Analysis of periodic structures for BAW and SAW resonators

A bulk acoustic wave (BAW) or a surface acoustic wave (SAW) resonator is an acoustic device with the frequency characteristic of standing acoustic waves in the substrate and electrodes. Sometimes, the standing waves are almost spatially periodic depending on the geometry of the electrodes and the substrate. This is especially true in SAW resonators with long arrays of inter-digital transducers (IDTs) on the surface of the substrate, and may also be true for BAW resonators with similar arrays of IDTs. In these situations where the standing waves are essentially periodic, substantial analytical and design information on the frequency characteristics of the acoustic resonator itself can be obtain from the analysis of one period of the standing waves. The advantage of analyzing just one period of the standing wave is the significant reduction in the size of the numerical model. Sometimes, it is not possible to perform an finite element (fem) analysis of the entire acoustic resonator. This is especially true for SAW resonators, and we have to resort to a periodic analysis. This paper discusses the finite element periodic analysis of BAW and SAW resonators. The boundary conditions and finite element meshing of a periodic structure are presented. Examples are provided which shows the results of the periodic analysis compared with the experimental results of the actual resonators or the results of the full analysis which include the frequency-temperature behavior, mode shapes and frequency spectra. Examples are drawn from BAW resonators and SAW resonators including leaky SAW resonators