Thin Piezoelectric Layer Research Articles

31-mode piezoelectric micromachined ultrasonic transducer with PZT thick film by granule spraying in vacuum process

A piezoelectric micromachined ultrasonic transducer (pMUT) is an ideal device for portable medical diagnosis systems, intravascular ultrasound systems, and ultrasonic cameras because of its favorable characteristics including small size, acoustic impedance matching with the body, low power consumption, and simple integration with the systems. Despite these advantages, practical applications are limited because of insufficient acoustic pressure of the pMUT caused by the thin active piezoelectric layer. Here, we report the fabrication of a thick piezoelectric Pb(Zr,Ti)O3 (PZT) film-based pMUT device having high deflection at low driving voltage using the granule spraying in vacuum (GSV) process. Pre-patterned high-density thick (exceeding 8 μm) PZT films were grown on 6-inch-diameter Si/SiO2/Ti/Pt silicon-on-insulator wafers at room temperature at a high deposition rate of ∼5 μm min−1. The fabrication process using the proposed GSV process was simple and fast, and the deflection of the pMUT exhibited a high value of 0.8 μm.

A mixing surface acoustic wave device for liquid sensing applications: Design, simulation, and analysis

This work presents the mixing wave generation of a novel surface acoustic wave (M-SAW) device for sensing in liquids. Two structures are investigated: One including two input and output interdigital transducer (IDT) layers and the other including two input and one output IDT layers. In both cases, a thin (1 μm) piezoelectric AlN layer is in between the two patterned IDT layers. These structures generate longitudinal and transverse acoustic waves with opposite phase which are separated by the film thickness. A 3-dimensional M-SAW device coupled to the finite element method is designed to study the mixing acoustic wave generation propagating through a delay line. The investigated configuration parameters include the number of finger pairs, the piezoelectric cut profile, the thickness of the piezoelectric substrate, and the operating frequency. The proposed structures are evaluated and compared with the conventional SAW structure with the single IDT layer patterned on the piezoelectric surface. The wave displacement along the propagation path is used to evaluate the amplitude field of the mixing longitudinal waves. The wave displacement along the AlN depth is used to investigate the effect of the bottom IDT layer on the transverse component generated by the top IDT layer. The corresponding frequency response, both in simulations and experiments, is an additive function, consisting of sinc(X) and uniform harmonics. The M-SAW devices are tested to assess their potential for liquid sensing, by dropping liquid medium in volumes between 0.05 and 0.13 μl on the propagation path. The interaction with the liquid medium provides information about the liquid, based on the phase attenuation change. The larger the droplet volume is, the longer the duration of the phase shift to reach stability is. The resolution that the output change of the sensor can measure is 0.03 μl.

Effect of initial stress on the propagation behavior of SAW in a layered piezoelectric structure of ZnO/Al2O3

Theoretical analysis of surface acoustic wave (SAW) propagation in a pre-stressed layered piezoelectric structure basing on the modified ordinary differential equation (ODE) is described. Numerical calculations involve a thin piezoelectric layer of ZnO bonded perfectly to an elastic substrate of Al2O3. ZnO thin films are deposited on Al2O3 substrates using plasma assisted molecular beam epitaxial (MBE). The crystallographic orientation of ZnO thin films and the surface morphology are analyzed by X-ray diffraction (XRD) and atomic force microscopy (AFM) respectively. The density and the thickness of the ZnO films are determined by X-ray reflectivity. The initial stress and strain of ZnO films are measured by X-ray diffraction method. The effect of initial stress on the propagation behavior of Rayleigh and Love waves and on the coupled electromechanical factor is discussed.

Thermoelastic analysis of functionally graded carbon nanotube reinforced composite cylindrical panel embedded in piezoelectric sensor and actuator layers

Based on theory of piezo-elasticity, bending behavior of functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical panel attached to thin piezoelectric layers subjected to thermal, mechanical loads and or electric field is investigated. It is assumed that thermo-elastic constants of the structure are independent of temperature gradient. In this paper, uniformly and various cases of functionally graded CNT distribution along the radial direction of host layer are considered. Governing differential equations are solved analytically by using the Fourier series expansion along axial and circumferential direction and state-space technique across the radial direction. Temperature, stress and displacement fields as well as induced electric voltage in sensor layer are obtained and used to study the thermo-piezoelastic behavior of hybrid FG-CNTRC cylindrical panel. Accuracy of present approach is validated by comparing the numerical results with the available reported results in literatures. Parametric studies are carried out to assess the effects of CNT volume fraction, case of CNT distribution along the radial direction, surface thermal/mechanical surface boundary conditions, applied voltage on the bending behavior of FG-CNTRC hybrid cylindrical panel.

