Electromechanical Quality Factor Research Articles

Temperature-dependent dielectric and electromechanical properties of co-modified calcium bismuth titanate (CaBi4Ti4O15) ceramics

Bismuth layer-structured ferroelectrics (BLSFs), Aurivillius-type ceramics, are of great interest primarily due to their exceptionally high Curie temperature (Tc), rendering them invaluable in various applications such as sensors, actuators, transducers, and micro-electro-mechanical systems designed for elevated temperature operations, including ferroelectric Random-Access Memory applications. This study delves into the dielectric and electromechanical properties of Cobalt-modified Calcium Bismuth Titanate (CaBi4Ti4O15, CBT) (CBT-xCo, with x = 2, 4, and 6 mol%) prepared using a conventional solid-state route followed by sintering. By incorporation of Co, insignificant structural changes were observed, disclosed by X-ray Diffraction analysis. Scanning Electron Microscope micrographs unveiled highly anisotropic grains. The sintered density measured by Archimedes method was maximum for x = 6 mol% with value of 99.1 %. A temperature-dependent dielectric study disclosed that the Curie temperature of the CBT ceramics improved with the increase in Co concentration. Notably, CBT-4Co exhibited the lowest dielectric loss of 0.0967 at 1 MHz and the highest resistivity value of 0.1975 × 105 (Ω cm) at a temperature of 775 °C. Moreover, the electromechanical coupling (kp) and mechanical quality factor (Qm) measured at elevated temperatures unveiled distinctive properties, asserting the potential of the ceramics for high-temperature piezoelectric applications up to 450 °C. CBT-4Co demonstrated the highest kp, with a negligible variation at high temperature, although Qm declined. Results confirmed that CBT-4Co stands distinguished showcasing high Tc, minimal dielectric loss, and consistent electromechanical properties making it the prime candidate for electromechanical applications spanning the gamut from room temperature to elevated temperatures.

Functionality in frequency tuning of magnetoelectric heterostructure integrated highly flexible bulk acoustic wave resonator

Functional flexible piezo-resonators are of vital interest for designing micro-electrometrical system (MEMS) based high-frequency wearable devices. The magnetoelectric (ME) heterostructure comprising highly magnetostrictive Ni–Mn–In and piezoelectric AlN films was fabricated over flexible substrates to develop the bulk acoustic wave (BAW) resonator. The BAW resonators fabricated over Ni and Kapton substrates show the fundamental resonance at ∼5.535 and 5.400 GHz, respectively. The comparative study of frequency tuning for both resonators has been executed in the presence of a dc magnetic field. A larger frequency shift (ΔfR) of ∼540 MHz was detected at 1200 Oe for a device fabricated over Ni with a sensitivity of ∼5.4 Hz/nT. However, it is 360 MHz in the case of Kapton, with a sensitivity of ∼3.0 Hz/nT. Moreover, the BAW resonator over the magnetostrictive Ni substrate shows a higher tunability of ∼11.4% compared to ∼8.5% for the resonator fabricated over non-magnetostrictive Kapton. The equivalent modified Butterworth–Van Dyke circuit parameters have been extracted by fitting the experimental data with and without an external magnetic field using advanced design system. The effect of an external magnetic field has been thoroughly investigated on device parameters, such as electromechanical coupling coefficient (K2), acoustic velocity, quality factor (Q), and figure of merit. The anisotropic functionality of the fabricated resonator has been studied by measuring the tunability of the resonator in parallel and perpendicular magnetic fields. The present study motivates the incorporation of flexible magnetostrictive substrates for futuristic multifunctional MEMS magnetic field sensor applications.

Analysis of variance (anova) of the influence of molybdenum and cobalt additives on piezoelectric, dielectric and ferroelectric properties of Pb(Zr0.52Ti0.48)O3

This study aims to determine how molybdenum and cobalt additives affect the structural and electrical characteristics of Pb(Zr0.52Ti0.48)O3. by substituting zirconate and titanate with molybdenum and cobalt, individually or in combination, in the range of 0–2%. The powders were initially made in order to achieve this via a wet chemical process. They were then calcined at 800 °C for 4 h. The calcined powders' XRD examination indicates that the tetragonal phase rapidly diminishes with dopant concentration and concurrently gives way to rhombohedral phase. With an increase in dopant concentration, a SEM analysis of sintered discs showed a considerable change in grain size initially at the Zr site. Detailed investigations of the PZT's piezoelectric properties Significant changes in the piezoelectric charge coefficient, electromechanical coupling coefficient, resonant frequency, and mechanical quality factor can be seen in the samples that were created and examined. Analysis of Variance was used to evaluate the impact of additives on resonance frequency, and the results revealed that the addition of molybdenum and cobalt has a significant impact on resonance frequency.

