  The Epoch of Reionization Spectrometer (EoR-Spec) is one of the instrument
modules to be installed in the Prime-Cam receiver of the Fred Young
Submillimeter Telescope (FYST). This six-meter aperture telescope will be built
on Cerro Chajnantor in the Atacama Desert in Chile. EoR-Spec is designed to
probe early star-forming regions by measuring the [CII] fine-structure lines
between redshift z = 3.5 and z = 8 using the line intensity mapping technique.
The module is equipped with a scanning Fabry-Perot interferometer (FPI) to
achieve the spectral resolving power of about RP = 100. The FPI consists of two
parallel and identical, highly reflective mirrors with a clear aperture of 14
cm, forming a resonating cavity called etalon. The mirrors are silicon-based
and patterned with double-layer metamaterial anti-reflection coatings (ARC) on
one side and metal mesh reflectors on the other. The double-layer ARCs ensure a
low reflectance at one substrate surface and help tailor the reflectance
profile over the FPI bandwidth. Here we present the design, fabrication
processes, test setup, and characterization of silicon mirrors for the FPI.
