Theoretical modeling and optimization design of T-shape cavity CMUTs for enhanced acoustic performances and lowered bias voltage

Capacitive micromachined ultrasonic transducers (CMUTs) are key components of ultrasonic technology, which have broad applications in medical, industrial, and military fields. The theoretical model enables rapid analysis of their electromechanical performances, which in turn guides the iterative design of CMUTs arrays. The parallel-plate capacitive devices with variable cavity height, such as T-shape cavity CMUTs, utilize the electrostatic softening effect to induce piston-like deflection in the membrane and have been demonstrated to significantly decrease the collapse voltage while improving the acoustic performance. However, the theoretical model is lacking for CMUTs with T-shape cavities, limiting their optimization design. This paper introduces theoretical models for CMUTs with T-shape cavities actuated by electrostatic force. The model integrates the Galerkin method, a partial expansion method of nonlinear electrostatic force, and an energy equivalence method, thus facilitating the derivation of theoretical expressions for key mechanical behaviors, such as static deflection, collapse voltage, and resonant frequency. The finite element model and experimental verification are used to demonstrate the theoretical results, showcasing generality and high analytical accuracy (error less than 5%) over a large range of bias voltages (up to 90% of the collapse voltage), membrane dimensions (diameter-to-thickness ratio of 30 to 110), and cavity heights (cavity height-to-membrane thickness ratio of 0.2 to 1.0). Meanwhile, theoretical models are used in the optimization analysis, which demonstrates that the CMUTs with T-shape cavities can achieve a 12% increase in average membrane displacement and 47% decrease in collapse voltage compared to conventional CMUTs. The theoretical expressions can serve as a basis for the design of a series of parallel-plate capacitive devices with variable cavity height.