An Analytical Model for CMUTs with Square Multilayer Membranes Using the Ritz Method

Capacitive micromachined ultrasonic transducer (CMUT) multilayer membrane plays an important role in the performance metrics including the transmitting efficiency and the receiving sensitivity. However, there are few studies of the multilayer membranes. Some analytical models simplify the multilayer membrane as monolayer, which results in inaccuracies. This paper presents a new analytical model for CMUTs with multilayer membranes, which can rapidly and accurately predict static deflection and response frequency of the multilayer membrane under external pressures. The derivation is based on the Ritz method and Hamilton’s principle. The mathematical relationships between the external pressure, static deflection, and response frequency are obtained. Relevant residual stress compensation method is derived. The model has been verified for three-layer and double-layer CMUT membranes by comparing its results with finite element method (FEM) simulations, experimental data, and other monolayer models that treat CMUTs as monolayer plates/membranes. For three-layer CMUT membranes, the relative errors are ranging from 0.71%–3.51% for the static deflection profiles, and 0.35%–4.96% for the response frequencies, respectively. For the double-layer CMUT membrane, the relative error with residual stress compensation is 4.14% for the central deflection, and −1.17% for the response frequencies, respectively. This proposed analytical model can serve as a reliable reference and an accurate tool for CMUT design and optimization.