A mixed FEM/analytical model of the electrode mechanical perturbation for SAW and PSAW propagation

Mechanical reflections of SAW or pseudo-SAW (PSAW) under metallic electrodes are the basic phenomena utilized for low loss bandpass filters. Their precise modelling is becoming a key element in the design of more and more compact filters. The mechanical perturbation depends on both the mass loading effect (density and elasticity) and the topographic effect (electrode profile). The first published modelizations of the electrode mechanical perturbation were only analytical and involved major simplifying assumptions on tile shape or on the height of metallizations leading to a poor determination of the topographic effect. Later, numerical models based on the Finite Element Method (FEM) were presented. They were able to take into account complex electrode profiles. Since most of them proposed to discretize both the electrode and tile substrate, important computational efforts were required. Recently, another method was presented mixing an electrode discretization and a periodic Green function formalism for the substrate. In the present paper, we propose a new method to compute the dispersion curve for SAW and PSAW propagation under electrode including the effect of mass loading. First the Floquet theorem is used to expand the acoustic fields into spatial harmonics. Then, the relationships between stresses and displacements are derived for the semi-infinite homogeneous anisotropic substrate. Finally, the FEM is applied only to the electrode in order to carry out the coupling between spatial harmonics of stress and displacement vectors at the electrode substrate interface. The calculation is not restricted to any particular crystalline symmetries and only involves the plane strain assumption, thus taking into account transverse components of the waves. The problem of the elementary reflection coefficient determination is also examined. Both theoretical explanations, validations and comparisons with experience will be shown