Texture-based ferroelectric hardening in Na1/2Bi1/2TiO3 -based piezoceramics

${\mathrm{Na}}_{1/2}{\mathrm{Bi}}_{1/2}\mathrm{Ti}{\mathrm{O}}_{3}$-based (NBT-based) ceramics offer a viable option to replace lead-based materials for high-power applications as they are characterized by a stable mechanical quality factor with increasing vibration velocity in comparison to lead-based piezoceramics. Recently, the minor and stable extrinsic contributions were revealed as the origin for the stability of the mechanical quality factor with increasing vibration velocity. This work identifies the very unusual high poling degree as cause for the small extrinsic contributions. To this end, complete pole figure densities have been quantified and correlated to the piezoelectric coefficient and electromechanical quality factor. This hypothesis is further strengthened by correlating the piezoelectric constant (sum of intrinsic and extrinsic contributions) with the remanent polarization (correlates to remanent texturing degree). In order to assess a full picture of NBT-based piezoceramics, $0.94{\mathrm{Na}}_{1/2}{\mathrm{Bi}}_{1/2}\mathrm{Ti}{\mathrm{O}}_{3}\text{\ensuremath{-}}0.06\mathrm{BaTi}{\mathrm{O}}_{3}$ has been considered with and without Zn doping and with quenching. It is compared to $0.79{\mathrm{Na}}_{1/2}{\mathrm{Bi}}_{1/2}\mathrm{Ti}{\mathrm{O}}_{3}\text{\ensuremath{-}}0.21\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}_{1/2}{\mathrm{Bi}}_{1/2}\mathrm{Ti}{\mathrm{O}}_{3}$ with and without Mg doping. Finally, a contrast to soft $\mathrm{Pb}({\mathrm{Zr}}_{1/2}{\mathrm{Ti}}_{1/2}){\mathrm{O}}_{3}$ (PZT) flushes out the impact of domain wall motion on the piezoelectric coefficient and the electromechanical quality factor. Whereas a PZT-based reference material exhibits a linear increase in the piezoelectric constant with increasing remanent polarization, the NBT-based materials deviate from the linear trend, indicating a decrease in extrinsic contributions.

Secondary phase softening effect in PZT‐based ceramics by introducing the random electric fields

AbstractIn this work, the random electric fields are constructed in the hard PZT ceramics by adding the ZnO particles as a secondary phase to tune the piezoelectric properties and losses. It is found that the internal bias electric field existing in the hard PZT ceramics has been tuned successfully by the random electric fields and its value reduces with the increased ZnO content. As a consequence, the piezoelectric constant d33 reaches up to 483 pC/N in the PZT/0.75 wt%ZnO composite, which is much higher than that of the hard PZT matrix. In the meantime, the electromechanical quality factor Qm, dielectric loss tan δ, and Curie temperature TC for this composite are about 1109, 0.55%, and 279°C, respectively. The promoted d33 is attributed to the small domain size and reduced internal bias electric field, whereas the low losses (large Qm and low tan δ) can be put down to the still existing nonzero internal bias electric field.

Fabrication and characterization of hybrid bulk and surface acoustic wave resonators with Ag/patterned-AlN/Mo/diamond/Si layered structure

Hybrid bulk acoustic wave and surface acoustic wave (BAW/SAW) devices attract extensive interests due to their high electromechanical coupling coefficient and quality factor. In this study, longitudinal BAW coupled SAW resonators with piezoelectric AlN inter-digital transducers (IDT) were simulated and fabricated on diamond substrates to increase the working frequency as well. The simulated figure of merit value is 104, 123 % improved comparing with the corresponding metal IDT of 46.5. The frequency response spectrum of single port reflection (S11) shows dominant harmonic resonance at 913 MHz with electromechanical coupling coefficient of 2.16 % and quality factor of 913. These results indicate mutual transductions between BAW and SAW occur with sufficient efficiency in hybrid structures, which is analyzed and interpreted by equivalent acoustic impedance theory.

