A new efficient combined FEM and periodic Green´s function formalism for the analysis of periodic SAW structures

Analyzing periodic structures on a semi-infinite piezoelectric substrate is one of the most important problems being investigated by SAW researchers. Recently, numerical mixed FEM/BEM models have been presented to analyze periodic transducers including mass loading effects and the effectiveness of these methods have been demonstrated. However, the numerical interpolation used (“pulse function” or FEM basis function) is not well suited for stress and charge distribution representations leading to a great number of coefficients for each electrode. On the other hand, it is well known that charge distribution has a 1/√(1-x²) singularity at both edges of each electrode and that T_n(x)/√(1-x²) type basis functions (where T_n(x) is the first kind Chebyshev polynomial of rank n) are of practical use to develop functions exhibiting such discontinuities. In this paper, we will present a new mixed FEM/BEM model using this efficient basis function interpolation. Furthermore, this method incorporates results on the periodic harmonic Green´s function for which only a very small number of spatial harmonics is necessary. As validation of this new periodic model, a comparison between simulation and experiment will be presented for the case of synchronous one port SAW resonators on 36° Y rotated cut LiTaO₃