Effective Electromechanical Coupling Factor Research Articles

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.

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.

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.

Design and Performance Enhancement of a Piezoelectric Micromachined Ultrasonic Transducer Based on NBBT Lead-Free Piezoelectric Single-Crystal Thin Film

Piezoelectric micromachined ultrasonic transducers (PMUTs) have attracted widespread attention due to their high performance, miniaturization, and easy integration with semiconductor processes. In this paper, a PMUT device based on high-performance and lead-free Na0.5Bi0.5TiO3-BaTiO3 (NBBT) piezoelectric single-crystal thin films was designed for the application of medical high-frequency ultrasonics. Three-dimensional modeling and analysis of PMUT elements on the proposed structure were performed via the finite element method. The relationship between structure configuration in terms of the top electrode and the cavity shape of the bottom was studied. The PMUT properties and its device performance, including resonant frequency, effective electromechanical coupling factor (keff2), and the static sensitivity of different device structures, were analyzed. In addition, by rotating the Euler Angle γ of the NBBT piezoelectric single-crystal film, the static sensitivity and keff2 of the model are improved to 1.34 when γ is rotated to 45 ± 5°. It was shown that the PMUT using rotated NBBT demonstrated an enhanced relative pulse-echo sensitivity of −46 dB and a bandwidth of 35% when the reflective surface was 200 μm. We conclude that the PMUT in accordance with an NBBT piezoelectric single-crystal film designed by simulation offers a high frequency, larger keff2, and high sensitivity, which provides application prospects in high-resolution and high-frequency medical ultrasonic imaging.

Onset and stabilization of delay-induced instabilities in piezoelectric digital vibration absorbers

The stability of a piezoelectric structure controlled by a digital vibration absorber emulating a shunt circuit is investigated in this work. The formalism of feedback control theory is used to demonstrate that systems with a low electromechanical coupling are prone to delay-induced instabilities entailed by the sampling procedure of the digital unit. An explicit relation is derived between the effective electromechanical coupling factor and the maximum sampling period guaranteeing a stable controlled system. Since this sampling period may be impractically small, a simple modification procedure of the emulated admittance of the shunt circuit is proposed in order to counteract the effect of delays by anticipation. The theoretical developments are experimentally validated on a clamped-free piezoelectric beam.

Lead-Free AE Sensor Based on BZT-BCT Ceramics.

In this study, an acoustic emission (AE) sensor was fabricated using lead-free Ba(Zr0.2Ti0.8)O3–0.5(Ba0.7Ca0.3)TiO3 (BZT–BCT) ceramics. The acoustic and electromechanical properties of the AE sensor were determined by the shapes of the piezoelectric ceramics. To optimize the AE sensor performance, the shapes of the ceramics were designed according to various diameter/thickness ratios (D/T) = 0.5, 1.0, 1.5, 2.0, 2.5, 3.0. The BZT–BCT ceramic with D/T = 1.0 exhibited excellent values of a piezoelectric charge coefficient (d33), piezoelectric voltage coefficient (g33), and electromechanical coupling factor (kp), which were 370 (pC/N), 11.3 (10−3 Vm/N), and 0.58, respectively. Optimum values of resonant frequency (fr) = 172.724 (kHz), anti-resonant frequency (fa) = 196.067 (kHz), and effective electromechanical coupling factor (keff) = 0.473 were obtained for the manufactured BZT–BCT ceramic with D/T = 1.0. The maximum sensitivity and frequency of the AE sensor made of the BZT–BCT ceramic with a D/T ratio of 1.0 were 65 dB and 30 kHz, respectively.

