Electromechanical Coupling Constant Research Articles

Alloying aluminum nitride with molybdenum could significantly enhance its electromechanical coupling constant

Aluminum nitride (AlN) has been widely used in bandpass filters for wireless communication applications, but its low electromechanical coupling factor (kt2) limits the bandwidth of the filter based on it. In this work, AlN alloys incorporated with various transition metals are theoretically studied, and Mo-alloy AlN (MoxAl1−xN) is predicted to be more prominent in improving kt2. Furthermore, the influence of Hubbard U correction on the kt2 of MoxAl1−xN is discussed, and the correction is found to show a crucial role at a high x. The magnitude of kt2 is more correlated with the piezoelectric stress constant e33, and both of them depend on the distribution of Mo atoms. The contribution of each atom to piezoelectric performance is described by an effective displacement-response internal-strain parameter Γ33 in this work, which is generally proportional to internal parameter u and response of u to applied strain along the z-axis. The increase of kt2 is ascribed to the Mo-induced larger u and Γ33, but the Mo dimer and line along the z-axis weaken the increase mechanism. To obtain a high kt2, it is better to alloy Mo atoms into more sublayers of AlN and with fewer Mo dimers and lines along the z-axis. The behavior that the Mo atoms distributed evenly in the xy plane is also beneficial. A high kt2 of 37.8% is predicted in a special quasirandom configuration of Mo0.167Al0.833N, which might be the highest value reported to date for the AlN alloys.

Sintering behavior and physical properties of Bi0.5(Na1–xKx)0.5SnO3 lead-free ceramics

In this study, Bi0.5(Na1–xKx)0.5SnO3 (BNKS) ceramics (x = 0, 0.1, 0.2, 0.3, and 0.4) were fabricated via ultrasound wave before milling. The time of ball milling decreased from 20 to 1 h. The X-ray diffraction patterns show that the BNKS has a single-phase structure. When the potassium content increases, the phase structure of the ceramics changes from rhombohedral to tetragonal. When sintered at 1100 °C and x = 0.2, the ceramics’ physical properties are the best with the mass density of 5.59 g/cm3, the electromechanical coupling constants kp of 0,31 and kt of 0.27, the remanent polarization of 11.9 µC/cm; the dielectric constant εr of 1131, and the highest dielectric constant emax of 4800.

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.

Large Piezoelectric Response and Ferroelectricity in Li and V/Nb/Ta Co-Doped w-AlN.

Enhancement of piezoelectricity in w-AlN is desired for many devices including resonators for next-generation wireless communication systems, sensors, and vibrational energy harvesters. Based on density functional theory, we show that Li and X (X = V, Nb, and Ta) co-doping in 1Li:1X ratio transforms brittle w-AlN crystal to ductile, along with broadening the compositional freedom for significantly enhanced piezoelectric response, promising them to be good alternatives to expensive Sc. Interestingly, these co-doped w-AlN also show quite large spontaneous electric polarization (e.g., about 1 C/m2 for Li0.125X0.125Al0.75N) with the possibility of ferroelectric polarization switching, opening new possibilities in wurtzite nitrides. An increase in piezoelectric stress constant (e33) with a decrease in elastic constant (C33) results in an enhancement of piezoelectric strain constant (d33), which is desired for improving the performance of bulk acoustic wave (BAW) resonators for high-frequency radio frequency (RF) signals. Also, these co-doped w-AlN are potential lead-free piezoelectric materials for energy harvesting and sensors as they improve the longitudinal electromechanical coupling constant (K332), transverse piezoelectric strain constant (d31), and figure of merit (FOM) for power generation. However, the enhancement in K332 is not as pronounced as that in d33 because co-doping increases dielectric constant. The longitudinal acoustic wave velocity (7.09 km/s) of Li0.1875Ta0.1875Al0.625N is quite comparable to that of commercially used piezoelectric LiNbO3 or LiTaO3 in special cuts (about 5-7 km/s) despite the fact that the acoustic wave velocities, important parameters for designing resonators or sensors, decrease with co-doping or Sc concentration.

