Electromechanical Coupling Factor Research Articles

Electromechanical properties and domain evolution of a tetragonal Er3+-doped Pb(Mg1/3Nb2/3)O3–PbTiO3 ferroelectric single crystal

Herein, a tetragonal Er3+-doped Pb(Mg1/3Nb2/3)O3–PbTiO3 single crystal is comprehensively investigated. The actual composition of the studied crystal is Pb(Mg1/3Nb2/3)O3–36PbTiO3 doped with 0.17-mol% Er3+ (PMN–36PT: 0.17-mol% Er3+). The crystal exhibits a high shear piezoelectric constant of ∼936 pC/N, approximately three times the longitudinal piezoelectric constant when poled along [001]c, as well as a higher Curie temperature of ∼170 °C and large coercive field of ∼4.58 kV/cm. At room temperature, the crystal presents a mass of domain walls along the <110>c direction and extinction is observed four times within a 360° rotation, showing typical domain features of the tetragonal phase. Under a direct current–electric field along the [010]c direction, the extinction rule remains unchanged; however, changes in the domain configuration can be observed. In addition, the orientation dependence of the piezoelectric constant, dielectric coefficient, elastic compliance constant, and electromechanical coupling factor is calculated using the coordinate transformation method. The findings of this study are of considerable importance for the fundamental studies and device design of tetragonal ferroelectric crystals.

Impacts of Electrode Resistance on Resonance Characteristics of Film Bulk Acoustic Resonators

In the actual manufacturing process of film bulk acoustic resonators (FBAR), metal leads are necessary to complete the electrical topological connection. However, the electrode resistance will significantly influence the characteristics of the resonator. In this paper, the influence of electrode resistance on resonance characteristics of FBAR is analyzed. To be specific, how different electrode resistances affect the quality factor, impedance value, and electromechanical coupling factor of the FBAR series-parallel resonance frequencies is studied by incorporating the electrode resistances into an overall equivalent electromechanical model (i.e., the Mason model) and the COMSOL finite element simulation method. The results show that the increase of electrode resistance will result in the decrease of the series resonant frequency, the impedance value increases significantly and the quality factor decreases significantly at series resonant, while the parallel resonant frequency does not change, the impedance value slightly increases and the quality factor slightly decreases at parallel resonant, and their electromechanical coupling factor slightly increases.

Use of periodic 2D pillar array for performance enhancement of AlN-based SMR BAW resonators

This paper discusses the applicability of a two-dimensional (2D) periodic pillar array as the first layer of an acoustic mirror for AlN-based solidly mounted resonators of bulk acoustic waves. It is based on the idea that the periodic pillar array behaves like a uniform layer when the period is much smaller than the wavelength and its behavior is given by the ensemble average of pillar materials. The simulation shows that the effective electromechanical coupling factor can be enhanced close to that of AlN-based film bulk acoustic resonators when the slot ratio is large. It is also shown that the use of a 2D pillar array can enhance the reflectivity of the Bragg reflector. It should be noted that the periodic 2D pillar array can also control the anisotropy of wave propagation along the surface. Owing to this, transverse mode resonances can be suppressed well by adjusting the wave dispersion curve properly.

Attempt for excellent piezoelectric performance in Sb-free (K,Na)NbO3-based ceramics

Piezoelectric temperature stability is often a very important item for piezoelectric materials when putting them into practical applications like filters and ultrasonic transducers. Phase transitions of (K,Na)NbO3-based compositions that contain neither toxic Pb nor Sb elements were tailored to simultaneously acquire enhanced piezoelectric properties and good piezoelectric temperature stability in this study. Specifically, dense 0.94(K0·48Na0.52)NbO3-0.03BaZrO3-0.01BaSnO3-0.02(Bi0·5Na0.5)ZrO3 ceramic and its further compositionally modified one by 1 wt% MnO2 were prepared. Both of these two ceramics display quite weak piezoelectric temperature dependence in the usage temperature range between −30 °C–100 °C, but the one modified by MnO2 has the significantly improved piezoelectric properties with a high piezoelectric coefficient d33 of 310 pC/N and large electromechanical coupling factors kp and k33 of 0.57 and 0.73 at room temperature. The obtained excellent piezoelectric performance is considered to be associated closely with the stable piezoelectric characteristic of the orthorhombic phase and the diffused rhombohedral-orthorhombic and orthorhombic-tetragonal phase transitions.

