Simulation of piezoelectric devices by two- and three-dimensional finite elements

A method for the analysis of piezoelectric media based on finite-element calculations is presented in which the fundamental electroelastic equations governing piezoelectric media are solved numerically. The results obtained by this finite-element calculation scheme agree with theoretical and experimental data given in the literature. The method is applied to the vibrational analysis of piezoelectric sensors and actuators with arbitrary structure. Natural frequencies with related eigenmodes of those devices as well as their responses to various time-dependent mechanical or electrical excitations are computed. The theoretically calculated mode shapes of piezoelectric transducers and their electrical impedances agree quantitatively with interferometric and electric measurements. The simulations are used to optimize piezoelectric devices such as ultrasonic transducers for medical imaging. The method also provides deeper insight into the physical mechanisms of acoustic wave propagation in piezoelectric media.     

A novel, single-mode piezoceramic plate actuator for ultrasonic linear motors

A new type of piezoelectric plate actuator for ultrasonic linear motors has been developed. These new piezoelectric actuators use the principle of asymmetric resonant excitation of the piezoceramic plate in a special resonant mode consisting of a standing two-dimensional extensional wave in a piezoceramic plate. The behavior of the actuator has been simulated with finite-element method (FEM) software and the simulation results checked with single-point contact measurements on the surface of the actuator. This paper describes this work and closes by describing the new ultrasonic translation stages based on this design.     

Determination of complex coefficients of radially polarized piezoelectric ceramic cylindrical shells using thin shell theory

A method is presented to determine the complex coefficients E/sub 33//sup T/, s/sub 11//sup E/, s/sub 12//sup E/, and d/sub 31/ of piezoelectric materials. The real parts of these coefficients are determined using axially polarized thin discs in the ANSI/IEEE Standard but are determined here using radially polarized cylindrical shells. The coefficients are determined by iteratively refining them until the values of the low-frequency complex admittance, three resonance frequencies, and three band-widths computed using a thin-shell analytical model and the coefficients are very nearly equal to measured values. The accuracy of the method is determined by using quantities computed using a finite-element model in place of measured values. Measurement errors are accounted for by using a resolution of 10 Hz to compute the critical frequencies. The differences between the coefficients input to the finite-element model and those obtained using the iteration method are the errors. It is shown that the method is sufficiently accurate to use thin radially polarized cylindrical shells to determine the properties of new materials as well as characterize those used in hydrophones or other devices.     

Vibration of infinite piezoelectric cylinders with anisotropic properties using cylindrical finite elements

Natural frequencies for free vibration of infinite piezoelectric cylinders are computed using finite elements that are formulated in cylindrical coordinates. The finite-element method is used to model the cross-section of the cylinder in r, theta coordinates using circular sectors. Material constants that are functions of theta are allowed to vary in each circular sector and are computed using standard tensor transformations. The accuracy of the finite-element formulation is verified using previous results for isotropic cylinders and axisymmetric piezoelectric cylinders. New results are tabulated for frequencies of free vibration of solid and hollow piezoelectric cylinders of LiNbO(3) of crystal class 3m. Displacements for typical mode shapes are illustrated graphically.     

Analysis of SAW properties of epitaxial ZnO films grown on R-Al2O3 substrates

ZnO thin films with a high piezoelectric coupling coefficient are widely used for high frequency and low loss surface acoustic wave (SAW) devices when the film is deposited on top of a high acoustic velocity substrate, such as diamond or sapphire. The performance of these devices is critically dependent on the quality of the ZnO films as well as of the interface between ZnO and the substrate. In this paper, we report the studies on piezoelectric properties of epitaxial (112¯0) ZnO thin films grown on R-plane sapphire substrates using metal organic chemical vapor deposition (MOCVD) technique. The c-axis of the ZnO film is in-plane. The ZnO/R-Al₂O₃ interface is atomically sharp. SAW delay lines, aligned parallel to the c-axis, were used to characterize the surface wave velocity, coupling coefficient, and temperature coefficient of frequency as functions of film thickness to wavelength ratio (h/λ). The acoustic wave properties of the material system were calculated using Adler's matrix method, and the devices were simulated using the quasi-static approximation based on Green's function analysis     

The piezoelectric semiconductor and acoustoelectronic device development in the sixties