Rayleigh waves in nonpolar Al0.7Sc0.3N(112¯0) films with enhanced electromechanical coupling and quality factor

This work reports on the growth of 1 µm nonpolar a-plane Al0.7Sc0.3N(112¯0) thin films on an r-plane sapphire Al2O3(11¯02) via magnetron sputter epitaxy. The electro-acoustic properties of the film structures were characterized using surface acoustic wave (SAW) resonators. Measured electrical responses were found to be strongly anisotropic in terms of the wave propagation direction. We identified a sagittal polarized Rayleigh wave mode with large coupling (keff2= 3.7%), increased phase velocity (v= 4825 m/s), as well as high quality factor (Q > 1000) for SAW propagation along the c-axis [0001] and normalized thicknesses h/λ=0.2. Finite element method simulations using electro-acoustic properties of Al0.7Sc0.3N obtained from the density functional theory reproduce our experimental results.

Coherent Precipitates with Strong Domain Wall Pinning in Alkaline Niobate Ferroelectrics.

High-power piezoelectric applications are predicted to share approximately one-third of the lead-free piezoelectric ceramic market in 2024 with alkaline niobates as the primary competitor. To suppress self-heating in high-power devices due to mechanical loss when driven by large electric fields, piezoelectric hardening to restrict domain wall motion is required. In the present work, highly effective piezoelectric hardening via coherent plate-like precipitates in a model system of the (Li,Na)NbO3 (LNN) solid solution delivers a reduction in losses, quantified as an electromechanical quality factor, by a factor of ten. Various thermal aging schemes are demonstrated to control the average size, number density, and location of the precipitates. The established properties are correlated with a detailed determination of short- and long-range atomic structure by X-ray diffraction and pair distribution function analysis, respectively, as well as microstructure determined by transmission electron microscopy. The impact of microstructure with precipitates on both small- and large-field properties is also established. These results pave the way to implement precipitate hardening in piezoelectric materials, analogous to precipitate hardening in metals, broadening their use cases in applications.

A Three-Dimensional Finite Element Analysis Model of SAW Torque Sensor with Multilayer Structure

A three-dimensional finite element analysis model of surface acoustic wave (SAW) torque sensor based on multilayer structure is proposed in this paper. Compared with the traditional saw torque sensor with quartz as piezoelectric substrate, the SAW torque sensor with multilayer structure has the advantages of fast propagation speed and high characteristic frequency. It is a very promising torque sensor, but there is very little related research. In order to successfully develop the sensor, it is essential to understand the propagation characteristics and torque sensing mode of SAW in multilayer structure. Therefore, in this study, we first established a multi-layered finite element analysis model of SAW device based on IDT/128° Y-X lithium niobate/diamond/Si (100). Then, the effects of different film thicknesses on the characteristic frequency, electromechanical coupling coefficient, s parameter, and mechanical quality factor of SAW device without changing the wavelength are analyzed. Then, based on the finite element analysis, a three-dimensional research model of a new SAW torque sensor suitable for small diameter torsion bar (d = 10 mm) is established, and the relationship between saw device deformation and torque under the condition of small torque (±40 Nm) is tested. The shape variable is introduced into the finite element analysis model of multi-layer SAW device. Finally, the relationship between saw torque sensor with multi-layer structure and torque is established by using the deformation relationship, which shows the perfect curve of sensor performance.

Effects of radial stress on piezoelectric ceramic tubes and transducers.

Static analysis is performed for fiber windings to quantitatively control the radial stress at the outer radius of the piezoelectric ceramic tube. The radial stress is verified both experimentally and theoretically, and the dependence of the resonant and material properties of the piezoelectric ceramic tubes on the radial stress is clarified. The resonance frequencies and dielectric loss remain relatively stable, but the relative permittivity and the short circuit elastic constant decrease with the radial stress. The variations of the increased bandwidth and decreased electromechanical coupling coefficient (k31), piezoelectric constant (d31 and g31), and mechanical quality factor (Qm) are associated with the height-to-radius ratio. The properties of three cylindrical transducers applied with various radial stress show similar change tendencies, and a difference of 0.34 MPa radial stress results in a variation of approximately 13 in the bandwidth, 14 in Qm, 15 in k31, d31, and g31, and 16 in the amplitude of the first pulse. These results suggest that the consistency of the radial stress is essential, and it should be relatively small. These findings guide the design and preparation of the enhanced transducer.