Calibration of multiple shunted piezoelectric transducers with correction for residual modes and shunt interactions

Piezoelectric shunt damping can be used for efficient vibration mitigation of a single or multiple vibration modes of a structure. Several analytical tuning expressions have been derived for numerous circuit topologies for a single shunt. However, when multiple shunted piezoelectric transducers are attached to a flexible structure, their individual interactions alongside the spill-over from residual modes affect the calibration accuracy. In this paper, explicit correction terms that represent these effects are presented for multiple shunted piezoelectric transducers targeting a single vibration mode. The correction terms are obtained from the evaluation of effective electromechanical coupling factors, while proper balancing between shunts follows from an assumed proportionality between shunt forces. The proposed correction method is applicable to general shunt architectures, for which tuning is available when targeting a single-degree-of-freedom structure. Its ability to regain nearby optimal damping properties is illustrated numerically for the classic series RL shunt.

The effect of busbar structure on Q factor enhancement and spurious mode suppression in Lamb wave resonators

Lamb wave resonators (LWRs) exhibiting high-quality factors and clean spectra demonstrate promising applications in RF communication and sensing. This paper discusses the relationship between the spurious mode, the quality factor, and the effective electromechanical coupling factor of resonators. When the resonant frequency of the spurious mode is slightly below the parallel resonant frequency (fp), the quality factor at fp (Qp) decreases dramatically. To enhance Qp and suppress the spurious mode, the LWRs with busbars including only the top electrode (non-overlap busbars) and the LWRs with busbars incorporating both top and bottom electrodes (overlap busbars) are designed and fabricated. The LWR with 12 μm-wide overlap busbars exhibits a notable enhancement in Qp, elevating it from 553.76 to 1488.17 and suppresses the spurious mode simultaneously. This research introduces a promising approach to suppress the spurious mode and enhance the quality factor of Lamb wave resonators, thereby holding great potential for applications in sensors and mobile communication.

Design Optimization of Piezocomposites Using a Homogenization Model: From Analytical Model to Experimentation.

In the process of activating non-conductive smart-structures using piezoelectric patches, one possible method is to add a conductive layer to ensure electrical contact of both electrodes of the ceramic. Therefore, depending on the stiffness and the thickness of this layer, changes in the overall piezoelectric properties lead to a loss in the electromechanical coupling that can be implemented. The purpose of this work is to study the impact of this added electrode layer depending on its thickness. A model of the effect of this layer on the piezoelectrical coefficients has been derived from the previous approach of Hashimoto and Yamagushi and successfully compared to experimental data. This global model computes the variation of all the piezoelectric coefficients, and more precisely of k31 or d31 for various brass electrode volumes relative to the ceramic volume. A decrease in the lateral electromechanical coupling factor k31 was observed and quantified. NAVY II PZT piezoelectric transducers were characterized using IEEE standard methods, with brass electrode thicknesses ranging from 50 to 400 microns. The model fits very well as shown by the results, leading to good expectations for the use of this design approach for actuators or sensors embedded in smart-structures.

