Investigation of spurious waves in thin-film bulk acoustic wave resonators

Abstract

With the development of the wireless communication systems, the frequency spectrum crowding increases constantly. This trend strengthens the need for high performance frequency control components steadily. Film bulk acoustic resonator (FBAR) has been widely used in the frequency control components because of its small size, low insertion loss, high quality factor and its capability of being integrated with other components on silicon substrate. However, FBARs are suffering from the laterally propagating spurious waves. These spurious waves degrade the performance of filters composed of FBARs by increasing the insertion loss, introducing ripples in their passband and narrowing the bandwidth. The goal of this study is to propose an efficient method to model the FBAR structure, aiming to investigate the lateral spurious modes generation and improve the quality factor of FBAR. A two-dimensional .nite-difference time-domain (FDTD) algorithm is proposed to model the FBAR resonators. The partial derivatives of the equations of motion and the quasi-static Maxwell's equations are discretized to centered finite differences. The free surface boundary condition is applied to the interface between the medium and air. At the interface between different materials, the material properties are averaged to ensure the stability under Courant condition. The two-dimensional fast Fourier transform (2D FFT) method is applied to extract the dispersion characteristic of the Rayleigh-Lamb modes propagating in the FBAR resonator. The proposed algorithm is validated by comparing the obtained dispersion curve with the one obtained by the effective acoustic impedance. Wave scattering analysis for multimode excitation is developed to investigate the lateral boundaries of FBAR resonators. To validate the proposed scheme, the reflection of simultaneously excited antisymmetric Lamb wave modes at the free edge of a steel plate is simulated using the FDTD method. By using the mode power coefficients, the power of the Lamb modes is determined from the displacements on the surface of the plate. The mode conversion coefficients obtained are in good agreement with the one calculated by taking multiple measurements with single Lamb wave mode excitation using the finite element method (FEM). The proposed scheme is then applied to investigate two generic free-standing bulk acoustic resonator (FBAR) structures. The scattering coefficients of these two FBAR structures are calculated and analyzed. Based on the scattering analysis of the two generic FBAR structures, a new structure of FBAR resonator with frame-like airgap on bottom electrode is proposed to suppress the spurious modes and improve the quality factor. Time domain and frequency domain analysis are conducted to investigate the spurious waves in the proposed structure. From both time domain and frequency domain results, it is observed that with an airgap on the bottom electrode the excitation of the spurious waves in the active region is suppressed, and the energy leaked into the passive region is reduced as well. The overall results of this work indicate that the FDTD scheme is an appropriate approach for modeling FBAR resonators, and the scattering analysis for multimode excitation provides a simple way to design the lateral boundaries of FBARs.