Finite element simulation and characterization of one-port heterostructured surface acoustic wave resonator

The research work presents the study of a heterostructured surface acoustic wave (SAW) resonator consisting of an interdigital transducer (IDT), lithium niobate (LN), and silicon (Si) substrate. In the proposed structure, Silicon is the base substrate, above it layer of LN is placed then IDT is designed on it. The presented analysis includes the variation of the quality factor and electromechanical coupling coefficient with the change in the width of the piezoelectric layer. The electromechanical coupling coefficient (K 2), quality factor (Q-factor), velocity, resonance, admittance, and anti-resonance frequency have been studied for the thickness of the different layers of LN film. The higher quality factor of one port SAW devices reduces the energy loss and the K 2 of the devices indicates faster energy conversion. The Q-factor and K 2 are found to be depending on the thickness of LN, resonance, and anti-resonance frequency.

Microwave Acoustic Devices: Recent Advances and Outlook

This paper presents a short review of the microwave acoustics area, where exciting material innovations and performance advancements have been made in the past decade. The ever-growing demand for more sophisticated passive signal processing functions on-chip has fueled these developments. As a result, microwave acoustic devices have maintained performance leadership in mobile applications. By evaluating three fundamental parameters, namely electromechanical coupling (k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), quality factors, and frequency scalability, of microwave acoustics, this paper aims to, extensively but not exhaustively, capture the rationales behind approaches achieving higher performance microsystems. Outlooks for different material systems and addressing their underlying challenges are also offered in hopes of establishing a balanced roadmap for future microwave acoustics development.

Highly Enhanced Electro-acoustic Properties of YAlN/Sapphire Based Surface Acoustic Wave Devices for Next Generation of Microelectromechanical Systems

The characteristics and performances of SAW devices based on YxAl1―xN/Sapphire are demonstrated. The electromechanical properties such as elastic, dielectric and piezoelectric constants of YxAl1―xN crystals with (0≤ x ≤ 0.375) are calculated by using first-principles calculations within the new Perdew-Burke-Ernzerhof-sol functional. Analysis of the elastic constants indicates that wurtzite YxAl1―xN are elastically stable for the full range of Y concentrations. The mechanical moduli (bulk modulus B, Young modulus Y, shear modulus G) are found to decrease by increasing Y contents. The 3D contours of surface anisotropy show that wurtzite YxAl1―xN is anisotropic material which slightly decreases with yttrium composition. We observed a decrease in Debye temperature ΘD and sound velocities as yttrium increases. Moreover, the piezoelectric coefficients are found to be d33= 17.5 pC/N, d15= ―11.07 pC/N and d31= ―8.65 pC/N for Y0.375Al 0.625N, which are respectively ∼ 300 %, ∼ 400 % and ∼ 370 % higher than that of pure AlN-crystal. The dielectric constants (ε11, ε33) increase from (3.7, 5.1) for AlN to (5.3, 5.7) for Y0.375Al 0.625N. To test the performance of the SAW device based on YxAl1―xN/sapphire substrates, the electromechanical coupling factor, phase velocity, insertion loss and quality factor are determined and analysed. It is observed that the phase velocity (Vphase) decreases by increasing normalized thickness and yttrium content. In contrast, the electromechanical coupling (K2) is improved by the incensement of the normalized thickness of YxAl1―xN layer and the Y dopants, the K2 can reach an improvement of ∼650 % than AlN. The insertion loss (IL) is found to be ―7.66 dB at fR=931.4 MHz for Y0.375Al 0.625N, less than ―27 dB at fR = 1.363 GHz for AlN devices. The quality factor enhances up to 1920 for Y0.375Al0.625N, by ∼6% higher than that for AlN SAW. The wurtzite YAlN is highly promising material for developing low-loss electroacoustic devices as surface acoustic wave (SAW) resonators and RF filters to be used for next generation of mobile communications.

