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Nanomechanical resonators based on strained silicon nitride (Si$_3$N$_4$)have received a large amount of attention in fields such as sensing and quantumoptomechanics due to their exceptionally high quality factors ($Q$s).Room-temperature $Q$s approaching 1 billion are now in reach by means ofphononic crystals (soft-clamping) and strain engineering. Despite greatprogress in enhancing $Q$s, difficulties in fabrication of soft-clamped sampleslimits their implementation into actual devices. An alternative means ofachieving ultra-high $Q$s was shown using trampoline resonators with engineeredclamps, which serves to localize the stress to the center of the resonator,while minimizing stress at the clamping. The effectiveness of this approach hassince come into question from recent studies employing string resonators withclamp-tapering. Here, we investigate this idea using nanomechanical stringresonators with engineered clampings similar to those presented fortrampolines. Importantly, the effect of orienting the strings diagonally orperpendicularly with respect to the silicon frame is investigated. It is foundthat increasing the clamp width for diagonal strings slightly increases the$Q$s of the fundamental out-of-plane mode at small radii, while perpendicularstrings only deteriorate with increasing clamp width. Measured $Q$s agree wellwith finite element method simulations even for higher-order resonances. Thesmall increase cannot account for previously reported $Q$s of trampolineresonators. Instead, we propose the effect to be intrinsic and related tosurface and radiation losses.

Influence of clamp-widening on the quality factor of nanomechanical silicon nitride resonators