Surface Acoustic Waves in an Infinite Plate of Functionally Graded Materials

We have found that the spatial variation of material properties such as elastic constants and density will result in significant changes in surface acoustic waves (Rayleigh waves) in a semi-infinite substrate including the wave velocity and deformation, implying potential advantages in modifying the velocity (frequency) and changing the surface deformation which are directly related to device performance and packaging, since it is generally required to obtain large electrical charge through surface deformation and minimizing energy leaking by limiting the deformation of bottom surface. With these positive results, we further consider the case that the substrate is finite in thickness, making the analytical model close to actual surface acoustic wave (SAW) resonators. Again by assuming the material properties varying along the thickness direction uniformly, we obtained the frequency equation by satisfying boundary conditions on the faces. Consequently, the deformation variation along the thickness is also obtained with specified variation parameters for possible optimal selection in variation schemes. Using the exponential variation of material properties in an isotropic plate as an example, we calculated the surface acoustic wave velocity and deformation for different parameters. It is found that unlike a homogeneous plate, the symmetric and anti-symmetric wave modes will not merge to one velocity even for smaller grading parameters and the deformation will also be distinctive. The gap between two velocities will be larger as the property variation increases. Also the surface acoustic wave modes exist for very small thickness of the plate. For surface acoustic wave resonators, such a phenomena demonstrates a possible way to have velocity (frequency) selectivity based on different operating modes, and the frequency selectivity can be further modified by using different material variation parameters. With the rapid advances of material processing techniques, such benefits of functionally graded materials (FGMs) in surface acoustic waves have great potential in the new generations of devices.