Resonant Frequency Analysis of Capacitive Micromachined Ultrasonic Transducers (CMUTs) with Layered Membranes

Capacitive micromachined ultrasonic transducers (CMUTs) show important applications in fields of 3D ultrasound and underwater imaging. The resonant frequency is one of the important performance parameters of CMUTs, which determines the imaging resolution. For CMUTs with multilayer circular membranes, the calculation methods for the equivalent structure and material property parameters of the multilayer membranes as well as the equivalent electrode distance are proposed. As such, the vibrating equation of the multilayer membranes under both DC bias and AC voltages is established. Both Galerkin method and energy equivalent method are utilized to solve the vibrating equation, and two types of analytical expressions for the resonant frequency are obtained. The numerical results based on finite element method (FEM) are used to validate the analytical expressions, and parametric study for the analytical expressions is further conducted. The results indicate that the analytical expression based on the energy equivalent method has higher accuracy in resonant frequency predication than the one based on the Galerkin method. The theoretical expression is applicable to the cases where the membrane diameter to its thickness ratio is in the range from 20 to 100, and the cavity height is less than or equal to the thickness of CMUTs membranes. The relative error of the theoretical analysis is within 5% with respect to the FEM simulation in almost the whole varying range of the bias voltages, i.e. from 0 V to the voltage closed to the collapse voltage. In addition, CMUTs with three layers of membranes are employed to experimentally validate the analytical expression. The results show that the experimental value of the resonant frequencies of the fabricated CMUTs chips under different bias voltages agree well with the theoretical value by the analytical expression. Therefore, the derived analytical expression for the resonant frequency can be widely used for the design and optimization of CMUTs with multilayer membranes.