A dual-frequency piezoelectric micromachined ultrasound transducer array with low inter-element coupling effects

This paper presents a dual-frequency piezoelectric micromachined ultrasonic transducer (PMUT) line array with low crosstalk level, which was fabricated on silicon-on-insulator (SOI) wafers with sputtered piezoelectric thin film (PZT) and Si diaphragm structure. The obtained array consists of 120 of 0.77 MHz and 192 of 2.30 MHz PMUT units in total with minimum interspace of 50 μm. Due to the high piezoelectric coefficient of PZT, the PMUT shows high transmitting sensitivity in air and good effective electromechanical coupling factor. The displacement sensitivities are assessed to be 595 nm V−1 and 112 nm V−1 at the resonant frequencies of 0.77 MHz and 2.30 MHz respectively in air. To reduce the vibration coupling, rectangular grooves in the bottom silicon are designed between the adjacent line elements, and the PMUT units in the array are arranged in a mis-aligned style. Modal analysis for the 0.77 MHz units indicates neighbouring coupling-vibration decreases greatly from 44.5% to 14.8% of the excited vibration when the excited line is driven at 4Vpp, which proves both the grooves and the mis-aligned ranking are effective for coupling effect reduction. Moreover, results indicate the coupling effect between different frequencies can be ignored due to their inherent resonance characteristics. The sound pressures for a single 0.77 MHz line element and 2.30 MHz line element are evaluated to be 53 kPa and 73 kPa at a distance of 1 cm in water. This high performance dual-frequency PMUT line array makes some high resolution imaging methods possible based on PMUT technology, such as those of dual-frequency, total focus.

Piezoelectric-on-Silicon Square Wine-Glass Mode Resonator for Enhanced Electrical Characterization in Water

We describe a piezoelectric square wine-glass (SWG) mode micromechanical resonator as a unique device topology for liquid phase sensing applications that offers enhanced quality (Q)-factor in water over other common contour modes. We show a Q-factor in water of 377 for 14.08-MHz SWG mode resonator (mean of multiple measurements), which is one of the highest Q-factors among piezoelectric resonators tested when covered in a fluid. We show that the Q-factor in water of the SWG mode increases much more significantly with a reduction in resonator size relative to the square-extensional (SE) mode, such that the Q-factor the SWG mode can be almost twice of the SE mode. We present an analytical model for the mode shape of the proposed SWG resonators and their effective electromechanical coupling factor $({k}_{\text {eff}}^{{2}})$ . Due to the enhanced Q-factor in water, reasonable ${k}_{\text {eff}}^{{2}}$ , and feedthrough cancelation (using fully differential transduction with the fluid loaded from the backside of the device), we show that a strong resonant peak of 29.8 dB is obtainable in water.

Boosting MEMS Piezoelectric Transformer Figures of Merit via Architecture Optimization

This letter documents the design and demonstration of microelectromechanical systems (MEMS) piezoelectric transformers with a measured boost in effective figure of merit as high as 4.2X. This boost is enabled by an architecture approach, which takes transformers with figures of merit limited by the inherent effective electromechanical coupling factor, ${k}_{\textsf {eff}}^{\textsf {2}}$ , and device quality factor, and provides enhanced effective transformer figures of merit through architecture optimization. This is enabled by a parallel input series out transducer architecture inspired by prior approaches with multi-layer bulk piezoelectric transformers but first demonstrated here in MEMS with discrete transformers fabricated with ~45-MHz lead-zirconate-titanate (PZT)-on-silicon electromechanical resonators.

Electrical properties of (Na,K,Li)(Nb,Sb,Ta)O3 ceramics for multilayer-type piezoelectric actuator

ABSTRACTIn this study, lead free CuO added (Na0.525K0.4425Li0.0375)(Nb0.8975Sb0.065Ta0.0375)O3 ceramics (NKL-NST) and multilayer actuator using the ceramics were fabricated and their physical and displacement properties investigated. The excellent physical properties of electromechanical coupling factor (kp) = 0.4159, piezoelectric constant (d33) = 166pC/N and mechanical quality factor (Qm) = 322 were obtained from the 2.5mol% CuO doped (Na0.525K0.4425Li0.0375)(Nb0.8975Sb0.065Ta0.0375)O3 ceramics sintered at low temperature of 1,000°C for 3 h.The multilayer-type piezoelectric actuators (abbreviated as MTPA) were fabricated with NKL-NST + 2.5mol% CuO ceramics with excellent piezoelectric properties by tape casting methods. The density and effective electromechanical coupling factor (keff) of manufactured haptic piezoelectric actuator were 4.4 g/cm3 and 0.225, respectively. Total-displacement of central part of the actuator was increased with increasing input voltage. With input voltage and driving frequency of 20 V and 420 Hz, the input current, consumption of electrical power and total-displacement under zero force were 324 µA, 5.405 mW and 36 µm, respectively. Whereas, under 2.8 g force, the input current was 358 µA, and electrical power consumption of 4.554 mW and total-displacement of 18 µm under 20 V and150 Hz appeared, respectively.