In the 1960s the properties of piezoelectric semiconductors, group III-V zinc-blende and group II-VI wurtzite structure, were explored for the development of acoustoelectronic (AE), devices. Bulk acoustic wave (BAW), delay lines, traveling wave amplifiers, and oscillators were developed. Although these elegant functional devices never made it into the realm of full-scale production and application, the piezoelectric semiconductor developments of the 1960s provided an exciting time for theoretical explanations and creative experimentation to explore device capabilities for electronic systems applications. Delay lines were formed from rectangular parallelepiped blocks of piezoelectric semiconductors with integral input and output transducers depleted of carriers at each end of the block. The ultrasonic traveling wave amplifier was based on the interaction of electrons under a bias field moving with a velocity faster than the piezoelectric field accompanying the acoustic traveling wave. The gain factor in a piezoelectric semiconductor under direct current bias was used to develop oscillators. The main research efforts were carried out by industrial laboratories with government funding support. This paper considers the work with piezoelectric semiconductors during the 1960s with examples from the author's own work.     

Analysis of piezoelectric ultrasonic transducers attached to waveguides using waveguide finite elements

A finite-element modeling procedure for computing the frequency response of piezoelectric transducers attached to infinite constant cross-section waveguides, as encountered in guided wave ultrasonic inspection, is presented. Two-dimensional waveguide finite elements are used to model the waveguide. Conventional three-dimensional finite elements are used to model the piezoelectric transducer. The harmonic forced response of the waveguide is used to obtain a dynamic stiffness matrix (complex and frequency dependent), which represents the waveguide in the transducer model. The electrical and mechanical frequency response of the transducer, attached to the waveguide, can then be computed. The forces applied to the waveguide are calculated and are used to determine the amplitude of each mode excited in the waveguide. The method is highly efficient compared to time integration of a conventional finite-element model of a length of waveguide. In addition, the method provides information about each mode that is excited in the waveguide. The method is demonstrated by modeling a sandwich piezoelectric transducer exciting a waveguide of rectangular cross section, although it could be applied to more complex situations. It is expected that the modeling method will be useful during the optimization of piezoelectric transducers for exciting specific wave propagation modes in waveguides.     

Effect of the crack length on the piezoelectric damage monitoring of glass fiber epoxy composite DCB specimens

A new nondestructive method using the piezoelectric characteristics of polymer matrix was suggested for the damage monitoring of glass fiber polymer composites, and the feasibility of the use of the method was proven through basic experiments. Heretofore, most studies have focused on basic material properties such as the piezoelectric properties of unidirectional glass fiber epoxy composites with respect to the fiber orientation or the loading speed. In this study, the effect of the crack length on the piezoelectric damage monitoring of glass fiber polymer composites was experimentally investigated. Dynamic tests of mode I were performed using double-cantilever-beam (DCB) specimens, and the relationship between the crack length and the electric-charge signals measured from the electrodes on the DCB specimens was analyzed. The experiment results showed that the magnitude of the electric-charge signals increased very slowly as the crack tip approached the electrodes, rose sharply when the crack tip was passing through the electrodes, and then decreased fast and maintained relatively very low values when the crack tip had completely passed through the electrodes. The investigation of the mechanical behaviors via finite-element analyses during the dynamic tests revealed that the tendency of electric-charge signals is quite similar to that of the strain changes in glass fiber epoxy composites near electrodes. Based on the results of the experiments and finite-element analyses conducted in this study, it was concluded that piezoelectric damage monitoring can detect crack propagation.     

Fabrication of piezoelectric ceramic micro-actuator and its reliability for hard disk drives

A new U-type micro-actuator for precisely positioning a magnetic head in high-density hard disk drives was proposed and developed. The micro-actuator is composed of a U-type stainless steel substrate and two piezoelectric ceramic elements. Using a high-d31 piezoelectric coefficient PMN-PZT ceramic plate and adopting reactive ion etching process fabricate the piezoelectric elements. Reliability against temperature was investigated to ensure the practical application to the drive products. The U-type substrate attached to each side via piezoelectric elements also was simulated by the finite-element method and practically measured by a laser Doppler vibrometer in order to testify the driving mechanics of it. The micro-actuator coupled with two piezoelectric elements featured large displacement of 0.875 microm and high-resonance frequency over 22 kHz. The novel piezoelectric micro-actuators then possess a useful compromise performance to displacement, resonance frequency, and generative force. The results reveal that the new design concept provides a valuable alternative for multilayer piezoelectric micro-actuators.     

