Clamp-Tapering Increases the Quality Factor of Stressed Nanobeams

Stressed nanomechanical resonators are known to have exceptionally high quality factors ( Q) due to the dilution of intrinsic dissipation by stress. Typically, the amount of dissipation dilution and thus the resonator Q is limited by the high mode curvature region near the clamps. Here we study the effect of clamp geometry on the Q of nanobeams made of high-stress Si₃N₄. We find that tapering the beam near the clamps, thus locally increasing the stress, leads to an increased Q of MHz-frequency low order modes due to enhanced dissipation dilution. Contrary to recent studies of tethered-membrane resonators, we find that widening the clamps leads to a decreased Q despite increased stress in the beam bulk. The tapered-clamping approach has practical advantages compared to the recently developed "soft-clamping" technique, as it enhances the Q of the fundamental mode and can be implemented without increasing the device size.