Analytical Modeling and Numerical Simulation of Capacitive Silicon Bulk Acoustic Resonators

This paper introduces two newly developed models of capacitive silicon bulk acoustic resonators (SiBARs). The first model is analytical and is obtained from an approximate solution of the linear elastodynamics equations for the SiBAR geometry. The second is numerical and is based on finite-element, multi-physics simulation of both acoustic wave propagation in the resonator and electromechanical transduction in the capacitive gaps of the device. This latter model makes it possible to compute SiBAR performance parameters that cannot be obtained from the analytical model, e.g. the relationship between transduction area and insertion loss. Comparisons with measurements taken on a set of silicon resonators fabricated using electron-beam lithography show that both models can predict the resonant frequencies of SiBARs with a relative error smaller than 1%.