Finite element analysis of piezoelectric thin film membrane structures

Thin film structures have found a wide variety of applications in electromechanical technologies. As the design flexibility for these structures increases, so does the demand for design software that can provide some good insights into the behavior of the structure before it is fabricated. In this study, a finite element code based on a combination of equivalent single-plate theory and classical laminated plate theory was used to predict the dynamic response of thin film structures in micro length scale. As a benchmark for the code development, thin film structures were also fabricated using MEMS technology, and their fundamental frequencies were characterized. It was demonstrated that the model predictions matched fairly well with the experimental data for the small membranes with widths less than 200 microm, but underestimated them for large ones with widths greater than 500 microm. The model also demonstrated that the fundamental frequencies increased with the thickness of the layers. The areas that need to be investigated further in order to improve the predicative capability of the calculations include effects of residual stress, dc bias voltage, parasitic capacitance, interaction of membrane vibration with the supports of the structure, and accurate measurement of the dimensions and material properties of the thin films.