RETRACTION: Lateral mode suppression and experiment for the ZnO ring thin-film bulk acoustic resonator (Retraction of Vol 64, art no 224601, 2015)

In this paper, we analytically study the spurious lateral mode of the ring (circular) thin-film bulk acoustic resonator (FBAR) by using Tiersten equation. The lateral mode displacement field and frequency dispersion equation are obtained. According to the electromagnetic mode analysis, we find that the mode frequency and spurious electrical responses relate to the ratio of inner radius to outer radius (a/b) of the ring resonator, and its lateral vibration mode can be obtained by coupling other circular FBAR modes. The ring electrode can greatly reduce the number of spurious electrical responses caused by lateral resonances. Suppressing lateral mode and adjusting fundamental frequency can be achieved by controlling a/b. In this paper, the experiments for the same batch of ring and circular FBARs are carried out by using a heterodyne interferometer and a vector network analyzer, including the measurements of acoustic wave fields and eigenmode spectra, which can provide the information about vibration localization and coupling between lateral mode and thickness extensional mode. The data indicate that the lateral vibration mode of ring FBAR can be obtained by coupling the two modes of circular FBARs, whose radii are a and b, respectively, and the lateral mode pattern of n' = 0 is suppressed. When the ring resonator is designed with an a /b ratio of 0.436, the fundamental frequency (similar to 1217 MHz) is the same as the (0, 1) mode frequency of the circular FBAR. Based on this observation, the acoustic wave field images and electrical spurious responses can accurately describe the lateral modes, and the obtained results accord well with the analyses of theoretical electromagnetic modes. This phenomenon may be found to have applications in the design and theoretical analysis of the resonators.