A Two-dimensional Theory for Surface Acoustic Wave Propagation in Finite Piezoelectric Solids

Abstract

Surface acoustic waves (Rayleigh waves) are analyzed for semi-infinite anisotropic solids only for essential propagation characteristics like the velocity and decaying parameters, which are important in engineering applications. The limitations of these results are obvious because devices are usually built on a finite piezoelectric substrate with propagation properties different from the analytical model with which the parameters are derived. For an accurate analysis of the dominant mode of surface acoustic wave propagation in plate-like finite piezoelectric solids, a two-dimensional theory has been developed based on the exponential expansion of displacements and electrical potential in the thickness direction, effectively creating a theory similar to popular plate theories of Mindlin, Lee, and others.

A two-dimensional analysis of surface acoustic waves in finite elastic plates with eigensolutions

“…Based on the similar principle and procedure, Wang and Hashimoto et al [16][17][18][19] derived a two-dimensional theory for the analysis of surface acoustic waves in finite solids, aiming at the accurate prediction of surface acoustic wave velocity and modes in resonators. This method has been applied to anisotropic materials, but the thickness of substrates has been assumed to be large enough, at least five wavelengths or more to ensure the vanishing of exponentially decaying waves in depth.…”

“…Following the two-dimensional expansion procedure [16][17][18][19][20][21] , we have the displacement expansion in the thickness coordinate as…”

“…For surface acoustic waves in a plate with finite thickness, as shown in Figure 1, we assume that the displacements take the same form as in a half-space with exponential variation along the thickness coordinate [1-5, [16][17][18][19] : [26][27][28] , the strains from eq. (1) are …”

“…Using known dominant modes in a plate as basis functions, the two-dimensional theory for surface acoustic waves in finite solids [11,12,[16][17][18][19] can be extended to include more vibration modes. A two-dimensional theory with the inclusion of the four vibration modes will be able to predict the surface wave velocity and mode coupling in a plate more accurately.…”

“…This study is part of our continuing effort on accurate analysis of surface acoustic waves in finite solids with typical applications in surface acoustic wave resonator design [16][17][18][19] . By expanding displacements in basis functions from eigenmodes of surface acoustic waves in an infinite plate, we should be able to improve the previous two-dimensional theory in cases where the plate thickness should be considered.…”