Substrate-decoupled silicon disk resonators having degenerate gyroscopic modes with Q in excess of 1-million

This paper details a center-supported solid disk resonator in <;100> single-crystalline-silicon (SCS) that uses a novel substrate decoupling feature to achieve ultra-low dissipation gyroscopic modes with small frequency split. The secondary bulk acoustic wave (BAW) elliptic modes (m = 3) of a 2mm diameter substrate-decoupled disk resonator exhibit quality factor (Q) of ~1.3 M with 40 ppm frequency split (as fabricated) at 2.745 MHz. Q-factor remained in excess of 1 million at pressure levels as high as 500 mTorr. The measured temperature behavior of the Q, which is mostly limited by thermoelastic damping (TED), is in very close agreement with FEM predictions.