A novel deflection shape function for rectangular capacitive micromachined ultrasonic transducer diaphragms

•A simplified finite element simulation method for CMUT is presented.•Effectiveness of the finite element model is validated by research results from a reference.•A novel deflection shape function for rectangular membranes is first proposed.•The function-calculated results show excellent agreements with FEA results.

A highly accurate analytical deflection shape function that describes the deflection profiles of capacitive micromachined ultrasonic transducers (CMUTs) with rectangular membranes under electrostatic pressure has been formulated. The rectangular diaphragms have a thickness range of 0.6–1.5 μm and a side length range of 100–1000 μm. The new deflection shape function generates deflection profiles that are in excellent agreement with finite element analysis (FEA) results for a wide range of geometry dimensions and loading conditions. The deflection shape function is used to analyze membrane deformations and to calculate the capacitances between the deformed membranes and the fixed back plates. In 50 groups of random tests, compared with FEA results, the calculated capacitance values have a maximum deviation of 1.486% for rectangular membranes. The new analytical deflection function can provide designers with a simple way of gaining insight into the effects of designed parameters for CMUTs and other MEMS-based capacitive type sensors.