Finite element simulations of thin-film composite BAW resonators

摘要

A finite element method (FEM) formulation is presented for thennumerical solution of the electroelastic equations that govern thenlinear forced vibrations of piezoelectric media. A harmonic timendependence is assumed. Both of the approaches, that of solving the fieldnproblem (harmonic analysis) and that of solving the correspondingneigenvalue problem (modal analysis), are described. A FEM softwarenpackage has been created from scratch. Important aspects central to thenefficient implementation of FEM are explained, such as memory managementnand solving the generalized piezoelectric eigenvalue problem. Algorithmsnfor reducing the required computer memory through optimization of thenmatrix profile, as well as Lanczos algorithm for the solution of theneigenvalue problem are linked into the software from external numericalnlibraries. Our FEM software is applied to detailed numerical modeling ofnthin-film bulk acoustic wave (BAW) composite resonators. Comparison ofnresults from 2D and full 3D simulations of a resonator are presented. Innparticular, 3D simulations are used to investigate the effect of the topnelectrode shape on the resonator electrical response. The validity ofnthe modeling technique is demonstrated by comparing the simulated andnmeasured displacement profiles at several frequencies. The results shownthat useful information on the performance of the thin-film resonatorsncan be obtained even with relatively coarse meshes and, consequently,nmoderate computational resources