A Hierarchical Cascading Technique With Subpitch Finite Element Decomposition for 2-D Modeling of Acoustic Wave Resonators

Thermal property of surface acoustic wave (SAW) resonators is always of interests to product design and applications with the objective of accurate prediction of device performance. Theoretical and experimental studies have been carried out for the prediction of the thermal effect of piezoelectric substrates undergoing temperature change and structural complications frequently encountered in acoustic wave resonators like the presence of metal electrodes. The analysis is usually done with experimental data for the frequency-temperature relation with improved analytical models for the consideration of electrodes. In this study, we employee the incremental thermal field theory and accompanying material constants for quartz crystals, which were intended for the bulk acoustic wave (BAW) resonators analysis, to the analysis of an ideal model of SAW resonators. By taking into account the material constant dependence on temperature through the cubic relation and thermal effects on strains and equations of motion, SAW propagating in quartz crystals is formulated with the incremental thermal field theory. Our calculation of the velocity-temperature relation of quartz crystal substrates is an improvement of earlier predictions.

This paper presents an original and simple coupling-matrix-based synthesis methodology for the design of a new class of bandpass filters (BPFs) that employ hybrid acoustic-wave-lumped-element resonator (AWLR) modules with improved out-of-band isolation (IS). The proposed BPFs feature quasi-elliptic-type frequency response—shaped by $N$ poles and $2N$ transmission zeros (TZs) for an $N$ th-order transfer function, compact physical size, and high effective quality factors $(Q_{\rm eff})$ of the order of 1000. Despite the use of acoustic wave (AW) resonators, passbands exhibiting fractional bandwidths (FBWs) that are no longer limited by the electromechanical coupling coefficient $(k_{t}^{2})$ of the constituent AW resonators are obtained. A coupling-matrix-based model of a multi-mode AW resonator is also reported. It facilitates the incorporation of high- and low-frequency spurious modes that are present in a realistic filter response so that they can be anticipated at the synthesis and simulation levels. For proof-of-concept validation purposes, two BPF prototypes at 418 MHz made up of commercially-available surface acoustic wave (SAW) resonators and surface mounted devices (SMD) were built and measured. They perform first- (one pole and two TZs) and second-order (two poles and four TZs) transfer functions with measured passband insertion losses (IL) between 2.4–5.4 dB, $Q_{\rm eff}$ between 1600–1900, 3-dB absolute bandwidths ranging from 0.52 to 1 MHz (i.e., 1.6–3.2 times $k_{t}^{2}$ ), and minimum IS levels between 25–46 dB.

A fully integrated two-port surface acoustic wave (SAW) resonator, fabricated using a standard 0.6-mum complementary metal-oxide semiconductor (CMOS) process is described in this paper. Only three micromachining processes, namely, reactive ion etching, zinc-oxide deposition, and wet etching, implemented subsequent to the standard process, are required to realize these resonators. Three design examples of these resonators are given to demonstrate the characteristics of these resonators at different operating frequencies. Experimental measurements of the S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> transmission characteristics were conducted on the fabricated resonators and they were found to have parallel resonant frequencies of 1.02 GHz, 941 MHz, and 605 MHz and quality (Q) factors of 44, 86, and 285, respectively. Based on these measurements and the fabrication layers of the device, an equivalent-circuit model tailored specifically for standard CMOS two-port resonators was developed. Finite-element modeling of the SAW resonators was performed to verify the measured series resonant frequency. Comparison between the developed model and measurement characteristics was also presented. Improvement in Q factor was observed when reflector height was increased

Since the 80's, RF-filtering has carried the developments of Bulk Acoustic Wave (BAW) resonators. At the same time, picosecond ultrasonics, a non-contact and non-destructive technique for mechanical characterization, sees the light of day as an on-product process control measurements technique. The operating principle of a BAW resonator is the excitation of the first thickness mode of a piezoelectric layer sandwiched between two electrodes, which is the natural geometry in picosecond ultrasonics. This technique uses a pulsed laser source to excite and detect longitudinal acoustic waves at very high frequencies (100 GHz to 1 THz). Thus, it enables the measurement of decisive parameters of materials in thin films for the modeling of BAW resonators (sound velocity, thickness, density, acoustic attenuation, temperature coefficients). Here we present the capability of the technique that has been applied to BAW materials (AlN, Mo, SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , W, SiN) for mechanical characterization. Then we present results obtained on BAW stacks that enables modeling of resonant frequencies and coupling coefficient. These results show that more than just a process control tool, picosecond ultrasonics can replace RF-tests for frequential characterization.

