IDT geometry and crystal cut effects on the frequency-temperature curves of a SAW periodic structure of quartz

Piezoelectric Lagrangian equations for the frequency-temperature behavior of quartz is presented. A finite element study of these Lagrangian equations is performed for a two-dimensional periodic SAW structure of quartz. Plane strain assumptions are used to enable a two-dimensional analysis of straight crested acoustic waves in the structure. Adaptive finite element meshes are employed to reduce the size of the finite element problem. The frequency-temperature characteristics of the two fundamental SAW modes are compared and contrasted. Numerical results are compared with experimental data for the ST- and K-cut of quartz. The finite element results for the turnover temperature and the 2nd temperature coefficient of the f-t curve as a function of the electrode height are found to compare well with the ST-cut experimental data. Similar numerical results for the change in frequency-temperature characteristics of the K-cut as a function of crystal cut angles phi is also found to be compare well with the experimental data. The experimental data are found to follow the lower bandgap frequency SAW1.