The calculation of quality factor of film bulk acoustic resonators with the consideration of viscosity

With the rapid sophistication of film bulk acoustic resonators (FBAR) technology and increased demands for precision frequency control products, it is natural to make use of the detailed analysis of acoustic waves propagating in the FBAR structures for design and estimating electrical parameters before actual fabrication. To this purpose, it is essential to consider the material viscosity, which is the source of energy loss and dissipation of acoustic wave devices. The dominant viscosity originated from the bonding layers between different materials may not be conveniently represented by additional layers in analysis. To explore the better consideration of viscosity, we assume the bonding layer will be blended into the metal and piezoelectric layers by adding complex elastic constants which are proportional to vibration frequency. The actual value of the viscosity factor is assumed first in our study to examine the effect of parameters, but they can be determined in actual devices through known quality factor of a resonator. In other words, the viscosity factor in our study is given as an equivalent parameter. Such a procedure is useful in understanding the effect of viscosity and their amplitudes while they are considered in different layers. The analytical approach based on wave propagation in layered structures will be important in improving design and conceiving new products.