Modeling and detecting response of micromachining square and circular membranes transducers based on AlN thin film piezoelectric layer

Vibration analysis of square and circular piezoelectric micro ultrasonic transducers (pMUTs) in the 100 kHz range as a function of experimental tools are reported. Analytical and 3D finite element method analysis using Comsol software has been performed to model static, modal and vibration behavior of these membranes. Comparison with standard impedancemeter measurement is shown to assess the performance of Laser Doppler Vibrometry system. Mechanical and electrical characterization and comparison with a model results are presented and discussed. The measured resonances frequencies of membrane can be weak and superimposed on important parasitic signal, which may mask the desired mechanical resonance signal. Our results revealed the real roles of the simulations and the combination of the experimental tools to get measurement accuracy. Subsequently, this piezoelectric micro-transducer was successfully tested as a sounder in air. These investigations offer guidance for the pMUTs design and associated electronic circuit but might at the same time be instructive and beneficial to further sensor applications.

Static magnetoelectric and magnetoelastic response of composite cantilevers: Theory of short vs. open circuit operation and layer sequence effects

The static bending-mode transverse magnetoelectric effect and the magnetic field-induced bending response of composite cantilevers with thin magnetostrictive (MS), piezoelectric (PE), and substrate (Sub) layers is investigated for the PE layer subjected to open and short circuit conditions. Analytic theories are presented for strain-coupled three layer composites of PE, MS, and Sub layers in all layer sequences. We use constitutive equations with linear coupling of stress, strain, H, E, and D fields and present results for the open and short circuit magnetoelectric and bending responses for arbitrary layer thickness ratios for the FeCoBSi-AlN-Si materials system. Besides a rich sequence dependent behavior the theory predicts great and systematic differences between the open and short circuit magnetoelectric response yielding maxima at similar MS and PE layer thicknesses in the open circuit and near vanishing PE layer thicknesses in the short circuit cases. In contrast, the open vs. short circuit bending response differences are pronounced but much smaller. Layer sequence systematics and implications for static H-field sensors will be discussed.

Elasticity Solution of Free Vibration and Bending Behavior of Functionally Graded Carbon Nanotube-Reinforced Composite Beam with Thin Piezoelectric Layers Using Differential Quadrature Method

Based on the theory of elasticity, bending and free vibrational analyses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam embedded in piezoelectric layers are carried out, using the state-space differential quadrature method (DQM). Applying the DQM to the governing differential equations and boundary conditions along the longitudinal directions, new state equations about state variables at discrete points are derived. By using the state-space technique across the thickness direction, semi- analytical closed form solutions are derived. The method is validated by comparing numerical results for beams without piezoelectric layers. Both the direct and the inverse piezoelectric effects are investigated and the influence of piezoelectric layers on the mechanical behavior of beam is studied. Furthermore, the effects of CNT volume fraction, kind of CNT distribution, length to thickness ratio and edge boundary conditions on the mechanical behavior of the beams are examined.

Detection and response characteristics of clamped-free giant magnetostrictive/piezoelectric laminates under concentrated loading

This work deals with the detection and response characteristics of clamped-free giant magne-tostrictive/piezoelectric laminates under concentrated loading both numerically and experimentally. The laminate is fabricated using thin magnetostrictive Terfenol-D and piezoelectric PZT layers. Three dimensional finite element analysis was carried out, and the electromagneto-mechanical fields in the two and three layered magnetostrictive/piezoelectric laminates were predicted by introducing a second-order magnetoelastic constant of Terfenol-D. The tip deflection, induced voltage and induced magnetic field were also measured, and comparison was made between simulation and experiment to verify the model.

Three-dimensional thermoelasticity solution of functionally graded carbon nanotube reinforced composite plate embedded in piezoelectric sensor and actuator layers

Based on theory of elasticity, static behavior of functionally graded carbon nanotube reinforced composite (FG-CNTRC) rectangular host plate attached to thin piezoelectric layers subjected to thermal load and or electric field is studied. It is assumed that temperature gradient does not affect the thermo-elastic constants of the plate. Distribution of CNT is uniformly or functionally graded along the plate thickness. Analytical solutions for the temperature, stress and displacement fields for the FG-CNTRC plate with simply-supported edges are derived by using the Fourier series expansion along in-plane coordinates and state-space technique across thickness direction. The present procedure is validated by comparing the numerical results with the available published results. Parametric studies are performed to assess the effects of CNT volume fraction, case of CNT distribution along the thickness direction, surface boundary conditions, applied voltage, aspect ratio and length to thickness ratio on the behavior of FG-CNTRC rectangular plate.

