Lamb Waves and Resonant Modes in Rectangular-Bar Silicon Resonators

This paper presents two newly developed models of capacitive silicon bulk acoustic resonators (SiBARs) characterized by a rectangular-bar geometry. The first model is derived from an approximate analytical solution of the linear elastodynamic equations for a parallelepiped made of an orthotropic material. This solution, which is recognized to represent a Lamb wave propagating across the width of the resonator, yields the frequencies and shapes of the resonance modes that typically govern the operation of SiBARs. The second model is numerical and is based on a finite-element multiphysics simulation of both acoustic wave propagation in the resonator and electromechanical transduction in the capacitive gaps of the device. It is especially useful in the computation of the SiBAR performance parameters, which cannot be obtained from the analytical model, e.g., the relationship between the transduction area and the insertion loss. Comparisons with the measurements taken on a set of silicon resonators fabricated using electron-beam lithography show that both models can predict the resonance frequencies of SiBARs with a relative error, which, in most cases, is significantly smaller than 1%.