Micromechanics-based predictions of effective properties of a 1-3 piezocomposite reinforced with hollow piezoelectric fibers

Abstract

Presented is a development of models for predicting the effective properties of a piezocomposite reinforced with hollow piezoelectric fibers. The models are established based on micromechanics of representative volume element so-called modified concentric cylinders model. Predicted are five effective elastic constants, two effective piezoelectric coefficients, one effective dielectric permittivity, and two thermal expansion coefficients. Numerical results of a chosen material system are discussed. Comparisons with finite-element method show very good agreements. The predicted effective properties of the piezocomposite with hollow fibers provide the enhancement in several performance parameters up to three times as high as those with solid piezoelectric fibers.     

FEM-Based determination of real and complex elastic, dielectric, and piezoelectric moduli in piezoceramic materials

We propose an enhanced iterative scheme for the precise reconstruction of piezoelectric material parameters from electric impedance and mechanical displacement measurements. It is based on finite-element simulations of the full three-dimensional piezoelectric equations, combined with an inexact Newton or nonlinear Landweber iterative inversion scheme.We apply our method to two piezoelectric materials and test its performance. For the first material, the manufacturer provides a full data set; for the second one, no material data set is available. For both cases, our inverse scheme, using electric impedance measurements as input data, performs well.     

GHz frequency ZnO/Si SAW device

The demand for high-frequency low-loss filters generates intensive research on innovative wave guide solutions. In this work, a GHz SAW device based on a ZnO/Si structure was fabricated using classical UV photolithography. The thickness of the piezoelectric thin film was optimized and a specific interdigital transducer structure was used to generate third and fifth harmonic guided waves at 2.5 GHz and 3.5 GHz, respectively, with an aluminum strip larger than 1 micrometer. Different modes have been measured and theoretically identified thanks to an advanced finite-element/boundary-elementbased model. Good agreement is found between theory and experiments. The high-frequency modes have been fully characterized, allowing for accurate design of SAW devices exploiting such modes.     

Surface acoustic wave characteristics and electromechanical coupling coefficient of lead zirconate titanate thin films

Lead zirconate titanate (PZT) thin films were created on ST-X quartz using radio frequency magnetron sputtering deposition. PZT films deposited on quartz are used as a new piezoelectric substrate for surface acoustic wave (SAW) devices. Microelectromechanical technique was used to fabricate interdigital transducers on the surface of the substrate to be used as a SAW delay line device. The results show that the PZT film was successfully deposited on ST-X quartz, and that the PZT film on ST-X quartz can enhance the electromechanical coupling coefficients of SAW.     

Evaluation on mass sensitivity of SAW sensors for different piezoelectric materials using finite-element analysis

The mass sensitivity of the piezoelectric surface acoustic wave (SAW) sensors is an important factor in the selection of the best gravimetric sensors for different applications. To determine this value without facing the practical problems and the long theoretical calculation time, we have shown that the mass sensitivity of SAW sensors can be calculated by a simple three-dimensional (3-D) finite-element analysis (FEA) using a commercial finite-element platform. The FEA data are used to calculate the wave propagation speed, surface particle displacements, and wave energy distribution on different cuts of various piezoelectric materials. The results are used to provide a simple method for evaluation of their mass sensitivities. Meanwhile, to calculate more accurate results from FEA data, surface and bulk wave reflection problems are considered in the analyses. In this research, different cuts of lithium niobate, quartz, lithium tantalate, and langasite piezoelectric materials are applied to investigate their acoustic wave properties. Our analyses results for these materials have a good agreement with other researchers' results. Also, the mass sensitivity value for the novel cut of langasite was calculated through these analyses. It was found that its mass sensitivity is higher than that of the conventional Rayleigh mode quartz sensor.     

Theoretical Analysis of Wireless Passive Impedance-Loaded SAW Sensors

This paper concentrates on the theoretical analysis of wireless passive surface acoustic wave (SAW) impedance-loaded sensors. A general method is proposed for simulating the impedance-loaded SAW sensors. It is based on the combined finite-element method and boundary element method (FEM/BEM). A FEM is used to account for the mass loading effect of electrodes and a Green's function is used to model the piezoelectric substrate. Comparison between the simulations and measurements on SAW devices shows a good agreement. The calculated amplitude variation of the impulse response in time domain shows a resonant characteristic with the change of the loaded impedance. It is found that the return loss reaches the maximum value when the resonant frequency of the loaded circuits matches the center frequency of the short-circuited SAW transponder. This phenomenon is successfully explained by using the proposed model. Some high-performance sensors with greater amplitude modulation and larger sensitive range could be designed using this method.      