Gravimetric sensors operating at 1.1\u2009GHz based on inclined c-axis ZnO grown on textured Al electrodes

Shear mode solidly mounted resonators (SMRs) are fabricated using an inclined c-axis ZnO grown on a rough Al electrode. The roughness of the Al surface is controlled by changing the substrate temperature during the deposition process to promote the growth of inclined ZnO microcrystals. The optimum substrate temperature to obtain homogeneously inclined c-axis grains in ZnO films is achieved by depositing Al at 100 °C with a surface roughness ~9.2 nm, which caused an inclination angle of ~25° of the ZnO c-axis with respect to the surface normal. Shear mode devices with quality-factors at resonance, Qr and effective electromechanical coupling factors, {{boldsymbol{k}}}_{{bf{eff}}}^{{bf{2}}}, as high as 180 and 3.4% are respectively measured. Mass sensitivities, Sm of (4.9 ± 0.1) kHz · cm2/ng and temperature coefficient of frequency (TCF) of ~−67 ppm/K are obtained using this shear mode. The performance of the devices as viscosity sensors and biosensors is demonstrated by determining the frequency shifts of water-ethanol mixtures and detection of Rabbit immunoglobin G (IgG) whole molecule (H&L) respectively.

Validity evaluation of ScxAl1−xN material constants based on SAW characteristics

This paper is aimed at examining the validity of material constants reported for use in surface acoustic wave (SAW) device simulations. First, based on the full set of material constants calculated by first principle, bulk acoustic wave velocities are calculated for ScxAl1−xN and compared with published experimental results. Then, the effects of the ScxAl1−xN material constants with different Sc content on acoustic characteristics are calculated and the influence of shear vibrations on SAW characteristics are recognized. Then, a series of SAW devices are fabricated on ScxAl1−xN film/Si substrate structure with various Cu and ScAlN thicknesses hCu and hScAlN, respectively, and measured variations of phase velocity V and effective electromechanical coupling factor with these parameters are compared with the calculation. The fairly well-agreed results indicate a reliable set of ScxAl1−xN material constants for SAW device simulations.

Enhancement of effective electromechanical coupling factor by mass loading in layered surface acoustic wave device structures

This paper describes a drastic enhancement of the effective coupling factor by mass loading in layered surface acoustic wave (SAW) device structures such as the ScAlN film/Si substrate structure. This phenomenon occurs when the piezoelectric layer exhibits a high acoustic wave velocity. The mass loading decreases the SAW velocity and causes SAW energy confinement close to the top surface where an interdigital transducer is placed. It is shown that this phenomenon is obvious even when an amorphous SiO2 film is deposited on the top surface for temperature compensation. This enhancement was also found in various combinations of electrode, piezoelectric layer, and/or substrate materials. The existence of this phenomenon was verified experimentally using the ScAlN film/Si substrate structure.

Theoretical and experimental analysis of a piezoelectric plate connected to a negative capacitance at MHz frequencies

In this paper, a theoretical and experimental study of the electric impedance of a piezoelectric plate connected to a negative capacitance is performed in the MHz frequency range. The negative capacitance is realized with a circuit using current conveyors (CCII+). This circuit allows us to achieve important values of negative capacitance, of the same order of the static capacitance of the piezoelectric plate studied. Mason’s model is considered for the theoretical characterization of the piezoelectric plate connected to the negative capacitance circuit. The experimental results show a large tunability of the frequency of the piezoelectric parallel resonance over a range of 1.1 MHz to 1.28 MHz. Moreover, according to the value of the negative capacitance, the effective electromechanical coupling factor of the piezoelectric plate is evaluated. With a very good agreement with the theoretical estimation, an increase of approximately 50% of the effective electromechanical coupling factor is experimentally measured.

