Edge mode engineering for optimal ultracoherent silicon nitride membranes

Due to their high force sensitivity, mechanical resonators combining low mechanical dissipation with a small motional mass are highly demanded in fields as diverse as resonant force imaging, mass sensing, or cavity optomechanics. "Soft-clamping" is a phononic engineering technique by which mechanical modes of highly-stressed membranes or strings are localized away from lossy regions, thereby enabling ultrahigh-Q for ng-scale devices. Here, we report on parasitic modes arising from the finite size of the structure which can significantly degrade the performance of these membranes. Through interferometric measurements and finite-element simulations, we show that these parasitic modes can hybridize with the localized modes of our structures, reducing the quality factors by up to one order of magnitude. To circumvent this problem, we engineer the spectral profile of the parasitic modes in order to avoid their overlap with the high-Q defect mode. We verify via a statistical analysis that this modal engineering reproducibly yields higher quality factors in fabricated devices, consistent with theoretically predicted values.