Systematic evaluation of the radial polarized piezoelectric ceramic micro-tube for high-temperature microfluidics

Piezoelectric ceramic micro-tube (PCMT) featuring quick response and driving displacement resolution has been widely applied in the microfluidic field. With more and more microfluidic applications being conducted in high temperatures, there is an increased demand for high-temperature PCMTs. However, few reports were focused on evaluating the performance of PCMTs especially in high-temperature conditions, which hinders its applications greatly. In this paper, a radial polarized high-temperature PCMT with an inner diameter (ID) of 0.75 mm, an outer diameter (OD) of 1.2 mm and a length of 15 mm was fabricated first. Scanning electron microscope (SEM) test shows that this ceramic tube presents a homogenous and dense microstructure. Impedance spectrum tests at different temperatures show that the effective electromechanical coupling factor (keff) of this PCMT remains stable from room temperature to 250 °C, indicating good high-temperature stability. Quasi-steady axial displacement tests executed by the instrument constructed by our group show that this PCMT represents a linear driving response under 100 V. Based on systematic evaluations, the PCMT was used to fabricate a piezoelectric high-temperature nozzle for generating high-frequency droplets, through which tin droplet targets with a repetition frequency of 20 kHz and a diameter of 100 μm was obtained at 250 °C. The successful application demonstrates that the PCMT which was evaluated systematically can be used in practical high-temperature applications.

Characterization of dielectric and piezoelectric responses in 0.76(Na0.5Bi0.5)TiO3-0.06BaTiO3-0.18(K0.5Bi0.5)TiO3 ceramics synthesized by the solid-state method

In this research, the authors explore the structural, dielectric, electrical insulating, electromechanical, and piezoelectric characteristics of ceramics that have been modified using BaTiO3 and (K0.5Bi0.5)TiO3.as key components. Specifically, they explore the composition (1-x-y)(Na0.5Bi0.5)TiO3-xBaTiO3-y(K0.5 Bi0.5)TiO3, where x (mol.%) varies between 0, 6, and NBT, and y (mol.%) varies between 0, 18, and KBT. These ceramics were fabricated using a solid-state synthesis technique. The optimized calcination temperature for achieving a pure perovskite phase was determined to be 1000 °C for a duration of 4 hours. The research involves a comprehensive analysis of the composition, microstructure, electrical insulating, and electromechanical characteristics of the ceramics. Rietveld analysis of X-ray diffraction (XRD) data was employed to accurately ascertain the morphotropic phase boundary (MPB) within this material. In this paper, we discuss the impact of crystallite size on the shifts in Raman band frequencies. Sintering at 1100 °C for 4 hours was found to enhance densification, with scanning electron microscopy (SEM) images illustrating a nearly uniform distribution of compact grains. Electrical insulating assessments demonstrate that each of the ceramics displays a scattered phase transition around the temperature Tm, with a diffusivity ranging from 1.4 to 1.8, and a shift of Tm towards elevated temperatures. Exceptional piezoelectric properties were observed at the morphotropic phase boundary (MPB), including a d33 value of 149 pC/N and electromechanical coupling factors kp of 0.297. These findings are attributed to the coexistence of rhombohedral and tetragonal phases, as well as precise grain size control. This research presents a novel approach to enhancing lead-free ferroelectric materials based on the composition 0.76(Na0.5Bi0.5)TiO3-0.06BaTiO3-0.18(K0.5Bi0.5)TiO3.

High‐performance bismuth titanate‐ferrite (Bi5Ti3FeO15) for high‐temperature piezoelectric applications