Direct sequence spread spectrum differential phase shift keying SAW correlator on GaAs

This paper presents the design, fabrication, and experimental results for a differential phase shift keying (DPSK) single SAW-based correlator on GaAs for direct sequence spread spectrum applications. The DPSK modulation format allows for noncoherent data demodulation; the SAW device correlator acts as the despreader. Unlike the conventional technique of using two parallel correlators and a one data bit delay element, this new system uses two inline correlators. When implemented on SAW devices, this in-line structure has the advantage of an inherent one data bit delay, lower insertion loss, and less signal distortion than the parallel structure. The DPSK correlator is fabricated on a {100} cut GaAs substrate with SAW propagation in the 110 direction, Using this cut, which is widely used in electronics, Rayleigh waves are generated with a piezoelectric coupling coefficient of the same order as ST-cut quartz. The piezoelectric semiconductor GaAs is of great interest because it is the only substrate that can be used to integrate SAW devices directly with electronics on the same chip, resulting in smaller packaging, reduction of packaging parasitics, lower cost, and greater system integration. This paper presents experimental results for SAW in-line correlator structures on GaAs along with their despreading system performances. Experimental measurements in both the time and frequency domains were performed and were found to be in good agreement with theoretical predictions.     

Magnetic Field-Based Eddy-Current Modeling for Multilayered Specimens

Eddy-current inspection for nondestructive evaluation has traditionally been investigated in terms of coil impedance signals via theoretical and experimental methods. However, advanced eddy-current techniques use solid-state sensors such as Hall devices, giant magnetoresistive sensors, anisotropic magnetoresistive sensors, and superconducting quantum interference devices for magnetic field measurement to achieve better sensitivity and high temporal and spatial resolution in material evaluation and characterization. Here, we review the Dodd and Deeds integral model and use the truncated region eigenfunction expansion (TREE) method for computation of the magnetic field. This results in series expressions instead of integral ones. Thus, the computation is both simplified and speeded up so that it becomes convenient for solving one-dimensional eddy-current inverse problems. We compare the theoretical results from the analytical model with the results from a numerical simulation based on the finite-element method in terms of accuracy and computation time.     

A tubular piezoelectric vibrator gyroscope

This paper proposes a vibrator gyroscope made of a piezoelectric tube, which has the same configuration as that used for the tri-axial sensors and actuators developed in our previous paper. The gyroscopic operation is the same as a circular rod, but the polarization (in thickness direction of the shell) and, accordingly, the electrode arrangement are much simpler. Wireless LAN arrangement is devised for remote data access with which the measurement is possible for the gyroscope under rotation. The experimental results are compared with the numerical simulation with three-dimensional finite-element calculation. The discrepancy between the measured and the experimental is found to depend on the asymmetrical deformation of the structure, and the cause is clearly demonstrated via simulation. This shows the usefulness of the numerical modeling to investigate the cause, in which the parameters of dimensions and boundary conditions can easily change.     

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.     

Finite-element simulation of wave propagation in periodic piezoelectric SAW structures

Many surface acoustic wave (SAW) devices consist of quasiperiodic structures that are designed by successive repetition of a base cell. The precise numerical simulation of such devices, including all physical effects, is currently beyond the capacity of high-end computation. Therefore, we have to restrict the numerical analysis to the periodic substructure. By using the finite-element method (FEM), this can be done by introducing periodic boundary conditions (PBCs) at special artificial boundaries. To be able to describe the complete dispersion behavior of waves, including damping effects, the PBC has to be able to model each mode that can be excited within the periodic structure. Therefore, the condition used for the PBCs must hold for each phase and amplitude difference existing at periodic boundaries. Based on the Floquet theorem, our two newly developed PBC algorithms allow the calculation of both, the phase and the amplitude coefficients of the wave. In the first part of this paper we describe the basic theory of the PBCs. Based on the FEM, we develop two different methods that deliver the same results but have totally different numerical properties and, therefore, allow the use of problem-adapted solvers. Further on, we show how to compute the charge distribution of periodic SAW structures with the aid of the new PBCs. In the second part, we compare the measured and simulated dispersion behavior of waves propagating on periodic SAW structures for two different piezoelectric substrates. Then we compare measured and simulated input admittances of structures similar to SAW resonators.