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

Abstract

This paper presents an analytical approach for 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 high-Q resonators without the need for geometrical suspension through narrow tethers or rigid anchors. The effectiveness of the dispersion engineering methodology is verified through development of experimental test-vehicles in 20㯌m-thick single-crystal silicon substrate with 500nm 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 guided wave resonators based on analytical derivation of dispersion relation followed by a systematic resonator design procedure. Numerical and experimental characterization for verification of the proposed design procedure and extensive measurement data on proof-of-concept resonators are presented in Part II.