The analysis of film acoustic wave resonators with the consideration of film piezoelectric properties

The vibration frequency analysis of film bulk acoustic resonators (FBAR) is based on the assumption of layered infinite plates vibrating at a working mode, which can be the thickness-extension or thickness-shear depending on the choice of the mode. A transcendental equation is used to determine the vibration frequency with given materials and plate thicknesses. Similar to the analysis and design of quartz crystal resonators of thickness-shear type, frequency equations and displacements in films can be used for the calculation of resonator properties which are important for improvement and modeling. By expanding the formulation to include the piezoelectric effect, we shall also be able to obtain the electrical field as a vital addition to mechanical solutions. Of course, the piezoelectric effect will also be included in the solutions of frequency and displacements. The solutions can be used to calculate the electrical circuit parameters of a resonator. We study vibrations of layered FBAR structures for both thickness-extension and thickness-shear modes and the solutions also include the electrical field under an alternating voltage. With these equations, solutions, and further formulations on the electrical circuit properties of FBAR, we can establish a systematic procedure for the analysis and design, thus completing the currently empirical methodology in resonator development. These one-dimensional formulation based on the infinite plate assumption can be further improved through the consideration of finite plates and numerical solutions based on the commonly used finite element analysis. These studies will be the basis for the formulation and calculation of electrical circuit parameters that are highly demanded as FBAR technology is expanding quickly to other applications. The accurate analysis and resonator property extension will contribute to the sophistication of FBAR technology with improved design procedure and performance.

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