Modeling, fabrication, and structural characterization of thin film ZnO based film bulk acoustic resonator

This work reports the finite element modeling, fabrication and structural characterization a film bulk acoustic resonator (FBAR) devices using shadow mask technique. For the performance analysis of the FBAR device, simulations were performed on COMSOL Multiphysics platform. RF sputtering technique is used to deposit c-axis oriented zinc oxide (ZnO) thin film on Aluminum electrodes. The Aluminum electrodes were deposited using e-beam evaporation technique. The X-ray diffraction (XRD), atomic force microscopy (AFM), and scanning electron microscopy (SEM) techniques were used to examine the surface morphologies of the deposited piezoelectric film (ZnO). The quality of the deposited piezoelectric material film was measured with the help of XRD spectra and AFM is used to measure surface roughness of the deposited ZnO film and its measured value is 6.94 nm. The resonant characteristics of fabricated FBAR device are evaluated with the help of COMSOL Multiphysics simulations and the obtained values of effective electromechanical coupling constant (k2eff), quality factors (Qs and Qp) and Figure of merit are 3.0025%, 1811.3, 1711.4 and 54 (approximately), respectively.

Mn‐ and Mn/Cu‐doped PIN‐PMN‐PT piezoelectric ceramics for high‐power transducers

AbstractThe effects of acceptor doping with manganese as either MnO2 or MnNb2O6 (MnN) with CuO on the dielectric, ferroelectric, and piezoelectric properties of PIN‐PMN‐PT ceramics were investigated. The 2% MnNb2O6‐doped PIN‐PMN‐PT (6Pb(Mn1/3Nb2/3)O3‐25Pb(In1/2Nb1/2)O3‐34Pb(Mg1/3Nb2/3)O3‐35PbTiO3) ceramics possessed hard properties such as high coercive field (EC) of 11.7 kV/cm, low dielectric loss (tan δ) of 0.7%, and high electromechanical quality factor (QM) of 1011. These properties were diminished in MnO2‐doped ceramics because of lower oxygen vacancy defect concentration, and exaggerated grain growth resulted in &gt;20 µm grain size. Co‐doping with 2 mol% MnNb2O6 and 0.5 mol% CuO retained hardened properties such as high EC of 9.6 kV/cm, low tan δ of 0.6%, and high QM of 1029. MnNb2O6‐doped and MnNb2O6 + Cu co‐doped ceramics display excellent figures of merit for resonance and off‐resonance applications as well as high energy conversion efficiencies which make them promising candidates for high‐power transducer elements.

Sol-Gel Synthesis and Piezoelectric and Structural Properties of Zr –rich PZT Nanoparticles

Lead zirconate titanate (PZT) nanopowders with spherical-shaped morphology, perovskite structure and an average size of 20 nm were successfully synthesized. The prepared PZT nanopowders were characterized by differential thermal analysis (DTA), X-ray diffraction (XRD), scanning electron microscopy (SEM), Energy dispersive X-ray (EDS) and Transmission electron microscopy (TEM) technique. Single-phase perovskite PZT nanopowders were obtained after heat treatment at a temperature of 700 °C. The effect of calcination temperature on crystal structure of PZT nanopowders has been discussed. Dielectric relaxation of the ferroelectric ceramics could originate from the alternations of the elastic and electric behavior and the movement of the domain walls at high-frequency regions. To determine a piezoelectric property of ceramics, resonant vibration spectrum of samples was measured at room temperature. A relative density of 7.53 g/cm3 was achieved at a sintering temperature of 1150 °C, which is close to the theoretical density (~95%). At higher temperature sint, the density of ceramic samples strongly decreases which can be attributed to the evaporation of excess PbO. The optimum values of piezoelectric constant, electromechanical quality factor and a mechanical quality factor are obtained at Sintering temperature 1150 °C: d33=64 pC/N, Ƙp=0.41 and Qm=34.3.

Giant Reflection Coefficient on Sc0.26Al0.74N Polycrystalline Diamond Surface Acoustic Wave Resonators

Since the commercialization of surface acoustic wave (SAW) devices, the technology is steadily increasing the device performances without compromising their power handling, size and price. Herein, one‐port SAW resonators are fabricated on scandium aluminum nitride (Sc0.26Al0.74N)/polycrystalline diamond heterostructures. SAW propagation properties are studied using three different piezoelectric thin‐film thicknesses within the heterostructure. The Rayleigh and Sezawa resonance frequencies are above 1.5 and 2.5 GHz, respectively, achieving Sezawa mode reflection coefficients below −50 dB. The polycrystalline diamond substrate is synthesized by microwave plasma chemical vapor deposition (MPCVD) on top of a 500 μm‐thick Si (001) substrate. The Sc0.26Al0.74N thin films are synthesized by reactive sputtering at nominally room temperature. The thin film's composition is analyzed by Rutherford backscattering spectrometry (RBS). The full width at half maximum (FWHM) of the X‐ray diffraction (XRD) ω scans below 3° indicates that the synthesized Sc0.26Al0.74N thin films are highly c‐axis oriented. The electromechanical coupling coefficient, quality factor, and dielectric loss parameters are computed by curve fitting the device electrical measurements to the simulation results of a modified Butterworth Van Dyke (mBVD) model implemented in the advance design system (ADS) tool.

