Control of Material Damping in High-QMembrane Microresonators

We study the mechanical quality factors of bilayer aluminum--silicon-nitride membranes. By coating ultrahigh-$Q$ ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ membranes with a more lossy metal, we can precisely measure the effect of material loss on $Q$'s of tensioned resonator modes over a large range of frequencies. We develop a theoretical model that interprets our results and predicts the damping can be reduced significantly by patterning the metal film. Using such patterning, we fabricate Al-${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ membranes with ultrahigh $Q$ at room temperature. Our work elucidates the role of material loss in the $Q$ of membrane resonators and informs the design of hybrid mechanical oscillators for optical-electrical-mechanical quantum interfaces.