Phononic loss in superconducting resonators on piezoelectric substrates

We numerically and experimentally investigate the phononic loss for superconducting resonators fabricated on a piezoelectric substrate. With the help of finite element method simulations, we calculate the energy loss due to electromechanical conversion into bulk and surface acoustic waves. This sets an upper limit for the resonator internal quality factor Qi. To validate the simulation, we fabricate quarter wavelength coplanar waveguide resonators on GaAs and measure Qi as function of frequency, power and temperature. We observe a linear increase of Qi with frequency, as predicted by the simulations for a constant electromechanical coupling. Additionally, Qi shows a weak power dependence and a negligible temperature dependence around 10 mK, excluding two level systems and non-equilibrium quasiparticles as the main source of losses at that temperature.

Frequency dispersion and temperature dependence of electrical behaviours in 0.4Bi(Ni1/2Zr1/2)O3–0.6PbTiO3

In this study, the temperature dependence of dielectric behaviours and the polarisation and electrostrain responses of 0.4Bi(Ni1/2Zr1/2)O3–0.6PbTiO3 (0.4BNZ–0.6PT) were studied to better understand their electrical performance. A Rietveld refinement analysis of the XRD pattern, supported by bright-field TEM images, suggests the coexistence of tetragonal and pseudocubic phases. Above 398 K, the normalised piezoelectric coefficient (d33∗) increases due to heating, reaching 941 pm/V at 453 K. Most importantly, 0.4BNZ–0.6PT displays obvious frequency dispersion in the ferroelectric state. A low-temperature dielectric anomaly occurred at approximately 175 K that was related to the origin of the frequency dispersion. The planar electromechanical coupling constant (kp) also changed considerably after heating, increasing from 0.14 at 90 K to 0.43 at 300 K. This indicates an intrinsic relationship between the dielectric and piezoelectric behaviours. Our study demonstrates that there is a significant difference between typical ferroelectrics and the ferroelectric state of 0.4BNZ–0.6PT relaxor ferroelectrics.

Piezoelectric and electromechanical coupling constants for GaxIn1-xSb semiconducting alloys

ABSTRACTThe compositional dependence of piezoelectric stress and strain constants and electromechanical coupling coefficient of GaxIn1-xSb have been investigated. The calculations were performed using a pseudopotential approach combined with the Adachi model where different concepts of ionicity are considered. Our results are compared with the available data and found to be in good accord with each other. Our findings show that as the Ga content varies, the piezoelectric and related constants and transport properties of the alloy system of interest are significantly affected.

Effect of holmium doping on structural, electrical and piezoelectric properties of lead-free (Ba,Ca)(Ti,Sn)O3 ceramics

Lead-free (Ba0.91Ca0.09Sn0.07Ti0.93)O3 (BCST) ceramics, doped with holmium (Ho) in the range 0–1.0 mol%, were synthesized using conventional solid-state sintering method. XRD analyses of these ceramic samples confirm single phase pure perovskite structure. Evidence of Ho3+ substituting Ba2+ via electronic charge compensation exists in the range 0–0.4 mol%, while ionic charge compensation mechanism dominates beyond 0.4 mol%. Crystallite size and lattice strain undergo systematic change, while the room temperature dielectric constant (ert) decreases with increasing Ho content. The Curie temperature Tc and maximum dielectric constant (em) at Tc remain almost unchanged. Remnant polarization (Pr), electromechanical coupling constant (kp) and piezoelectric charge coefficient (d33) exhibit increasing trend with increasing Ho content and reach their maximum values of 8.2 µC/cm2, 25% and 220 pC/N respectively at 1.0 mol% of Ho content. The study reveals that doping of BCST system with appropriate quantity of Ho can improve its ferroelectric and piezoelectric properties.

Enhanced piezoelectric and ferroelectric properties of Nd doped Ba0.85Ca0.15Zr0.1Ti0.9O3 ceramic system

Conventional solid state reaction method was employed to synthesize Ba(0.85-x)NdxCa0.15Zr0.1Ti0.9O3(x = 0.000, 0.005, 0.010, 0.015, 0.020, and 0.025 mol%) ceramics. Ceramic samples sintered at 1450 °C were characterized for dielectric, ferroelectric and piezoelectric properties. XRD study confirms the presence of pure perovskite structure in ceramic samples without any secondary peaks, with tetragonal phase from x = 0 to x = 0.015, and cubic phase for x = 0.020 and x = 0.025.The remnant polarization (Pr), room temperature dielectric constant (εrt), piezoelectric coefficient (d33) and electromechanical coupling constant (kp) increase with x and attain the maximum value of 4.3 μC/cm2, 2128, 270pC/N and 0.31 respectively for x = 0.010.