Green’s function for an anisotropic piezoelectric half-space bonded to a thin piezoelectric layer

The Green’s function for an anisotropic piezoelectric half-space bonded to a thin piezoelectric layer subject to a generalized line force and a generalized line dislocation is presented. The thickness of a thin layer is assumed to be small compared with a reference length. Thus, the existence of the layer is replaced by effective boundary conditions to avoid finding solutions in the layer. Combining with the Stroh formalism gives explicit solutions in a more compact form.

An improved model of thin cylindrical piezoelectric layers between isotropic elastic media

Radially polarized piezoelectric fibers are now considered to be used in smart composites. The piezoelectric layers in these fibers are generally anisotropic in the transverse direction and therefore difficult to analyze when dynamic loads are involved. The present paper presents a theoretical study of the dynamic behavior of radially polarized cylindrical piezoelectric layers between isotropic elastic media. A new interphase model is developed to provide simple yet accurate evaluation of the dynamic response of such anisotropic elastic layers. Unlike the traditional interface-spring model, the current interphase model satisfies the equations of motion of the layers and can provide reliable prediction of the stress and displacement. A comparison between the developed model, the interface-spring model and the finite element analysis is conducted. The results clearly show the advantages of the current model over the traditional interface-spring model in simulating anisotropic layers. Numerical examples based on this interphase model for different interphase thicknesses, loading frequencies and material combinations are presented to evaluate the dynamic behavior of multilayered elastic media.

Study on SH-SAW in imperfectly bonded piezoelectric structures loaded with viscous liquid

We analytically investigate shear horizontal surface acoustic wave (SH-SAW) propagation in layered piezoelectric structures loaded with viscous liquid, which involves a thin piezoelectric layer imperfectly bonded to an unbounded elastic substrate. The coupling wave equations are obtained based on the linear piezoelectric theory. The governing equations are solved by means of the analytical method with consideration of electrically open and shorted cases, respectively. The dispersive relations are obtained, and the effects of the imperfect constant on the properties of waves are presented and discussed. From the numerical results, we can find that the phase velocity decreases with the increase of the interface parameter n, and for a specified viscosity, the attenuation increases with the interface parameter. The results show that the effects of the imperfect constant on the properties of SH-SAW are remarkable.

Nanoscale Numerical and Reliability Method for Nano-Cantilever

Most of nanostructures are desired in nanodevices in order to perform their characteristics. Tiny, strong and stable nanomaterials are needed to get functional nanosensor, nanoactuator and nanodevices. For those reasons, we introduce the single walled carbon nanotube (SWCNTS) as a high flexural and cylindrical nanocantilever to reduce the electrical and mechanical lost energy. Therefore, a bundle of SWCNTs in cylindrical geometry with a diameter of about 5 nm and 60 nm as long was designed in clamped-free cantilever feature. Due to the exceptional mechanical and geometrical characteristic of SWCNT, the first resonance frequency was calculated by analytical method to be of 150MHz. Further research, the SWCNT nanocantilever could be covered with a thin piezoelectric layer such as PZT, ZNO, AlN, PVDF...to realize nanactuators, nanosensors and nanodevices. The proposed methodology directly supports quality engineering aspects enabling to specify the manufacturing to achieve desired product reliability. Within this context, the robust design obtained is optimal over the range of variable conditions because it considers uncertainties during the optimization process. The large number of exact evaluations of problem, combined with the typically high dimensions of Finite Element models, makes reliability-based optimization procedures very costly, sometimes unfeasible. Those difficulties motivate the study reported in this paper, in which a strategy is proposed consisting in the use of reliability-based optimization strategy combined with measurement and sensitivity technique specially adapted to the structures of industrial interested. Keywords: single walled carbon nanotubes, nanocantilever vibration, clamped-clamped, clamped-free. Reliability, Finite Element Method.

Nonlinear vibration control of functionally graded laminated cylindrical shells

An analytical method and a new simplifying model of smart FG (functionally graded) laminated cylindrical shells with thin piezoelectric layers are presented based on Hamilton’s principle, Von Kármán nonlinear theory and constant-gain negative velocity feedback approach. The thin piezoelectric layers embedded on inner and outer surfaces of the smart FG laminated cylindrical shell are acted as distributed sensor and actuator, which is used to control nonlinear vibration of the smart FG laminated cylindrical shell. The coupled nonlinear partial differential equations are discretized based on a series expansion of linear modes and a multiterm Galerkin’s method. The coupled nonlinear equations of motion are then solved by Runge–Kutta numerical method.

Calculation of the spectral characteristics of an acoustic resonator containing layered multiferroic structure

Multifrequency composite acoustic resonators for bulk acoustic waves with piezoelectric and ferromagnetic layers are studied. The structures with a thick ferrite substrate layer and a thin ferrite film on a nonmagnetic dielectric substrate and multilayer structures are considered. A thin piezoelectric layer that is placed between two metal electrodes serves as a transducer. Analytical expressions for the input electric impedance of the electroacoustic transducer are derived for various structures under study in the presence of the transverse control magnetic field. The amplitude-frequency and phase-frequency characteristics of the cavity are numerically calculated. The resonance frequency can be controlled in the interval ±1.2 MHz (about 25% of the intermode distance) due to variations in the magnetic field.

