  In the context of a recoil damping analysis, we have designed and produced a
membrane resonator equipped with a specific on-chip structure working as a
"loss shield" for a circular membrane. In this device the vibrations of the
membrane, with a quality factor of $10^7$, reach the limit set by the intrinsic
dissipation in silicon nitride, for all the modes and regardless of the modal
shape, also at low frequency. Guided by our theoretical model of the loss
shield, we describe the design rationale of the device, which can be used as
effective replacement of commercial membrane resonators in advanced
optomechanical setups, also at cryogenic temperatures.