A novel indirect-drive regenerative shock absorber for energy harvesting and comparison with a conventional direct-drive regenerative shock absorber

Energy harvesting from the shock absorbers is now becoming an important technology in developing the electrical vehicles. Compared with other kinetic energy sources such as engine and brake systems which are continuous or periodic, the shock absorber is subjected to the fluctuated linear motion with relatively small displacement. This paper presents a novel indirect-drive regenerative shock absorber system that utilizes an arm-teeth mechanism to achieve linear to rotary motion conversion and to amplify its input speed for increasing energy harvesting output. The fluctuation of road randomness can be smoothed out through the flywheel. The proposed design has the advance of achieving all the targets with less number of components. Two prototypes of the direct-drive and indirect-drive regenerative shock absorbers have been built. The simulation models have been developed and validated by experimental results. The performance of this new indirect-drive system has been compared, through experimental testing and analytical modeling, with that of a conventional direct-drive system of the same generator configuration. The results show that this indirect-drive system can achieve greater peak power output and broader frequency bandwidth than the conventional direct-drive system. The indirect-drive system also presents a better ride comfort up to 13 Hz. Using Monte Carlo simulation, a parameter sensitivity analysis of both the indirect-drive and direct-drive systems has been carried out to compare their energy harvesting performances in terms of increasing the peak power output and broadening the energy harvesting frequency bandwidth. In both the systems, choosing the right tyre stiffness and electromechanical coupling constant is beneficial to increasing the peak power output ratio and the harvesting frequency bandwidth. The right choice of the gear ratio can further improve the peak power output ratio of the indirect-drive system. The variation of these parameters will allow for possibility of achieving higher power output when vehicle is driven on random road surfaces.

Bistability and displacement fluctuations in a quantum nanomechanical oscillator

Remarkable features have been predicted for the mechanical fluctuations at the bistability transition of a classical oscillator coupled capacitively to a quantum dot [Phys. Rev. Lett. 115, 206802 (2015)]. These results have been obtained in the regime $\omega$0 $\ll$ kBT $\ll$ $\Gamma$, where $\omega$0, T , and $\Gamma$ are the mechanical resonating frequency, the temperature, and the tunneling rate, respectively. A similar behavior could be expected in the quantum regime of $\Gamma$ $\ll$ kBT $\ll$ $\omega$0. We thus calculate the energy and displacement fluctuation spectra and study their behavior as a function of the electro-mechanical coupling constant when the system enters the Frank-Condon regime. We find that, in analogy with the classical case, the energy fluctuation spectrum and the displacement spectrum widths show a maximum for values of the coupling constant at which a mechanical bistability establishes.

Effect of Bismuth Doping on the Dielectric and Piezoelectric Properties of Ba1-xBixTiO3 Lead-Free Ceramics

In this paper we report the dielectric and piezoelectric properties of Bi modified Ba1-xBixTiO3 lead-free ceramics. These ceramic samples were synthesized by conventional solid state reaction method. The XRD spectra recorded at room temperature (RT) suggested decrease in the tetragonality (c/a) for Bi doped derivatives with the presence of minor rhombohedral phase for heavily doped specimens. The grain boundary pinning occurring in slightly Bi-doped derivative (x = 0.025) was found to reduce the grain size to submicron regime. However, for higher Bi doping the presence of liquid phase led to the grain coarsening. The doped derivatives exhibited shifting of the paraelectric-ferroelectric (PE-FE) phase transition towards RT with rather diffused Curie peak. The substitution of Bi3+ (with different ionic radii and electronegativity) on A-site of ABO3 structure resulted in regions with modified polar structure giving rise to diffused PE-FE phase transition. The specimen with x = 0.025 exhibited enhanced planar electro-mechanical coupling constant (kp) ∼ 25% with longitudinal piezoelectric constant (d33) of ∼112 pC/N. The sample with x = 0.025 also exhibited 0.085% electric-field induced strain along with the remnant polarization (2Pr) of ∼15 μC/cm2 and coercive field (2Ec) of ∼22 kV/cm. The increased Ec with reasonable Pr is an important material characteristics for the stable functionality of the memory devices.