Exact analysis of radial vibration of functionally graded piezoelectric ring transducers resting on elastic foundation

An exact solution is obtained to analyze the electromechanical characteristics of functionally graded piezoelectric ring transducers in radial vibration. The material properties of piezoelectric ring transducers are assumed to be graded in power-law distribution form along the radial direction. The material inhomogeneity index of mass density can be different from that of the elastic, piezoelectric and dielectric constants. Analytical solution is obtained in terms of Bessel functions. The characteristic equations governing the resonant and anti-resonant frequencies are presented. Numerical results are depicted graphically to illustrate the effect of material inhomogeneity index and elastic foundation stiffness on the radial vibration characteristics, such as resonant/anti-resonant frequencies, effective electromechanical coupling factor and model shape.

Temperature and Stress Induced Electromechanical Coupling in Relaxor Ferroelectric Compounds

Temperature and stress induced electromechanical coupling studies were carried out for relaxor ferroelectric ceramics Ba(NdxTi(1-2x)Nbx)O3, Ba(NdyTi(1-2y)Nby)O3 and [Ba(Nd0.1Ti0.8Nb0.1)O3](1-z)[Na0.5Bi0.5TiO3]z. The thickness mode of electromechanical coupling and effective electromechanical coupling factors obtained from capacitance measurements were in the range 0.40–0.78 depending up on the compound, its composition and temperature. From modulus measurements the thickness and effective mode of electromechanical coupling factors obtained are in the range 0.9960–0.9998 depending up on the composition z.

Design and Fabrication of S<sub>0</sub> Lamb-Wave Thin-Film Lithium Niobate Micromechanical Resonators

Commercial markets desire integrated multifrequency band-select duplexer and diplexer filters with a wide fractional bandwidth and steep roll-off to satisfy the ever-increasing demand for spectrum. In this paper, we discuss the fabrication and design of lithium niobate (LN) thin-film S0 Lamb-wave resonators on a piezoelectric-on-piezoelectric platform. Filters using these resonators have the potential to fulfill all the above requirements. In particular, we demonstrated one-port high-order S0 Lamb-wave resonators with resonant frequencies from $\sim 400$ MHz to $\sim 1$ GHz on a black rotated y-136 cut LN thin film. The effective electromechanical coupling factor ( $k_{eff}^{2}$ ) ranges from 7% to 12%, while the measured quality factor ranges from 600 to 3300. The highest $k_{eff}^{2} \times Q$ achieved on this chip is 194, significantly surpassing contour mode resonators manufactured in other technologies. [2014-0280]

Theoretical Simulation and Optimization on Material Parameters of Thin Film Bulk Acoustic Resonator

The resonance frequency,fs, and the effective electromechanical coupling factor,keff2, of thin film bulk acoustic resonators (FBARs) are derived by transfer matrix method. The effects of thickness and density of electrode onfsandkeff2with different piezoelectric layers are investigated by numerical calculation method. The results show that thickness and density of electrode affectfsobviously, especially in large thickness and density area. Moreover, the effects of thickness, density, and acoustic velocity of electrode onkeff2of FBAR were also studied. The results show that there is a maximumkeff2corresponding to the composition of thickness and density of electrode which is about 20% over the original electromechanical factor of piezoelectric film.keff2is in the direct proportion to the densityρeandveof electrode, respectively. The electrode thickness affectskeff2small with highve; moreover, whenveis high enough, thenkeff2has almost nothing to do withde.keff2always rises with electrode thickness first and then descends with its rising, and the thickness corresponding to the maximumkeff2is different with different electrode, but it always locates in the special area. All above results indicate that the thickness, density, and acoustic velocity of electrode are so important that these results can be applied to design FBAR.

2E3-3 Enhancement of Effective Electromechanical Coupling Factor by Mass Loading in Layered SAW Device Structures

2E3-3 Enhancement of Effective Electromechanical Coupling Factor by Mass Loading in Layered SAW Device Structures