Clamp-tapering increases the quality factor of stressed nanobeams

TL;DR

This paper demonstrates that tapering the clamps of high-stress nanobeams enhances their quality factor by increasing local stress and dissipation dilution, offering a practical method to improve resonator performance without enlarging device size.

Contribution

It introduces a novel tapered-clamping design that increases the quality factor of stressed nanobeams by locally boosting stress at the clamps, differing from previous soft-clamping techniques.

Findings

Tapered clamps increase the $Q$ of MHz-frequency modes.

Widening clamps decreases $Q$ despite higher stress.

Tapered-clamping is practical and does not require larger devices.

Abstract

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 $\mathrm{Si_3N_4}$. We find that tapering the beam near the clamp - and locally increasing the stress - leads to 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 decreased $Q$ despite increased stress in the beam bulk. The tapered-clamping approach has practical advantages compared to the recently developed "soft-clamping" technique. Tapered-clamping enhances the $Q$ of the fundamental mode and can be implemented without increasing the device size.