This article describes the study of loss mechanisms in an incredible high-performance surface acoustic wave (IHP SAW) resonator on the 42°YX-LiTaO3/SiO2/Si structure. The full 3-D finite element method (FEM) is applied with the assistance of the hierarchical cascading technique (HCT). Excellent agreement is obtained between calculation and measurement not only for the effective electromechanical coupling factor ${k} ^{{2}}_{\text {eff}}$ but also the Bode Q without the inclusion of empirical loss mechanisms. The behavior of calculated Bode Q is mostly governed by the number of IDT finger pairs ${N} _{\text {I}}$ and aperture length W. SAW field distribution is derived from the FEM result. Oblique SAW leakage is observed in the busbar region of reflectors and becomes negligible when ${N} _{\text {I}}$ is large. From this, it is concluded that the Bode Q reduction discussed here is mainly occurred by the oblique SAW leakage caused by the in-plane diffraction. Finally, the modified Butterworth-van Dyke (mBVD) model is applied for quantitative characterization. It is shown that the in-plane SAW diffraction can be modeled well by the mBVD model and gives significant impact only to the anti-resonance Q. Surprisingly its loss is dominant even when ${N} _{\text {I}} =100$ .

Theoretical modeling and experimental characterization of rate and temperature dependent electromechanical behavior of piezocomposites

Bulk acoustic wave (BAW) resonators exhibit attractive properties in terms of power handling capacity and on-chip integration to realize filters in the GHz range [K. M. Lakin, IEEE Ultrason. Symp. pp. 895–905 (1999)]. In a BAW resonator, a thin piezoelectric layer (a few mm) deposited between two electrodes is driven in its thickness extensional mode of vibration. To get a high quality factor, this structure is decoupled from the substrate by a multilayer Bragg reflector or a back-etched membrane. A current problem in the design of BAW resonators is the existence of spurious resonances close to the thickness extensional mode which generate ripple in the filter passband. In this paper, these spurious modes are analyzed in terms of Lamb waves resonances. Physical modeling of BAW resonators using finite element ATILA code is presented. The influence of lateral dimensions and electrode geometry on spurious resonances is emphasized. With specific electrode design and electrical excitation, it is demonstrated that lateral modes of Lamb waves can be used to realize resonators in the 50–250-MHz range. Experiments on an AlN piezoelectric layer between Pt electrodes on a SiN membrane are presented. [Work supported by a ST Microelectronics grant (CIFRE).]

By nature, acoustic wave resonators are structurally dynamic components undergoing constant vibrations in the vicinity of resonant frequency at their functioning mode, which is definitely adversary with other components used in the same board and product. One particular concern in the design and packaging of acoustic wave resonators is that all packaging parameters and structures will cause changes of device performance in terms of frequency, circuit parameters, and thermal sensitivity, among others. We start with a complete finite element analysis model of a quartz crystal resonator with the consideration of structural complications including packaging, while the quartz crystal blank is analyzed with the Mindlin plate equations of five vibration modes for coupled thickness-shear vibrations. Other parts of structure are formulated with the three-dimensional theory of elasticity from Comsol. With this finite element model, many of the key features and parameters of the quartz crystal resonator are considered and a practical model and design process is established.

The frequency-adaptive loss mechanism of Mason model is established to improve the simulation accuracy of bulk acoustic wave (BAW) resonators. By introducing intrinsic loss factors of piezoelectric material, values of loss components in Mason model are modified to be frequency-adaptive, which avoids repetitive extractions of loss parameters for different working frequencies of BAW devices. To verify the accuracy of the modified loss mechanism, a BAW resonator is simulated by the Mason model and the two-dimensional (2D) model based on finite element method (FEM). Without considering the transverse effects of BAW resonator, simulation results of the two models fit well with each other in the full-frequency range.

The effect of loading rate on ferroelectric and ferroelastic behavior of 1-3 piezocomposites is presented in this work. Experiments are conducted for various loading rates under different loading conditions such as electrical and electromechanical to measure the rate dependent response of 1-3 piezocomposite compared with bulk piezoceramics. A thermodynamic based rate dependent domain switching criteria has been proposed to predict the ferroelectric and ferroelastic behavior of homogenized 1-3 piezocomposites. In this model, volume fraction of six distinct uni-axial variants are used as internal variables to describe the microscopic state of the material. Plasticity based kinematic hardening parameter is introduced as a function of internal variables to describe the grain boundary effects. Homogenization of 1-3 piezocomposite material properties are obtained by finite element (FE) resonator models using commercially available FE tool Abaqus. To evaluate the possible modes of vibration of 1-3 piezocomposite four different configuration of FE resonators are modeled. The FE resonator model is validated with the impedance spectra obtained experimentally for length extensional and thickness extensional resonator models. The predicted effective properties using the resonance based technique are incorporated in the proposed rate dependent macromechanical model to study the behavior of 1-3 piezocomposites. The simulated results are compared with the experimental observations.