Ultrafast optical technique for measuring the electrical dependence of the elasticity of piezoelectric thin film: Demonstration on AlN

We present a technique based on ultrafast acoustics which permits us to measure the electrical dependence of the elastic properties of a thin piezoelectric layer. Ultrafast acoustics offers a unique way of measuring elastic properties of thin-layer in a non-destructive way using ultrashort optical pulses. We apply this technique to a thin layer to which a dc voltage is simultaneously applied. Both the film thickness and the sound velocity are affected. The two effects can be separated by use of a semi-transparent top electrode. A demonstration is made on a thin aluminum nitride (AlN). From that the d(33) piezoelectric coefficient and the stiffness variation induced by the bias in AlN are measured.

Dynamic electromagneto-mechanical behavior of clamped-free giant magnetostrictive/piezoelectric laminates under AC electric fields

This work deals with the dynamic electromagneto-mechanical behavior of clamped-free giant magnetostrictive/piezoelectric laminates under AC electric fields both numerically and experimentally. The laminate is fabricated using thin magnetostrictive Terfenol-d and piezoelectric PZT layers. The magnetic field-dependent magnetoelastic constant and domain wall motion effect were incorporated to describe the nonlinear behavior of Terfenol-d and PZT layers, respectively, and three-dimensional finite element analysis was employed to calculate the displacement, stress and induced magnetic field. Experiments were also conducted to measure the displacement and induced magnetic field for the magnetostrictive/piezoelectric laminates under AC electric fields. Comparison was then made between simulation and experiment.

Static analysis of functionally graded carbon nanotube-reinforced composite plate embedded in piezoelectric layers by using theory of elasticity

Based on three-dimensional theory of elasticity, bending behavior of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate embedded in thin piezoelectric layers subjected to mechanical uniform load with simply supported boundary conditions is investigated. By using Fourier series expansion along the longitudinal and latitudinal directions and state space technique across the thickness direction closed form solution is derived. Accuracy and convergence of the presents approach, is validated by comparing the numerical results with the published numerical results in the literature. In addition, the effects of volume fraction of CNT, two case of FG-CNTRC, piezoelectric layer thickness, length to thickness ration and modes number on the static behavior of the hybrid plate are also examined.

Dynamic modeling and determination of effective properties of smart composite plates with rapidly varying thickness

A new comprehensive micromechanical model for the analysis of the dynamic problem of a smart composite piezo-magneto-thermo-elastic thin plate with rapidly-varying thickness is developed in the present paper. A rigorous three-dimensional formulation is used as the basis of multiscale asymptotic homogenization. A complete dynamic approach is adhered to beginning with the equations of dynamic equilibrium, the time-varying form of Maxwell’s equations and dynamic thermal balance. The asymptotic homogenization model is derived, the governing equations are determined and subsequently general expressions called unit cell problems that can be used to determine the effective elastic, piezoelectric, piezomagnetic, electrical conductivity etc. properties are presented. Of particular interest in this work is the development of general expressions pertaining to the so-called product properties which are manifested in the macroscopic composite plate via the interaction of the different phases but may be absent from some individual constituents of the composite. Examples of product properties are the magnetoelectric, pyroelectric and pyromagnetic coefficients. The derived expressions pertaining to the unit-cell problems and the resultant effective coefficients are very general and are valid for any geometry of the unit cell. In addition to the effective properties, the developed model also computes the local mechanical displacement and stress, electric displacement, magnetic field, heat flux and free current density. The work is illustrated by means of a 3-layer anisotropic plate consisting of an elastic middle layer sandwiched between thin piezoelectric and piezomagnetic carrier layers.

Elasticity solution for the free vibration analysis of functionally graded cylindrical shell bonded to thin piezoelectric layers

Based on the three-dimensional theory of elasticity, free vibration analysis of a functionally graded cylindrical shell embedded in piezoelectric layers is performed by using an analytical method for simply supported boundary conditions and a semi-analytical method for non-simply supported conditions. Material properties are assumed to vary along the thickness according to an exponential law with Poisson’s ratio held constant. For non-simply supported conditions, this method can give an analytical solution along the graded direction using the state space method (SSM) and an effective approximate solution along the axial direction using the one dimensional differential quadrature method (DQM). Numerical results are compared to those available in the literature to validate the convergence and accuracy of the present approach. The effects of material property gradient index, edge conditions, mid-radius to thickness ratio, length to mid-radius ratio and the piezoelectric thickness on vibration behavior of shell are investigated.