Structural Optimization for Uniform Displacement Variations in ZnO FBAR Mass Sensor Using Rectangular Frame-Like Driving Electrodes

This paper aims to achieve the uniform displacement variations in a rectangular ZnO thin film bulk acoustic resonator (FBAR) with frame-like electrodes operating at the thickness-extensional (TE) mode. The variational formulation based on two-dimensional scalar equations provides a theoretical foundation for the Ritz method adopted in our analysis, and the resonant frequencies and vibration distributions of TE modes are obtained. A nearly uniform displacement distribution at the active area of the frame-like electroded FBAR is achieved by designing proper electrode size, which exhibits more uniform displacement distributions than ring electroded FBAR under the same structural sizes. Moreover, the principle of the achievement of a very uniform displacement distribution in the active area is illustrated. These conclusions provide a theoretical guidance for the design and optimization of ZnO FBAR mass sensor with high performance.