A dispersion-guided design methodology for super-high-frequency solidly mounted resonators

Solidly mounted resonators (SMRs) are critical components in radio frequency (RF) filters and sensors. However, for the upcoming 6G communication systems operating in the super-high-frequency (SHF) bands and beyond, the miniaturization of SMR structures results in a significant proportion of electrode layers. Due to the mass loading and elastic effects of the electrodes, conventional half-wavelength resonator designs for SMRs exhibit substantial frequency deviation, making it difficult for Bragg reflector to effectively confine acoustic energy. To address these issues, this paper proposes a novel design and optimization approach for SMR structures. Based on the Stroh formalism and the transfer matrix method, the dispersion equations of the laminated Bragg reflector structures are derived. To overcome the challenge of accurate dispersion calculation in intricate SMR configurations, a novel Moduli Ratio Convergence Method is applied to solve the complex dispersion equations. An initial SMR structure is first established according to the conventional half-wavelength piezoelectric layer and quarter-wavelength Bragg reflector design principles. Subsequently, the Bragg reflector is redesigned according to the actual cutoff frequency of the real piezoelectric stack structure incorporating electrodes, while a global scaling adjustment method is employed to accurately tune the operating frequency to the target value. The resulting optimized SMR structure demonstrates highly concentrated energy within the resonant region, reduced energy penetration into the Bragg reflector, and minimal energy leakage into the substrate. Through structural dispersion analysis, this study provides a reliable and efficient approach for designing SMRs in the super-high-frequency band, offering valuable guidance for the development of next-generation RF devices.