High Q resonators are a critical component of stable, low-noise communication systems, radar, and precise timing applications such as atomic clocks. In electronic resonators based on Si integrated circuits, resistive losses increase as a result of the continued reduction in device dimensions, which decreases their Q values. On the other hand, due to the mechanical construct of bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators, such loss mechanisms are absent, enabling higher Q-values for both BAW and SAW resonators compared to their electronic counterparts.¹ The other advantages of mechanical resonators are their inherently higher radiation tolerance, a factor which makes them attractive for NASA's extreme environment planetary missions, for example to the Jovian environments where the radiation doses are at hostile levels.² Despite these advantages, both BAW and SAW resonators suffer from low resonant frequencies and they are also physically large which precludes their integration into miniaturized electronic systems.

With the rapid miniaturization and increasing performance demands of bulk acoustic wave (BAW) devices, more accurate and sophisticated design and modeling methods are required. Accurate simulation results and appropriate software tools as well as their correct application are essential for a precise characterization of BAW devices. Depending on the simulated device, its complexity, required accuracy and available computational resources, different modeling and simulation methods have to be applied. For this modeling task it is important to know what details to model, how to model them and at what extent. In order to capture all relevant effects that are important to characterize the device with high accuracy, deep knowledge of the simulation software's working principles as well as its computational limits and capabilities are necessary. This paper presents different enhanced electromagnetic models of mirror-type BAW resonators that are simulated with a 3D electromagnetic solver, whereas the acoustic effects are computed with a 1D solver. The electromagnetic effects of different resonator models are analyzed by fitting the simulated resonator admittance to an equivalent lumped circuit and comparing the fitted values. Further, the effects of the electromagnetic mesh-cell-density in simulations for the different resonator models are analyzed. The computational costs for these resonator models are shortly discussed by comparing mesh size, required memory and computational time. With the understanding of the model and electromagnetic mesh properties from the resonator simulations, an enhanced electromagnetic BAW duplexer model is simulated and compared to a measurement. The simulations of BAW resonators and duplexers can be improved by appropriate electromagnetic modeling and specific knowledge about the simulated device.

This article investigates a spurious resonance appearing near the antiresonance when the double-busbar configuration is applied to layered surface acoustic wave (SAW) resonators using 42°YX-LiTaO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> thin plates, and possible mitigation methods are studied both theoretically and experimentally. First, the origin of the spurious resonance is revealed, and the influence of structural parameters is studied using the periodic 3-D finite-element method (FEM) powered by the hierarchical cascading technique (HCT). Then, possible methods are discussed for spurious mitigation. Finally, experimental data are provided for validation of the present analysis.

The surface acoustic wave (SAW) resonator is modeled according to the coupling-of-mode (COM) model of the interdigital transducer (IDT) and the reflectance of the reflector. With the COM model of the SAW resonator, the SAW resonator admittance is derived and its variation with the frequency is simulated. The resonance admittance is the peak of the admittance curve. In resonance condition, the output signal of the SAW resonator is the maximum of all the output signals with different frequency input signals. The pressure on the surface of the SAW resonator substrate can change the velocity and wavelength of the SAW propagating along the substrate, so the resonance frequency will change with the pressure. According to the relation between the pressure variation and the resonance frequency shift, the wireless passive pressure sensor based on the SAW resonator is modeled and simulated. The model of the wireless passive pressure sensor can simulate the frequency variation with the pressure well, and it can be used as an effective tool for designing and analyzing the pressure sensor based on SAW resonators

MEMS based Bulk Acoustic Wave (BAW) resonators are rapidly growing highly integrated devices which can offer high Quality Factor (Q) values at operating frequencies up to the VHF and UHF ranges i.e. high f-Q product. In a BAW resonator, a piezoelectric layer which is the main part of the resonator generates the vertical acoustic standing waves within the layer. The resonant frequency of the BAW resonators is mainly determined by the thickness and the material of the piezolayer. In this paper, the BAW resonators are analyzed for finding out the Q values and hence f-Q product at different resonant frequencies using eigen frequency analysis. Higher Q results in a lower damping ratio and a longer resonance decay function. Larger values of f-Q products are preferred for low phase noise systems. Different piezomaterials are analyzed for providing the high f-Q product. As the piezoelectric layer determines the resonance frequency, its temperature coefficient also affect the thermal drift of the resonator. The material selection for the piezolayer is done based on certain parameters like f-Q scaling, temperature drift, thermal conductivity, power handling capability and high chemical stability. Modeling and simulation of BAW resonators and material optimization is done using COMSOL Multiphysics software.