Nonlinear Dynamics of Circular Capacitive Micromachined Ultrasonic Transducers

A multiphysics model for capacitive micromachined ultrasonic transducers (CMUTs) is developed taking into account the main sources of nonlinearities in the case of circular plates. The equation of motion is reduced to an asymmetric Duffing equation which is solved using the harmonic balance method coupled with the asymptotic numerical method. Multiple-valued solutions, indicating the occurrence of jump phenomena, are observed numerically and confirmed experimentally on measured frequency responses of micro-machined CMUTs based on anodic bonding of a SOI wafer on a glass wafer. This purely numerical approach allows designers to control the resonator bifurcation topology by tuning the design parameters and thus gives the possibility of driving the CMUT beyond its critical amplitude. As a consequence, the CMUT performances can be enhanced in terms of bandwidth and generated acoustic power.