AbstractAdvancing the development of high‐temperature piezoelectric sensors requires high‐performance piezoelectric materials with high Curie temperatures, wherein the charge signals can be efficiently collected at elevated temperatures. The bismuth layer‐structured ferroelectric (BLSF) bismuth titanate‐ferrite (Bi5Ti3FeO15, BTF) has recently attracted considerable attention because of its high Curie temperature (TC) of ∼761°C. However, the piezoelectric properties of BTF‐based compounds have not been extensively investigated because of their extremely poor piezoelectric performances and low electrical resistivities at elevated temperatures. Herein, tungsten‐substituted BTF (BTF‐100xW) ceramics were synthesized using a solid‐state reaction method. X‐ray diffraction refinement results confirmed the lattice distortion of the BO6 octahedron, while piezoelectric force microscopy images verified an increase in the domain wall density with tungsten modification, both of which contribute to significant enhancement of the piezoelectric properties of BTF‐100xW as intrinsic and extrinsic contributions, respectively. Remarkably, BTF‐3W exhibits a high TC of 793°C and a large piezoelectric constant (d33) of 24.3 pC/N, which is over three times that of BTF (7.1 pC/N). Importantly, the substitution of tungsten decreases the concentration of oxygen vacancies, increases the direct current electrical resistivity, and improves the electrical homogeneity at high temperatures, resulting in extremely stable piezoelectric and electromechanical properties at high temperatures, with a high in‐situ relative d33 of &gt;90% at 400°C and a small variation in the electromechanical coupling factor (kp) of &lt;8% at temperatures up to 450°C. These results suggest that the tungsten‐substituted BTF is a potential candidate for high‐temperature piezoelectric ceramics, and is a promising material for applications in high‐temperature piezoelectric sensors.

SAW velocity reduction and spurious modes suppression on the layer structure

This paper discusses the use of the layered structure for the SAW velocity reduction. First, it is shown that the insertion of SiO2 is crucial between the piezoelectric layer and the base substrate to keep a large electromechanical coupling factor even when the SAW velocity is reduced. It is also shown that the use of a high-velocity substrate such as Si is also crucial for bringing spurious resonances much higher than the main resonance. The impact of Si orientation is also discussed. Next, suppression of transverse mode resonances and lateral leakage is studied. It is shown that the double busbar structure offers Q enhancement through good lateral energy confinement, and its combination with the piston design also gives good transverse mode suppression. Furthermore, discussions are extended to a strong spurious resonance that appears near the anti-resonance.

S0-like SAW mode resonator on LiNbO3/SiO2/SiC structure

Abstract This paper discusses the basic properties of a surface acoustic wave (SAW) mode like the zeroth-order symmetric (S0) Lamb mode in the LiNbO3/SiO2/SiC configuration in detail. At first, the influence of the SiO2 insertion is discussed, and it is shown that SiO2 insertion offers significant enhancement of the electromechanical coupling coefficient K 2 for the S0-like SAW mode without significant reduction of the phase velocity. Then, the discussion is extended to spurious resonance characteristics. It is shown that the dummy electrodes are not necessary in this case. Then, two kinds of piston design are applied for the transverse suppression, and their effectiveness is discussed.

Use of periodically slotted SiO2 in a layered surface acoustic wave structure for transverse mode suppression

This work demonstrates the applicability of periodically slotted SiO2 (PSS) structures (PSSs) for controlling the urface acoustic wave (SAW) slowness shape and eliminating the transverse modes in layered SAW structures represented by the Incredible High Performance SAW. The use of PSS comprising SiO2 blocks and air gaps provides larger acoustic anisotropy for slowness shape manipulation. The effect of PSSs on transverse mode suppression is revealed. The slowness curves and frequency responses with different structural parameters of PSS are calculated by FEM analysis. Then, an electrode is designed for further spurious resonance suppression. A hammer-head configuration and Si3N4 overlay are applied. It is shown that higher-order transverse modes in the passband were well suppressed without reduction of the electromechanical coupling factor.

Nonlinear effects and applications of AlN: A comprehensive physical formulation approach

Piezoelectric materials have nonlinear effects that can be used in 5G and IoT technologies. However, since most nonlinear problems in this area do not have analytic solutions, FEM simulations are an essential design tool. In this study, we have developed a stress-charge formulation for non-linear piezoelectric materials compatible with commonly used simulation tools in industry and research. FEM simulation results for AlN with three nonlinear phenomena are presented: variation of effective electrical permittivity, shift of the effective elasticity constants, and enhancement of electromechanical coupling factor. These simulations were conducted with the same material parameters, having great agreement with recent and important experimental results. The simulations allow us to deduce the values of the components of the high-order tensors for the first time as qr_331 = qr_333 = −1600 and g_333 = −80N/V m. The maximum percent errors obtained for the simulations of theeffective electrical permittivity and effective elasticity constants were 0.1% and 1.77%, respectively.

