A highly accurate mathematical method has been presented for analytical characterization of capacitive micromachined ultrasonic transducers (CMUTs) built with square diaphragms. The method uses a new two-dimensional polynomial function to more accurately predict the deflection curve of a multilayer square diaphragm subject to both mechanical and electrostatic pressure and a new capacitance model that takes into account the contribution of the fringing field capacitances. Both of the models have been experimentally verified by comparing the models predicted values with measurement results and are found to be in excellent agreement with a maximum deviation of less than 2% for experimentally measured capacitance values. 3-D electromechanical finite element analysis (FEA) for a wide range of material properties, geometric specifications, and loading conditions show that the presented method is highly consistent in accuracy over the typical square-diaphragm CMUT design space.

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