Theoretical and experimental analyses of tunable Fabry-Perot resonators using piezoelectric phononic crystals.

Theoretical and experimental analyses of piezoelectric stacks submitted to periodical electrical boundary conditions via electrodes are conducted. The presented structures exhibit Bragg band gaps that can be switched on or off by setting electrodes in short or open circuit. The band gap frequency width is determined by the electromechanical coupling coefficient. This property is used to design a Fabry-Perot cavity delimited by a periodic piezoelectric stack. An analytical model based on a transfer matrix formalism is used to model the wave propagation inside the structure. The cavity resonance tunability is obtained by varying the cavity length (i.e., by spatially shifting boundary conditions in the stack). 26% tuning of resonance and antiresonance frequencies with almost constant electromechanical coupling coefficient of 5% are theoretically predicted for an NCE41 resonator. To optimize the device, the influence of various parameters is theoretically investigated. The cavity length, phononic crystal (number and length of unit cells), and transducer position can be adapted to tune the frequency shift and the coupling coefficient. When the transducer is located at a nodal plane of the cavity, the value of the coupling coefficient is 30%. Experimental results are presented and discussed analyzing the effects of damping.

GaN/SiC based surface acoustic wave structures for hydrogen sensors with enhanced sensitivity

In this article, we present an application of GaN/SiC heterostructures for Surface Acoustic Wave (SAW) hydrogen sensors with enhanced sensitivity. We demonstrate that the mass-loading sensitivity of such sensors can be increased by using shorter acoustic wavelengths and by confining the acoustic wave energy in an epitaxial waveguide. The effect of different Rayleigh-like modes on the mass-loading sensitivity is also discussed. The SAW wavelength-dependent phase and group velocity and electromechanical coupling constants were determined from electrical measurements. The outcome was used to design a microwave SAW delay-line oscillator. Its sensing characteristics are presented. The oscillator frequency shift was larger than 60kHz after exposure to 1000ppm H2/N2. The sensor reaction time was about 12s for the same sensing conditions at room temperature.

The effect of frequency detuning and seismic energy scavenging on the host structure and harvesting performance under broadband excitation

In this work, the effect of seismic energy harvesting on the host structure and the harvesting performance will be discussed under broadband excitation with a view to exploring a more practical case. This work focuses on the harvester design for a fixed host structure under broadband force excitation. The modeling of the whole system is based on stochastic theory and the system performance is discussed with numerical calculations using this stochastic modeling. In addition to analysis on the coupling between the host structure and the harvester, the effect of frequency detuning between the harvester and host structure resonant frequencies is also presented. Two design criteria (constant force factor and constant electromechanical coupling factor) are proposed to show different energy conversion processes. In both cases, the optimal harvested powers are found when the resonant frequency of the harvester is perfectly matched with the resonant frequency of the host structure. With a constant force factor, the harvester performance is very sensitive to the frequency detuning effect. With a constant electromechanical coupling factor, however, there is very little variation in the harvested power when the two resonant frequencies are detuned.

Enhancing detection sensitivity of piezoelectric plate sensor by increasing transverse electromechanical coupling constant

In this study, we examined how the materials’ properties of a lead magnesium niobate-lead titanate solid solution, [Pb(Mg1/3Nb2/3)O3]0.63[PbTiO3]0.37 (PMN-PT) piezoelectric plate sensor (PEPS) affected the enhancement of the relative detection resonance frequency shift, −Δf/f of the sensor, where f and Δf were the resonance frequency and resonance frequency shift of the sensor, respectively. Specifically, the electromechanical coupling constant, −k31, of the PMN-PT PEPS was varied by changing the grain size of the piezoelectric layer as well as by applying a bias direct current electric field. Detection of streptavidin at the same concentration was carried out with biotin covalently immobilized on the surface of PEPS. It is shown that the −Δf/f of the same streptavidin detection was increased by more than 2-fold when the −k31 increased from 0.285 to 0.391.

