engineering methodology is verified through the development of experimental test vehicles in 20- $\mu \text{m}$ -thick single-crystal silicon substrate with 500-nm aluminum nitride transducers. Various proof-of-concept resonators, representing guided waves with different dispersion types, are presented and compared to highlight the optimum design procedures for $Q$ enhancement and spurious mode suppression. Part I of this paper presents the operation principle of guided-wave resonators based on the analytical derivation of dispersion relation followed by a systematic resonator design procedure. Numerical and experimental characterizations for verification of the proposed design procedure and extensive measurement data on proof-of-concept resonators are presented in Part II. [ABSTRACT FROM AUTHOR]

This work describes a new method to enhance the electromechanical coupling coefficient ($k_{t}^{2}$) of 2-D mode resonators (2DMRs). This approach exploits the multimodal excitation of different Lamb waves to achieve a quasi-uniform vertical displacement distribution in the electrode regions of 2DMRs. To do so, the 2DMRs reported in this work rely on the use of metal frame structures placed at the edges of each metal strip forming the electrode gratings. To demonstrate the effectiveness of this new technique in enhancing $k_{t}^{2}$ , we report the design and simulated performance through the finite-element methods of a 2.5-GHz 2DMR using metal frames. Our analysis proves that this device can simultaneously exhibit high $k_{t}^{2}$ in excess of 6.4% and wide lithographic frequency tunability in excess of 10%, thus approaching the reported performance of aluminum nitride (AlN) film bulk acoustic resonators (FBARs) operating within the same frequency range. [ABSTRACT FROM AUTHOR]

Coplanar electrodes are used with the c-axis-oriented piezoelectric film to form the pure longitudinal mode and the pure shear mode solidly mounted resonators (SMRs). Aluminum and molybdenum are used as electrode materials to achieve different excitation pure shear mode and pure longitudinal mode. There is no need to make a bottom electrode or etch the piezoelectric layer, which simplifies the manufacturing and makes the structure stable. Furthermore, the cycle time of the process is significantly reduced. However, the control of the thickness of the Bragg reflectors, roughness control, and electrode photolithography are all challenging aspects of SMR manufacturing. In this study, ZnO piezoelectric film, which has a good electromechanical coupling factor and low transmission loss, was used as the c-axis-oriented piezoelectric film. An RF magnetron sputtering system was used to sputter a seed layer to encourage the growth of the zinc-oxide piezoelectric film and improve the c-axis orientation. The pure longitudinal mode and pure shear mode resonance signals were excited using the room temperature positive axis method. The quality factor and electromechanical coupling coefficient of the pure shear mode were 398% and 4.43%, respectively. The quality factor and electromechanical coupling coefficient of the pure longitudinal mode were 171% and 3.83%, respectively. Stability and feature recognition were accomplished in the pure longitudinal mode and the pure shear mode via a simplified and accelerated manufacturing process using electrodes with the same specifications. [ABSTRACT FROM AUTHOR]