Two-dimensional analysis of spurious modes in aluminum nitride film resonators.

In this paper, a hybrid method, which combines the traditional concept of guided waves and the finite element method (FEM), is proposed to analyze the spurious modes of aluminum nitride (AIN) film with electrodes. First, the guided wave modes in the plated area are obtained by 1-D FEM. Second, a mode-match method is used to satisfy the boundary conditions. The vibration of the film resonator is a superposition of all of the guided modes. With respect to an A1N film resonator, which is a thickness-stretch mode resonator, we have identified three families of spurious modes: extension, thickness-stretch, and thickness-shear. The spectrum of spurious modes is calculated and the influence of the spurious modes is discussed.