Thickness shear mode vibrations in silicon bar resonators

This paper demonstrates a dielectrically transduced high quality factor (Q) quarter-wave thickness shear silicon resonator. Dielectric transduction provides a κ 2 reduction in motional impedance relative to air-gap electrostatic transduction. The resonator is fabricated on the 1.8 µm thick device layer of a heavily doped SOI wafer with 68 nm thick silicon nitride thin-film on top. The quarter-wave thickness shear mode of the silicon bar resonator has a resonant frequency of 713 MHz, a motional impedance Rx of 10.5 kΩ and Q of 1,517 in air. After partial release, the bar resonates at 723 MHz, exhibiting a motional impedance Rx of 2.4 kΩ and Q of 4,400 in air. Additionally, by varying a tuning voltage between the resonator and silicon substrate from 50 V to 150 V across a 2.5 micron gap, approximately 5 MHz of frequency tuning is observed.