Characterization of the electromechanical properties of YCa4O(BO3)3 single crystals up to 800 °C

In this paper, the significant electromechanical properties of the novel high-temperature piezoelectric single crystals YCa4O(BO3)3 (YCOB) were fully characterized over the temperature range from room temperature to 800 °C, including the dielectric, elastic, and piezoelectric properties, and electromechanical coupling coefficients and mechanical quality factor. More importantly, the complex coefficients were completely determined which take into account the mechanical and electrical losses of the material and, therefore, can describe the crystal behavior more accurately. The complete measurement procedures and calculation methods required to obtain all of these parameters were proposed. YCOB resonators with 23 different types of orientations were designed and measured, and all of the independent dielectric, piezoelectric, and elastic coefficients (4, 10, and 13, respectively), 6 important coupling factors, and the mechanical quality factor were determined. It was found that (1) the dielectric permittivity and loss increase dramatically and nonlinearly with the rise of temperature; (2) the elastic compliance constants basically increase linearly as the temperature rises, while the stiffness constants decrease linearly; (3) the piezoelectric charge constants dij increase slightly with the elevated temperatures; (4) the coupling factors and mechanical quality factor decrease linearly with an increase of the temperature, and the coupling factors are in the range of 0.005–0.052, and the quality factor drops from 10 300 to 1300 with the temperature increasing from room temperature to 800 °C.

Direct growth of few-layer graphene on AlN-based resonators for high-sensitivity gravimetric biosensors.

We present the successful growth of few-layer graphene on top of AlN-based solidly mounted resonators (SMR) using a low-temperature chemical vapour deposition (CVD) process assisted by Ni catalysts, and its effective bio-functionalization with antibodies. The SMRs are manufactured on top of fully insulating AlN/SiO2 acoustic mirrors able to withstand the temperatures reached during the CVD growth of graphene (up to 650 °C). The active AlN films, purposely grown with the c-axis tilted, effectively excite shear modes displaying excellent in-liquid performance, with electromechanical coupling and quality factors of around 3% and 150, respectively, which barely vary after graphene integration. Raman spectra reveal that the as-grown graphene is composed of less than five weakly coupled layers with a low density of defects. Two functionalization protocols of the graphene are proposed. The first one, based on a covalent binding approach, starts with a low-damage O2 plasma treatment that introduces a controlled density of defects in graphene, including carboxylic groups. After that, 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide hydrochloride/N-hydroxysuccinimide (EDC/NHS) chemistry is used to covalently bind streptavidin molecules to the surface of the sensors. The second functionalization protocol is based on the non-covalent bonding of streptavidin on hydrophobic graphene surfaces. The two protocols end with the effective bonding of biotinylated anti-IgG antibodies to the streptavidin, which leaves the surface of the devices ready for possible IgG detection.

Investigation of mechanical nonlinear effect in piezoelectric MEMS vibration energy harvesters

Nonlinear resonance in piezoelectric vibration energy harvesters (pVEHs) has a large effect on the characteristics of power generation. In this study, the origin of nonlinearity was investigated on MEMS pVEHs using a 3-µm-thick-Pb(Zr,Ti)O3 film. The resonant frequency and mass of the pVEHs were 180.6 Hz and 3.63 mg, respectively. From the resonance curves of the output voltage and tip displacement measured at a low acceleration, where linear resonance was obtained, the electromechanical coupling and mechanical quality factors of the pVEHs were determined to be 0.3% and 430, respectively. Although the high output power density of 4.1 µW·mg−1·G−2 was obtained at the acceleration of 0.024 G, the effect of nonlinear resonance appeared and suppressed the output power density at the acceleration of 0.07 G and more (G is the gravitational acceleration). The comparison between the results of experiment and numerical analysis using an equivalent circuit model revealed that the nonlinear damping effect has a larger contribution than a nonlinear spring on the suppression of the output power density at a high acceleration.