Microscale pierced shallow shell resonators: A test vehicle to study surface loss

Abstract

This paper reports on various energy dissipation mechanisms that limit the quality factor (Q) of micro-scale pierced shallow shell resonators (PSSRs). While low-frequency thick-film shells (1>50μm) exhibit Qs in excess of 1M, thin-film shells (t<;5μm) of same frequency have so far failed to do so. PSSRs are ideal test vehicles to study the contribution of surface loss to the overall energy damping of thin-film shells. Optical measurements confirm mode confinement that stems from curvature discontinuities, which efficiently decouple the resonating rim from the dissipative anchor, and suppress anchor loss. Surface loss is found to be the main dominant damping mechanism of trapped modes in 2μm thick SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and TEOS PSSRs. We compare TEOS and thermally-grown SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (hereinafter referred to as SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) as structural materials for high Q resonators and extract surface loss parameters for both. Quality factors as high as 111,000 have been measured, which corresponds to a 30% improvement to the state-of-the-art thin-film SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> resonators.