J. E. Lefebvre

Legendre polynomial modeling of composite bulk acoustic wave resonators

The Legendre polynomial method has been extended to the modeling of bulk acoustic wave (BAW) resonators. Modifications have been made to the formulation in order to account for large differences in the physical properties of adjoining layers and to take into account the electric source. A unique formalism has been obtained which allows for both harmonic and modal analyses. Resonance and antiresonance frequencies, electric input impedance, electromechanical coupling coefficients, and quality factors have been obtained for an aluminum/zinc oxide/aluminum (Al∕ZnO∕Al) BAW resonator. The results are in excellent agreement with analytical results.

Wave propagation in the circumferential direction of general multilayered piezoelectric cylindrical plates

The Legendre polynomial approach has been proposed to solve wave propagation in multilayered flat plates and functionally graded structures for more than ten years, but it can deal with a multilayered plate only when the material properties of two adjacent layers do not change significantly. In this paper, an improvement of the Legendre polynomial approach is proposed to solve wave propagation in what, from now on, we will call general multilayered piezoelectric cylindrical plates, to mean indifferently with or without very dissimilar materials. Detailed formulations are given to highlight the differences from the conventional Legendre polynomial approach. Through numerical comparisons among the exact solution (from the reverberation-ray matrix), the conventional polynomial approach, and the improved polynomial approach, the validity of the proposed approach is illustrated. Then, the influences of the radius-to-thickness ratio on the dispersion curves, the stress, and electric displacement distributions are discussed. It is shown that the conventional orthogonal polynomial approach cannot obtain correct continuous normal stress and normal electric displacement shapes, unlike the improved orthogonal polynomial approach, which overcomes these drawbacks. It is also found that three factors determine the distribution of mechanical energy and electric energy at higher frequencies: the radius-to-thickness ratio, the wave speed of component material, and the position of the component material.

Two-dimensional Legendre polynomial modeling of composite bulk acoustic wave resonators

A bidimensional analysis of 6 mm hexagonal resonators is described using a double orthonormal basis set for the expansion of field quantities. The analysis takes into account the electrical voltage source and by means of a unique formalism along with a single calculation restitutes all the types of resonance whatever the thickness to width ratio value through either modal solutions or electrical impedance. An illustrative example gives the capabilities of the method to investigate spurious modes in laterally bounded resonators.

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 high contrast partially electroded resonators by means of a polynomial approach

This work presents the modeling of high contrast partially electroded resonators by means of a polynomial approach. This method allows easily solving the equations that govern the structure. The boundary, symmetry, and continuity conditions are automatically incorporated into the equations of motion by the use of delta functions for the variables stress (T) and electric displacement (D) and appropriate analytical expression forms for the independent variables, mechanical displacements (u), and electric potential (ϕ). Structure symmetry was used to reduce the number of unknowns. For the zinc oxide (ZnO) resonator in extreme geometrical cases (thin plate and bar cases), a good agreement was obtained between the results of the proposed polynomial approach and those of an analytical approach for both the modal and harmonic analyses. The proposed polynomial approach was used to calculate the 2D resonator electrical admittance (full and partial metallization) near the 1D thickness fundamental mode, and the resu...

SAW characteristics in a layered ZnO/GaAs structure for design of integrated SAW filters

In this paper, characteristics of the lowest order SAW mode in a ZnO film on a GaAs structure are studied. Velocity and coupling coefficient (K/sup 2/) are calculated versus film thickness, film polarity orientation, and interdigital transducer (IDT) location. It is found that velocity varies with the product of the frequency and film thickness (fh), K/sup 2/ increases nearly monotonically with fh when the IDTs are located on the upmost surface with an interface free of metallization. When the interface is metallized, K/sup 2/ exhibits a maximum value of 1% for fh=230 m/s and a minimum value of 0.5% for fh=750 m/s. Burying the IDT at the interface gives rise to a higher K/sup 2/ (1.5% for fh=1500 m/s). These results are obtained using a (+Z)-oriented ZnO film, those with a (-Z)-oriented one are also given for comparison. Also given is the SAW displacement-potential ratio directly involved in the determination of the inter-electrode reflectivity.

Acoustic modes in cylindrically orthotropic hollow cylinders

At the 2000 IEEE International Ultrasonics Symposium, we presented a polynomial approach to study guided waves in infinite homogeneous solid cylinders. In this article, we extend equations to infinite homogeneous hollow cylinders. The crystalline axis Z is coincident with the cylinder axis and lateral surfaces are stress-free. Dispersion curves are presented for both a thin and a thick cylinders made of a cylindrically orthotropic material.

Lamb wave acousto-optic modulator in ZnO/MgO multiple quantum wells and comparison with classical modulator.

An analysis of a ZnO/MgO multiple quantum well (MQW) acousto-optic modulator with Lamb waves is performed. With the MQW thickness in the range of 0.2 times the Lamb wavelength, the only observed Lamb modes are the lowest-order symmetric S0 and antisymmetric A0 modes. These modes induce strain and electric field components which influence the absorption coefficient of the modulator by the associated variation of the excitonic energies of MQW. The optical absorption coefficient spectra of the modulator as a function of the Lamb waves power is presented. The Lamb-wave-based modulator gives a better absorption coefficient than the Rayleigh-wave-based one. An analysis of a classical acousto-optic modulator is also performed for comparison of performance.

Polynomial modeling of acoustic guided wave propagation in homogeneous cylinder of infinite length

In this paper, we present a polynomial approach for determining the acoustic guided waves in homogeneous infinitely long cylinders using elastic materials of cylindrical anisotropy. The formulation is based on linear three-dimensional elasticity using an analytic form for the displacement field. The approach incorporates the stress-free boundary conditions directly into the equations of motion which are solved numerically by expanding each displacement component using Legendre polynomials and trigonometric functions. The problem is then reduced for anisotropic homogeneous structures to a tractable eigenvalue problem allowing the dispersion curves and associated profiles to be easily calculated. Numerical results of the guided waves for axisymmetric and flexural modes are presented and compared with those published earlier in order to check up the accuracy and range of applicability of the approach. The developed software proves to be very efficient to retrieve the guided waves of any nature and the modes of all orders. The computational advantages of the approach are described.