Side-Supported Radial-Mode Thin-Film Piezoelectric-on-Silicon Disc Resonators.

In this paper, anisotropy of single crystalline silicon (SCS) is exploited to enable side-supported radial-mode thin-film piezoelectric-on-substrate (TPoS) disc resonators. In contrast to the case for isotropic material, it is demonstrated that the displacement of the disc periphery is not uniform for the radialmode resonance in SCS discs. Specifically, for high order harmonics, nodal points are formed on the edges, creating an opportunity for placing suspension tethers and enabling sidesupported silicon disc resonators at very-high-frequency (VHF) 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 3D perfectly-matched-layer (PML) in COMSOL. Through modeling, it is shown that 8th harmonic sidesupported SCS disc resonators could potentially have orders of magnitude lower anchor loss in comparison to their nanocrystalline diamond (NCD) disc resonator counterparts given the tethers are aligned to the [100] crystalline plane of silicon. It is then experimentally demonstrated that in thin-film piezoelectric-onsilicon disc resonators fabricated on an 8μm silicon-on-insulator (SOI) wafer, unloaded quality factor improves from ~450 for the second harmonic mode at 43 MHz to ~11,500 for the eighth harmonic mode at 196 MHz if tethers are aligned to [100] plane. The same trend is not observed for NCD disc resonators and SCS disc resonators with tethers aligned to [110] plane. Finally, temperature coefficient of frequency (TCF) is simulated and measured for the radial-mode disc resonators fabricated on the 8μm thick degenerately n-type doped SCS and the TFC data is utilized to guarantee proper identification of the harmonic radialmode resonance peaks amongst others.