Topology-optimized 2D silicon–air phononic crystal slabs for enhancing quality factor of laterally vibrating resonators

Abstract

Two-dimensional phononic crystal (PnC) slabs have shown advantages in enhancing the quality factors Q of piezoelectric laterally vibrating resonators (LVRs) through topology optimization. However, the narrow geometries of most topology-optimized silicon–air 2D PnC slabs face significant fabrication challenges owing to restricted etching precision, and the anisotropic nature of silicon is frequently overlooked. To address these issues, this study employs the finite element method with appropriate discretization numbers and the genetic algorithm to optimize the structures and geometries of 2D silicon–air PnC slabs. The optimized square-lattice PnC slabs, featuring a rounded-cross structure oriented along the ⟨110⟩ directions of silicon, achieve an impressive relative bandgap (RBG) width of 82.2% for in-plane modes. When further tilted by 15° from the ⟨100⟩ directions within the (001) plane, the optimal RBG width is expanded to 91.4%. We fabricate and characterize thin-film piezoelectric-on-silicon LVRs, with or without optimized 2D PnC slabs. The presence of PnC slabs around anchors increases the series and parallel quality factors Qs and Qp from 2240 to 7118 and from 2237 to 7501, respectively, with the PnC slabs oriented along the ⟨110⟩ directions of silicon.