Victor Y. Zhang

Acoustic wave propagation in continuous functionally graded plates: an extension of the Legendre polynomial approach

The propagation of guided waves in continuous functionally graded plates is studied by using Legendre polynomials. Dispersion curves, and power and field profiles are easily obtained. Our computer program is validated by comparing our results against other calculations from the literature. Numerical results are also given for a graded semiconductor plate. It is felt that the present method could be of quite practical interest in waveguiding engineering, non-destructive testing of functionally graded materials (FGMs) to identify the best inspection strategies, or by means of a numerical inversion algorithm to determine through-thickness gradients in material parameters.

LEGENDRE POLYNOMIAL APPROACH FOR MODELING FREE-ULTRASONIC WAVES IN MULTILAYERED PLATES

Modeled on the Laguerre polynomial approach used for surface acoustic waves, a formulation is presented for the study of free-acoustic wave propagation in layered plates. It uses the Legendre polynomials. Each layer can be of arbitrary anisotropy and piezoelectricity with arbitrary crystal orientation with the only restriction that the parameters of the constituent materials are close to each other. Formulations are given for open-circuit and short-circuit surfaces. Phase velocity dispersion curves, attenuations, power distributions, and field profiles are easily obtained from an algorithm easily implemented on a computer using commercial software. Numerical results are given for AlAs/GaAs multilayered structures which illustrate the capabilities of the described method. Its major advantages are: (i) in a unified formulation, all types of modes, surface modes, interface modes, and plate modes are naturally encompassed. (ii) Large values of the frequency-thickness product as compared to the values allowed ...

A unified formalism using effective surface permittivity to study acoustic waves in various anisotropic and piezoelectric multilayers

A unified formalism is presented that uses the effective surface permittivity (ESP) to study surface acoustic waves (SAW) in layered substrates and guided waves in layered plates. Based on known mathematical tools, such as ordinary differential equation and transfer matrix, a generalized surface impedance (GSI) concept is developed and exploited to investigate the acoustic propagation in various anisotropic and piezoelectric layered structures. The ESP function, originally defined for the surface of a homogeneous and semi-infinite piezoelectric substrate, is extended to both the top surface of and an interface in a layered half space, as well as to either surface of a finite-thickness plate. General ESP expressions for all mentioned configurations are derived in terms of an equivalent GSI matrix. It is shown that, when using the appropriate GSI matrices, the same form of the ESP expressions applies no matter whether the structure is a homogeneous half space alone or coated with a layered plate or a layered plate alone. GSI matrices are explicitly given in terms of the bulk partial mode solutions for a substrate and via the transfer matrix for a plate. Modified GSI matrices for structures consisting of both a plate and a substrate are also specified. Analytical development is fully detailed to suit program implementation. To illustrate its versatility, the formalism is also applied to two-substrate configurations, allowing one to analyze guided waves in a plate sandwiched between and interfacial waves existing along the boundary of two different media. Numerical examples are given to illustrate the spectrum features that the ESP shows for various structures. Deduced ESP expressions allow one to locate directly all piezoelectrically active waves in any structure including at feast one piezoelectric layer. Acoustic modes that are not piezoelectrically active and those in non-piezoelectric materials can be also obtained by using the intermediate results, such as derived GSI matrices.

Conceptual advantages and limitations of the Laguerre polynomial approach to analyze surface acoustic waves in semi-infinite substrates and multilayered structures

Laguerre polynomial approach is used to calculate velocities, coupling coefficients, and field distributions of surface acoustic waves in both semi-infinite substrates and multilayered structures. Approximation used in boundary conditions for applying the Laguerre polynomial method is investigated. Effectiveness of the method to calculate the coupling coefficient is checked. Its capabilities with regard to the various types of waves are reviewed. It is shown that Laguerre polynomial method cannot be used to study leaky surface acoustic waves. For true surface acoustic waves it can, but for deep penetration, computing time becomes prohibitive. Laguerre polynomial method is interesting for true surface acoustic waves modes if decay length is of the order of one acoustic wavelength: velocities, coupling coefficient and, continuous field profiles are quite well returned. However, for multilayered structures, very dissimilar parameters of the constituent materials give rise to significant field level discontinuities at the interfaces. It is shown that the Laguerre polynomial method does not return, within reasonable computing time and required memory, these discontinuities of which multiple quantum well-based devices can take advantage.

Piezoacoustic wave spectra using improved surface impedance matrix: Application to high impedance-contrast layered plates

Starting from the general modal solutions for a homogeneous layer of arbitrary material and crystalline symmetry, a matrix formalism is developed to establish the semianalytical expressions of the surface impedance matrices (SIM) for a single piezoelectric layer. By applying the electrical boundary conditions, the layer impedance matrix is reduced to a unified elastic form whether the material is piezoelectric or not. The characteristic equation for the dispersion curves is derived in both forms of a three-dimensional acoustic SIM and of an electrical scalar function. The same approach is extended to multilayered structures such as a piezoelectric layer sandwiched in between two metallic electrodes, a Bragg coupler, and a semi-infinite substrate as well. The effectiveness of the approach is numerically demonstrated by its ability to determine the full spectra of guided modes, even at extremely high frequencies, in layered plates comprising up to four layers and three materials. Negative slope in f-k curve for some modes, asymptotic behavior at short wavelength regime, as well as wave confinement phenomena made evident by the numerical results are analyzed and interpreted in terms of the surface acoustic waves and of the interfacial waves in connection with the bulk waves in massive materials.

