Dispersion-Engineered Guided-Wave Resonators in Anisotropic Single-Crystal Substrates—Part I: Concept and Analytical Design

This paper presents an analytical approach for the implementation of high quality-factor (Q) resonators with arbitrary cross-sectional vibration mode shapes in anisotropic single-crystal substrates. A closed-form dispersion relation is analytically derived to characterize the dynamics of guided waves in rectangular waveguides. Three categories of waves with propagating, standing-evanescent, and propagating-evanescent dynamics are identified and used for energy localization of acoustic excitations with arbitrary cross-sectional vibration patterns. An analytical design procedure is presented for dispersion engineering of waveguides to realize highQ resonators without the need for geometrical suspension through narrow tethers or rigid anchors. The effectiveness of the dispersion engineering methodology is verified through the development of experimental test vehicles in 20-μm-thick single-crystal silicon substrate with 500-nm aluminum nitride transducers. Various proof-of-concept resonators, representing guided waves with different dispersion types, are presented and compared to highlight the optimum design procedures for Q enhancement and spurious mode suppression. Part I of this paper presents the operation principle of guidedwave resonators based on the analytical derivation of dispersion relation followed by a systematic resonator design procedure. Numerical and experimental characterizations for verification of the proposed design procedure and extensive measurement data on proof-of-concept resonators are presented in Part II.