Finite element modeling of CMUTs using a perfectly matched layer for fast simulation

Capacitative micromachined ultrasonic transducer (CMUT) cells generate plate waves within the substrate on which they are constructed. Analysis of CMUT cells using finite element simulation requires a solid model with an absorbing boundary for elimination of plate wave reflections from the model boundary. Although this method performs well for eliminating the reflections, it significantly increases the mesh size and hence the simulation time. An observation on the nature of the plate wave modes generated by a CMUT cell shows that more than 97% of the outgoing power is carried in the lowest order anti-symmetric (A₀) Lamb wave mode. In this paper, a perfectly matched layer for the termination of the A₀ mode is proposed. Boundary elements tuned for the A₀ mode, reduce the reflected wave amplitude to -6 dB of the incident wave amplitude for operation frequencies up to 5 MHz. For a particular simulation model with 17,000 nodes, the proposed boundary elements reduce the mesh size by 30%.