Quality Factor Enhancement of Piezoelectric MEMS Resonators Based on Cross-Hole Fractal Phononic Crystals

In this paper, a cross-hole fractal phononic crystal (CHF-PnC) structure is proposed, which consists of vertical cross-holes repeating their original shapes in a certain ratio. Using the finite element method, the complex energy band curves and frequency responses of the CHF-PnC are calculated, and three complete bandgaps with strong attenuation characteristics are obtained, with bandwidths of 193.4, 55.7 and 216.8MHz, respectively. The mechanism of the generation of the bandgap of the CHF-PnC structure is analyzed, and the sensitivities of the geometrical parameters W and theta to the band gap are investigated. Subsequently, applying this structure to piezoelectric microelectromechanical systems (MEMS) resonators, it is found that the anchor point loss quality factor (Q(anc)) of the CHF-PnC resonator is 116,951.5% higher than the conventional resonator when a 6-row x 5-column combination is used. In addition, compared to the conventional resonator, the CHF-PnC resonator has a 69.7% reduction in insertion loss and a 3.6-fold improvement in unloaded quality factor, while maintaining the same electromechanical coupling coefficient.