High- ${Q}$ Butterfly-Shaped AlN Lamb Wave Resonators

Butterfly-shaped aluminum nitride (AlN) plates with anchor-to-plate angle smaller than 90° are proposed to boost the quality factor (<inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula>) of Lamb wave resonators (LWRs) thanks to the elimination of the anchor loss. Finite-element method simulation shows that the butterfly-shaped plate can efficiently reduce mechanical energy leakage via the supporting anchors and accordingly enhance the mechanical <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula>. Furthermore, the rounded butterfly-shaped LWRs show better suppression in the anchor loss in comparison with the beveled butterfly-shaped LWRs. More specifically, the measured frequency response of an 863-MHz beveled butterfly-shaped AlN LWR yields an unloaded <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> of 4189, representing 25% improvement over an LWR on a rectangular AlN plate; another AlN LWR based on the rounded butterfly-shaped plate shows an unloaded <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> of 5352, enabling 60% improvement in unloaded <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> values.