Rate-dependent electro-mechanical coupling response of ferroelectric materials: A finite element formulation

This paper presents a three-dimensional (3D) constitutive model for predicting nonlinear polarization and electro-mechanical strain responses of ferroelectric materials subject to various histories of electric fields and mechanical stresses. The electro-mechanical coupling constants are expressed as functions of a polarization state and it is assumed that in absence of the polarization, the material does not exhibit electro-mechanical coupling response. The polarization model due to an electric field input is additively decomposed into time-dependent reversible and irreversible parts. The model also incorporates the effect of compressive stresses on the polarization response. Thus, the constitutive model is capable of incorporating the effect of loading rates, mechanical stresses, and electric fields on the overall hysteretic electro-mechanical and polarization switching response of ferroelectric materials. The constitutive model is implemented in a continuum 3D finite element in order to perform rate-dependent electro-mechanical coupling analyses of smart structures. The experimental data on the polarization switching and hysteretic butterfly strain responses of lead zirconate titanate (PZT) reported by Fang and Li (1999) are used to validate the constitutive model. Parametric studies are also conducted to examine the effect of loading rates and coupled electro-mechanical boundary conditions on the overall performance of PZT. Finally, FE analyses are performed to simulate shape changing in smart composite structures.

Extracting the electromechanical coupling constant of piezoelectric thin film by the high-tone bulk acoustic resonator technique

In this paper, a new approach is proposed to rapidly and accurately measure the electromechanical coupling constant K(t)(2) of thin film piezoelectric material, which is critically important for real-time quality control of the piezoelectric film growth in mass production. An ideal lossy bulk acoustic resonator (LBAR) model is introduced and the theory behind the method is presented. A high-tone bulk acoustic resonator (HBAR) was fabricated on a silicon wafer. The impedance response of the resonator was measured, from which the K(t)(2) of the piezoelectric material was extracted. To illustrate the potential of the proposed technique to extract material properties, two HBAR devices employing AlN as the piezoelectric material were fabricated using an RF sputter system with known good and bad deposition conditions; the extracted K(t)(2) values of the piezoelectric material are compared.

Generalised Butterworth-Van Dyke equivalent circuit for thin-film bulk acoustic resonator

A generalised Butterworth-Van Dyke (GBVD) equivalent circuit model for a thin-film bulk acoustic resonator (FBAR), especially for a FBAR with a high electromechanical coupling constant (kt2), is presented. The derivation starts from the ideal impedance formula for the FBAR, then acoustic loss, dielectric loss, and electrode electrical loss are introduced step by step. Results show that the widely used modified Butterworth-Van Dyke (MBVD) model is a special case of a GBVD model using a low kt2 approximation.

Influence of substrate temperature to prepare (1 0 3) oriented AlN films

(1 0 3) Oriented AlN films is an attractive piezoelectric material for the applications on surface acoustic wave (SAW) and film bulk acoustic wave (FBAR) devices. As regards the SAW properties of the (1 0 3) oriented AlN films, the electromechanical coupling constant ( K 2) is larger than the (0 0 2) oriented AlN films. As regards the bulk acoustic wave (BAW) properties of (1 0 3) oriented AlN films, it can excite a quasi-shear mode (velocity = 5957 m/s, K 2 = 3.8%) that can be used for FBAR liquid sensor. In this research, the (1 0 3) oriented AlN films were successfully prepared on the silicon substrate by rf magnetron sputtering. Different temperatures (100 °C, 200 °C, 300 °C, and 400 °C) were used in this experiment process. The crystalline structure of films was determined by X-ray diffraction (XRD) and the surface microstructure was investigated by the atomic force microscope (AFM). The result exhibited the optimal substrate temperature is 300 °C. The optimal (1 0 3) oriented AlN films have the strongest XRD intensity, the smallest full width at half maximum (FWHM) value (0.6°), the largest grain size (15.8 nm) and the smoothest surface (Ra = 3.259 nm).