Improved electromechanical properties of Pb(Ni1/3Nb2/3)O3–PbZrO3–PbTiO3 ferroelectric ceramics via Sm-modification

Sm-modification has recently attracted widespread attention as an optimized method for enhancing the electromechanical properties of Pb-based perovskite ferroelectrics. The present study extends the application of Sm-modification to the Pb(Ni1/3Nb2/3)O3–PbZrO3–PbTiO3 (PNN-PZT) ceramics, aiming to improve their electromechanical properties. The impact of Sm-doping on the phase structure, microstructure, domain morphology, dielectric and piezoelectric properties was comprehensively investigated. The results demonstrate that the Sm-doping enhances the dielectric and piezoelectric properties while retaining competitive ferroelectric-paraelectric phase transition temperature (Tm). Notably, for the 2 mol% Sm-doped samples, a significant piezoelectric coefficient d33 of 1130 pC/N and a high Tm of 130 °C were achieved, accompanied by an improved dielectric constant (εr) and electromechanical coupling factor (kp). The comprehensive properties of Sm-doped PNN-PZT ceramics exceed the general trend observed in current Pb-based ferroelectric ceramics. This research confirms the effectiveness of the Sm-modification method in PNN-PZT systems, establishing it as a promising candidate for high-performance electromechanical applications.

Electromechanical sensitivity of ZnO thin films at high-pressure regime for SAW strain sensor applications

This paper employs Density Functional Theory (DFT) to investigate the influence of high hydrostatic pressure on the piezo-elastic properties of ZnO with a specific focus on its repercussions for Surface Acoustic Wave (SAW) devices. Our findings reveal a significant enhancement in the piezoelectric coefficient d33 under high-pressure conditions, particularly reaching 13.09 pC/N at 8 GPa compared to the unpressurized state. This noteworthy improvement directly contributes to an overall enhancement in the electromechanical coupling coefficients (K2), emphasizing for the first time the potential of high-pressure conditions to positively influence the performance of ZnO/Al2O3 SAW devices. To confirm that, we utilized the Finite Element Method (FEM) to analyze the performance of a Surface Acoustic Wave (SAW) device based on ZnO for both propagating modes, namely Rayleigh and Sezawa, under elevated pressure conditions. We observed an improvement in the electromechanical coupling factor (K2) for the Rayleigh and the Sezawa modes, with enhancements of approximately 23% and 52%, respectively, under an applied pressure of 8 GPa compared to 0 GPa. Furthermore, we found that the Sezawa mode exhibits eight times greater sensitivity to pressure variations compared to the Rayleigh mode. These findings provide designers with a better understanding of the electromechanical responsivity and sensitivity of the ZnO-SAW devices to high level of applied pressure.

Characterization of high-field properties of 0.28PIN-0.42PMN-0.30PT single crystal/epoxy 1–3 composite for acoustic transducer applications

The (1-x-y)Pb(In1/2Nb1/2)O3-yPb(Mg1/3Nb2/3)O3-xPbTiO3 (PIN-PMN-PT) single crystal/polymer composites have been widely employed in high-performance acoustic transducers, while the high-field properties characterization of the piezoelectric composites is still relatively lacking. In this research, a high-field impedance spectrum characterization system was used to investigate high-field properties of a 0.28PIN-0.42PMN-0.30PT single crystal/epoxy 1–3 composite. The impedance spectra of the PIN-PMN-PT composite thin plate in thickness resonance mode were measured under the constant-voltage mode with different voltage amplitudes. By measuring the resonance and antiresonance frequencies, the ac electric field dependence of the properties of the composite plate were investigated. The experimental results showed that both the resonance frequency and antiresonance frequency decreased gradually as the driving electric field was increased from 5.13 Vpp/mm to 51.3 Vpp/mm, but the impedance spectra did not become distorted in this electric field range. By analyzing the impedance spectra, it was found that the electromechanical coupling factor kt and the piezoelectric coefficient d33 increased with the rising field, while the elastic stiffness c33D and the mechanical quality factor Q both decreased with the field. Under a high ac field, compared to PZT8 1–3 piezoceramic composites, the PIN-PMN-PT single crystal 1–3 composites were found to have more superior electromechanical performances such as higher kt and d33 values. These results are helpful for the design and application of acoustic transducers.

