A new deflection shape function for square membrane CMUT design

A new deflection shape function that can predict the deflection profile of a uniformly loaded microfabricated clamped square membrane with a much higher accuracy compared to existing models has been presented. The model has been developed by using an empirical data fit technique to identify new terms and new parameter values that compensate for the deviation of the existing deflection shape functions for square membranes from experimental and FEA results. The model has been optimized for typical design space of square diaphragm capacitive micromachined ultrasonic transducers (CMUT). The new model predicted deflection profiles exhibit excellent agreement with experimental and 3-D FEA results. CMUT capacitance values calculated after pressure loading using the new deflection shape function show a maximum deviation of 3.4% from the FEA results compared to ~7-21% maximum deviations when existing models are used. The new model will be helpful to implement a much higher accuracy design methodology for CMUTs.