The propagation of Rayleigh waves in layered piezoelectric structures with viscosity

Layered structures of piezoelectric films are the core of recently emerged film acoustic resonators of both film bulk acoustic resonators (FBAR) and surface mounted resonators (SMR). As products of film acoustic wave resonators are being accepted in telecommunication applications, notable advantages and acceptable performance have been subjected to possible improvements with structures, materials, and other modifications to meet demands for miniaturized devices from the preferred manufacturing process. These improvements, as the products are already sophisticated with the manufacturing process and design techniques, have to be made with the combination of analytical model and actual fabrication. For practical applications as a frequency control element in circuits, we need to have the electrical parameters from design and actual products, but we can rarely obtain the estimation before we make actual measurement like the resistance, capacitance, and the quality factor. With the known functioning mechanism and energy loss mechanism of acoustic wave resonators, we have been able to formulate the wave propagation in resonators with viscosity of materials for solutions which can be used for the estimations of electrical parameters. Such a procedure has been established for bulk acoustic wave resonators of both traditional quartz crystal and film bulk acoustic wave types, and the key issue is now the determination of the viscosity, which usually is not the ideal value we can obtain from material testing. Not hard to imagine, the dominant energy loss, or the viscosity, is from the bonding process of layers which brought contamination and surface modification which play more important roles in the overall performance of a typical resonator. With these principles and experiences, we start with a surface mounting resonator model with viscous piezoelectric layers. Following the familiar procedure for the viscosity consideration, a complex system of wave propagation equations a- - re obtained, and the vibration frequency, which is no longer real-valued, the deformation, and electrical fields are obtained. Our focus is on the effect of the viscosity on the vibration frequency and wave propagation. With the known major properties such as the quality factor, we can obtain a relatively good estimation of the dominant viscosity in the piezoelectric layer, which in turn will be essential for the calculation of other electrical parameters as we have done for FBAR type. Of course, the usual structure of surface wave resonators with discrete electrodes (IDTs) will result in more complicated formulations which will be our focus the future studies.