Boundary Conditions Analysis of Circular Capacitive Micromachined Ultrasonic Transducer (CMUT) Devices

Background: Capacitive Micromachined Ultrasonic Transducer (CMUT) is a new type of ultrasound transducer that has gained much research interest in ultrasound imaging because of its wider bandwidth, higher receiving sensitivity, and is more likely to be integrated with an integrated circuit (IC). The analytical solution is intuitive, fast, and convergent among simulation methods. The membrane deflection is important to the CMUT performance. The deformation of a circular CMUT under an external force can be described by von Kármán equations. Objective: To find suitable boundary conditions that are crucial for the governing equations to be properly solved to get the analytical solutions for membrane deformation. Methods: Features of two commonly used CMUT fabrication methods, Sacrificial Release method (SR) and Wafer Bonding (WB) method, are introduced. The force and moment equilibrium conditions of the supporting post are analyzed to get the boundary condition equations. Results: The analytical results match well with the Finite Element Method (FEM) results for the fixed boundary condition while there are still some differences for the elastic boundary condition. Conclusion: The boundary conditions for SR fabricated devices are elastic support while the boundary conditions for WB fabricated devices are fixed.