3D FEM modeling of composite BAW resonators

We employ the finite element method (FEM) for numerical modeling of composite bulk acoustic wave (BAW) resonators. Our formerly 2D FEM software package has been extended into 3D through implementing linear and quadratic brick elements and by using the Gibbs-King algorithm for optimization of node numbering. A harmonic time dependence is assumed. The software package is capable of solving the field problem as well as the corresponding eigenvalue problem. Our 3D FEM enables modeling the electrical characteristics of a given resonator structure, including the effect of the top electrode geometry. A 2D FEM does not have such a capability. Although accurate results require a dense FEM mesh which renders the 3D simulations computationally intensive, the qualitative behavior of the resonator can be simulated with moderate computational resources. We present simulated results for composite BAW resonators with square, circular, and triangular top electrode shapes and compare the simulated displacement profiles with measurements