A perturbation analysis of the attenuation and dispersion of surface waves

Abstract

A perturbation formulation of the equations of linear piezoelectricity is obtained using a Green’s function approach. Although the resulting equation for the first perturbation of the eigenvalue strictly holds for real perturbations of real eigenvalues only, it is formally extended to the case of purely imaginary perturbations of real eigenvalues. The extended equation is applied in the calculation of the attenuation of surface waves due to the finite electrical conductivity of thin metal films plated on the surface and air loading. The influence of the viscosity of the air is included in the air-loading analysis, and the calculated attenuation increases accordingly. Since the metal films are thin compared with a wavelength, an approximate thin-plate conductivity equation is employed in the determination of the attenuation due to the electrical conductivity of the films. The resulting attenuation is obtained over a very large range of values of sheet conductivity. This is accomplished by using the equation for the first perturbation of the eigenvalue iteratively to determine the solution and attendant attenuation to any desired degree of accuracy. The phase velocity dispersion curve due to the mechanical effect of a thin film plated on a substrate is determined for relatively large wavelengths by employing the perturbation equation iteratively, and excellent agreement is obtained with the results of other more direct approaches. The calculations have been performed for an aluminum film on either ST-cut quartz or Y-Z lithium niobate.

Acoustic Wave Sensors

“…For a given polymer material, the temperature at which film resonance is observed decreases with increasing device frequency and increasing film thickness. The film resonance model for polymer-coated SAW devices provides a more comprehensive understanding of polymer film behavior on SAW devices than previous models based on perturbation theory, [33,105,106] and helps to define a difference between acoustically thin and acoustically thick films [99].…”

In situ observation and measurement of the SAW thin-film acoustoelectric effect

“…This may be attributable to changes in the film profile, which are not accounted for by this simple model. The measured change in group delay, Δτ g , begins to diverge from the data fit around 500 Å because of mass-loading effects of the film and may be accounted for using Tiersten's equation [2], [16].…”

Precise modeling of complex SAW structures using a perturbation method hybridized with a finite element analysis

“…The theoretical analysis of SAW subject to mechanical prestress is mainly based on the perturbation method developed by Tiersten and Sinha [9]. It provides the frequency shift of a given SAW device induced by a mechanical perturbation applied to the propagation substrate.…”

“…An implicit summation is performed on all the indices i, k, j, and m of (6) [7]- [9], [13], [14]. Equation (6) approximates (1) quite well for a dense mesh using elements with typical dimensions much smaller than the acoustical wavelength.…”

“…The principal difficulty was to calculate the quasi-static mechanical behavior of anisotropic substrates of a complex geometry subject to an arbitrary stress condition and to couple the result with the Tiersten-Sinha 3D perturbation method [9]. Considering the dramatic increase in computer performance, available at lower and lower costs, switching from analytical methods to finite element analysis (FEA) appears to be a logical choice.…”