A two-dimensional electromechanical composite plate model for piezoelectric micromachined ultrasonic transducers (pMUTs)

Abstract

A two-dimensional composite plate model was developed as part of the design methodology for micro-scale thin membrane structures in general and pMUTs in particular. The model was compared with a one-dimensional beam model developed earlier and experimental measurements. The two-dimensional model was shown to converge to the one-dimensional model for the structures with a large aspect ratio. Compared to the experimental data, the qualitative trends regarding the dependence of transducer performance on the aspect ratio predicted by the model were validated by the experimental measurements in all cases except that of the electromechanical coupling factor k2eff. The quantitative agreement between model and experimental data was quite good for all parameters at a transducer width of 180 µm, and became worse as the transducer width became smaller. The resonance frequency was predicted very well by the model, and did not depend on the aspect ratio. With the enhanced flexibility provided by the two-dimensional model, some optimization study was also performed. It was found that among different geometries, a square membrane, i.e. a membrane with the aspect ratio equal to 1, appears to have the highest effective coupling coefficient. On the other hand, for a given square membrane, the electrode which covers about 25% of the membrane, i.e. 50% of the width and length measured from the center, possesses the optimized coupling coefficient. In practice, the model can be used to first optimize the dimension of the membrane for pMUTs to obtain the targeted frequencies and then the electrode coverage area for optimized coupling coefficient.