  The Epoch of Reionization Spectrometer (EoR-Spec) is an instrument module for
the Prime-Cam receiver of the 6 m aperture CCAT-prime Telescope at 5600 m in
Chile. EoR-Spec will perform 158 $\mu$m [CII] line intensity mapping of
star-forming regions at redshifts between 3.5 and 8 (420 - 210 GHz), tracing
the evolution of structure during early galaxy formation. At lower redshifts,
EoR-Spec will observe galaxies near the period of peak star formation - when
most stars in today's universe were formed. At higher redshifts, EoR-Spec will
trace the late stages of reionization, the early stages of galaxy assembly, and
the formation of large-scale, three-dimensional clustering of star-forming
galaxies. To achieve its science goals, EoR-Spec will utilize CCAT-prime's
exceptionally low water vapor site, large field of view ($\sim 5$ degrees at
210 GHz), and narrow beam widths ($\sim 1$ arcminute at 210 GHz). EoR-Spec will
be outfitted with a cryogenic, metamaterial, silicon substrate-based
Fabry-Perot Interferometer operating at a resolving power
($\lambda/\Delta\lambda$) of 100. Monolithic dichroic arrays of cryogenic,
feedhorn-coupled transition edge sensor bolometers provide approximately 6000
detectors, which are read out using a frequency division multiplexing system
based on microwave SQUIDs. The novel design allows the measurement of the [CII]
line at two redshifts simultaneously using dichroic pixels and two orders of
the Fabry-Perot. Here we present the design and science goals of EoR-Spec, with
emphasis on the spectrometer, detector array, and readout designs.
