Analytical model with lateral force for conventional CMUT membranes under large deflection using Von Kármán equations

Capacitive Micromachined Ultrasonic Transducer (CMUT) is a new type of ultrasound wave generator and detector. Analytical method is intuitive to understand the mechanism and physical effects through modeling of CMUT. To optimize the design procedures of CMUT membrane undergoing large deflection, a new analytical model with the consideration of the lateral force using Von Kármán equations is proposed. This model is capable of calculating the membrane profile of the CMUT since it includes the effect of the lateral force. The calculated results match well with the simulated results and the maximum deflection error in the center of the CMUT is less than 1% of the simulation results. The lateral force increases with the deflection of the membrane and it can be found that with the introduction of the lateral force, the proposed model can accurately estimate the membrane large defection profile in both single and double-layer membrane cases. The capacitance of the CMUT can be derived when the deflection profile of the membrane is available.