Finite element calculation of the dispersion relations of infinitely extended SAW structures including bulk wave radiation

In the design procedure of surface acoustic wave (SAW) devices simple models like equivalent circuit models or the Coupling of Modes (COM) model are used to achieve short calculation times. Therefore, these models can be used for iterative component optimization. However, they are subject to many simplifications and restrictions. In order to improve the parameters required for the simpler models and to achieve better insight ot the physics of SAW devices analysis tools solving the constitutional partial differential equations are needed. We have developed an efficient calculation scheme based on the finite element method. It makes use of newly established periodic boundary conditions (PBCs) allowing the simulation of an infinitely extended SAW device. This is a good approximation of many SAW devices which show a large number of periodically arranged electrodes. We have developed two different formulations for the PBCs: One leads to a small quadratic eigenvalue problem operating on a larger matrix. These formulations allow the calculation of the complete dispersion relation. Bulk acoustic waves (BAWs) which are generated due to mode conversion at electrode edges are allowed to leave the calculation area nearly without reflection. Therefore, the calculation scheme also considers damping coefficients caused by the conversion of surface waves into bulk waves. This behavior coincides well with real SAW devices in which the substrate thickness is large compared to the used wavelengths and, additionally, the bulk waves are scattered in all directions at the rough substrate bottom. In the paper, a short introduction to the basic theory of the numerical calculation scheme will be given first. The applicability of the calculation scheme will be demonstrated by comparing analytical, measured and simulated results.

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