Integration of RF filters on GaAs substrate

Up to now, RF front-end and interstage surface acoustic wave (SAW) filters for mobile communication are mainly fabricated on LiNbO/sub 3/ and LiTaO/sub 3/ substrates. A monolithic integration of these filters on semiconductor substrates is highly desirable to miniaturize the outer dimensions of the cellular phones. Direct realization of SAW filters on non piezoelectric or weakly piezoelectric substrates is impossible. One alternative is the deposition of a piezoelectric film on the semiconductor substrate. In this paper, we present an analysis and realization of a ladder SAW filter built up on a two-layered structure made up of a ZnO film on a GaAs substrate in the 900 MHz frequency range.

Two true surface acoustic waves and other acoustic modes in (110) plane of Li2B4O7 substrate

The surface acoustic waves (SAWs) and other acoustic modes propagating in the (110) plane of Li2B4O7 are investigated by means of the effective surface permittivity (ESP). It is demonstrated that the velocity of all piezoactive SAWs, both true and pseudo, as well as surface skimming bulk waves (SSBWs) can be numerically determined by computing the ESP as a function of acoustic trace slowness. A physical phenomenon not reported has been found for certain propagation directions, namely, simultaneous existence of two true SAWs, both being of the generalized Rayleigh type, together with a pseudo SAW of similar polarization. Propagation velocity, electromechanical coupling coefficient, and decay factor have been verified and confirmed by using two different sets of material constants and two numerical methods. The obtained values and accuracy of SAWs parameters are compared, and the validity conditions discussed. The generalized slowness diagram, plotted for the sagittal plane, enables to determine the total n...

Theoretical study of surface acoustic waves in (n11) GaAs-cuts

The propagation characteristics of true and leaky or pseudo surface acoustic waves (TSAW and PSAW=LSAW) on (n11) GaAs-cuts, n=1, 2, 3 and 4, are theoretically calculated as a function of propagation direction. They include phase velocity (V), electromechanical coupling constant (K/sup 2/), and attenuation factor (/spl alpha/) of wave propagation on a metallized surface. The results show that PSAW mode velocities are significantly higher than corresponding TSAW velocities, and for certain propagation directions the attenuation factor is extremely small (10/sup -5/ dB//spl lambda/). Highly coupled PSAW modes exist for propagation directions where the TSAW are very poorly coupled. For certain isolated directions, attenuation of the wave is null (/spl alpha/=0), PSAW becoming a non-leaky SAW with partial polarization. And in this case the corresponding TSAW are decoupled from the surface electric excitation. Analysis of relations between various modes (TSAW, PSAW and SSBW, surface skimming bulk wave) is made with the help of the effective surface permittivity function and the generalized slowness diagram. A coupling constant definition different from the usual 2/spl Delta/V/V is used, its validity and application conditions are discussed.

Modeling of bulk acoustic wave devices built on piezoelectric stack structures: Impedance matrix analysis and network representation

The fundamental electro-acoustic properties of a solid layer are deduced in terms of its impedance matrix (Z) and represented by a network for modeling the bulk acoustic wave devices built on piezoelectric stacked structures. A piezoelectric layer is described by a three-port equivalent network, a nonpiezoelectric layer, and a short- or open-circuit piezoelectric layer by a two-port one. Electrical input impedance of the resonator is derived in terms of the Z-matrix of both the piezoelectric layer and an external load, the unique expression applies whether the resonator is a mono- or electroded-layer or a solidly mounted resonator (SMR). The loading effects of AZ-electrodes on the resonating frequencies of the piezoelectric ZnO-layer are analyzed. Transmission and reflection properties of Bragg mirrors are investigated along with the bulk radiation in SMR. As a synthesizing example, a coupled resonator filter (CR.F) is analyzed using the associated two-port equivalent network and by calculating the power transmission to a 50 Omega-load. The stacked crystal filter is naturally included in the model as a special case of CRF. Combining a comprehensive matrix analysis and an instructive network representation and setting the problem with a full vectorial formalism are peculiar features of the presented approach.

Polynomial method applied to acoustic waves in inhomogeneous cylinders

We present a numerical method for calculating the waves in inhomogeneous cylinders utilizing elastic materials of cylindrical anisotropy. The formulation is based on linear three dimensional elasticity using an analytic form for the displacement field. We have developed the required formulas to apply it to cylinders in which the inhomogeneity in the elastic moduli and density is a function of the radial coordinate giving rise to functionally graded material (FGM) cylinders. The method incorporates the stress-free boundary conditions directly in the equations of motion by assuming position-dependent elastic constants and mass density. The technique is applied to analyze several inhomogeneous cylinders made up of a mixture of ceramic and metal and results are compared with those published earlier. The agreement is very good for both thin and thick cylinders which clearly illustrates the effectiveness of using the presented method to numerically model guided waves in inhomogeneous cylinders.