The natural vibrational modes of axially symmetric piezoelectric ceramic disks have been calculated by the finite-element method. The disks are of the type used as active elements in compressional wave ultrasonic transducers, and are electrically polarized in thickness with full electrodes on the disk's major faces. To optimize disk geometry for ultrasonic transducer application, the dependence of the vibrational modes on the disk diameter-to-thickness ratio for ratios from 0.2 (a tall cylinder) to 10.0 (a thin disk) has been studied. Series and parallel resonance frequencies for each of the modes are determined through an eigenfrequency analysis, and effective electromechanical coupling coefficients are calculated. The modal displacement fields in the disk are calculated to determine the physical nature of each mode. An analysis of the complete spectrum of piezoelectrically active modes as a function of diameter-thickness ratio is presented for the ceramic PZT-5H, including and identification of radial, edge, length expander, thickness shear, and thickness extensional vibrations. From this analysis, optimal diameter-to-thickness ratios for good transducer performance are discussed.

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Measurements show an upward shift on the order of 50 ppm in the resonant frequency of a surface acoustic wave (SAW) resonator, as taken before and after the device is hermetically sealed in vacuum following a certain glass-frit sealing process. The authors analyze some of the thin-film phenomena that are potential sources of the observed frequency shift and that may affect the long-term stability of such devices. Various factors contributing to the shifts include: 1) intrinsic or structural stresses in the bonding layers as well as in the interdigital transducer (IDT) fingers; 2) thermal stresses due to the differences in thermal expansion coefficients of the metallic IDT fingers and the bonding agent (glass frits) from those of quartz; 3) partial oxidation of the IDT fingers and transmission lines during the frit glazing process; and 4) possible metal diffusion into quartz. Quantitative estimates of the contribution of two factors to the total observed frequency shift after a certain glass-frit sealing process are provided. Rough estimates of the frequency shifts due to the oxidized film are made from the dispersion curves for a uniform thin aluminum film and for its oxide film as fully plated on a quartz substrate. It is concluded that the results may provide a way of estimating the magnitude of the intrinsic stress for a given long-term stability of the SAW device.