Novel Piezo-active 2–1–2 Composites with Sets of Large Hydrostatic Parameters

A 2–1–2 composite with two single-crystal components is studied for the first time to highlight large hydrostatic piezoelectric coefficients dh * and gh *, figure of merit dh *gh *, and electromechanical coupling factor kh *. Each 2–1–2 composite contains layers of domain-engineered [011]-poled relaxor-ferroelectric (1–x)Pb(Zn1/3Nb2/3)O3 – xPbTiO3 single crystal (x = 0.0475–0.09) and heterogeneous layers being systems of aligned piezoelectric Li2B4O7 single crystal rods in polyethylene, and these rods have an elliptic cylindrical shape. New diagrams show the volume-fraction ranges wherein large values of dh *> 10−9 C/N, dh *gh *> 2.10−10 Pa−1 and kh *≈ 0.5–0.6 are observed.

Vibration control of a cantilever plate immersed in water using shunted piezoelectric patches

Minimizing structural vibrations is an important engineering requirement in many applications. This study theoretically investigates the vibration control of an in-water cantilever plate using piezoelectric patches and resonant shunt circuits (including a resistance R and an inductance L in series or parallel). To do this, an analytical model for predicting the point-forced vibration response of a fluid-loaded cantilever plate with two piezoelectric patches is developed. The electromechanical coupling factor and optimum values for R and L are then estimated by considering the dynamics of the system in short-circuit and open-circuit conditions. The effect of piezoelectric patch size, location and electromechanical properties on the vibration response of the plate is also investigated through numerical examples. The results from this study show that optimized piezoelectric patches could provide a significant vibration reduction for underwater applications.

Structural and electrical properties of PLZT x/65/35 ceramics prepared via mechanical activation method near the morphotropic phase boundary

This paper reports the effect of lanthanum addition on the structural and electrical properties of (Pb1-xLax)(Zr0.65Ti0.35)O3 (PLZT x/65/35, x = 8%,10%,12%,15%) ceramics near the morphotropic phase boundary. Studies were conducted on the PLZT x/65/35 ceramics synthesized via a combinatorial approach of high-energy ball milling (mechanical activation method) followed by Cold Isostatic Pressing (CIP). Due to the application of CIP, PLZT ceramics exhibited improved density and a closely packed microstructure. The SEM analysis showed that PLZT x/65/35 ceramics exhibited an increase in grain size with higher concentrations of La3+ ions. Room temperature X-ray diffraction results revealed the formation of perovskite PLZT phase. The investigation on temperature-dependent dielectric, ferroelectric properties of PLZT x/65/35 ceramics provided experimental confirmation of structures cited in XRD analysis. Among all the compositions, PLZT 8/65/35 samples showed a well saturated, uniform P–E hysteresis loop with a high remanent polarization (Pr). Poled PLZT 8/65/35 samples displayed electric field induced large strains with limited hysteresis. Piezoelectric charge coefficients (d33), electromechanical coupling factors (kp, k33, k31) were determined for poled PLZT x/65/35 ceramics and it was found that PLZT 8/65/35 ceramics reveal properties superior to other compositions. Furthermore, the unipolar strain, Pr, d33, kp, k33, k31 values of PLZT 8/65/35 composition exceeded the previously reported ones for the same composition prepared via sol-gel synthesis technique.