Side-Supported Radial-Mode Thin-Film Piezoelectric-on-Silicon Disk Resonators

In this paper, anisotropy of single-crystalline silicon (SCS) is exploited to enable side-supported radial-mode thin-film piezoelectric-on-substrate (TPoS) disk resonators. In contrast to the case for isotropic material, it is demonstrated that the displacement of the disk periphery is not uniform for the radial-mode resonance in SCS disks. Specifically, for high-order harmonics, nodal points are formed on the edges, creating an opportunity for placing suspension tethers and enabling side-supported silicon disk resonators at the very high-frequency band with negligible anchor loss. In order to thoroughly study the effect of material properties and the tether location, anchor loss is simulated using a 3-D perfectly matched layer in COMSOL. Through modeling, it is shown that eighth-harmonic side-supported SCS disk resonators could potentially have orders of magnitude lower anchor loss in comparison to their nanocrystalline diamond (NCD) disk resonator counterparts given the tethers are aligned to the [100] crystalline plane of silicon. It is then experimentally demonstrated that in TPoS disk, resonators fabricated on an 8- [Formula: see text] silicon-on-insulator (SOI) wafer, unloaded quality factor improves from ~450 for the second-harmonic mode at 43 MHz to ~11500 for the eighth-harmonic mode at 196 MHz if tethers are aligned to [100] plane. The same trend is not observed for NCD disk resonators and SCS disk resonators with tethers aligned to [110] plane. Finally, the temperature coefficient of frequency is simulated and measured for the radial-mode disk resonators fabricated on the 8- [Formula: see text]-thick degenerately n-type doped SCS, and the TFC data are utilized to guarantee proper identification of the harmonic radial-mode resonance peaks among others.