P Matrix Analysis of Surface Acoustic Waves in Piezoelectric Phononic Crystals

Large time/memory costs have constituted a significant obstacle for accurately analyzing surface acoustic waves (SAWs) in large size two-dimensional (2-D) piezoelectric phononic crystals (PnCs). To overcome this obstacle, this study introduces the unit P matrix and its associated cascading. To obtain an accurate unit P matrix, the Y parameters of the SAW delay lines were derived using a three-dimensional (3-D) finite element model (FEM) with and without 2-D piezoelectric PnCs, respectively, on the transmitting path. A time window function was adopted to extract the desired signals from the P matrix analysis. Then, unit P matrix cascading was used to obtain SAW propagation parameters for the large size piezoelectric PnCs. Using this method, the SAW in aluminum (Al) /128º-YXLiNbO3 PnCs was analyzed over 150 periods. Experiments were also conducted. To choose the appropriate size of the unit P matrix, the variance between experimental results and theoretical results, and time/memory cost were compared for different periods. The results indicate that cascading by unit P matrix of 25 PnCs periods can be appropriately adopted to accurately derive the SAW propagation parameters over 150 periods. This indicates the accuracy of the unit P matrix derived by 3-D FEM and the effectiveness of P matrix analysis.