Long thickness-extensional waves in thin film bulk acoustic wave filters affected by interdigital electrodes

We studied free vibrations of thin-film bulk acoustic wave filters with interdigital electrodes theoretically using the scalar differential equations by Tiersten and Stevens. The filters are made from AlN or ZnO films on Si substrates with ground and driving electrodes. They operate with thickness-extensional modes. The basic vibration characteristics including resonant frequencies and mode shapes were obtained. Their dependence on various geometric parameters was examined. It was found that for properly design filters there exist trapped modes whose vibrations are strong in regions with a driving electrode and decay away from the electrode edges. These trapped modes are essentially long plate thickness-extensional modes modulated by the electrode fingers. The number of trapped modes is sensitive to the geometric parameters.