  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.
