  SuperSpec is an ultra-compact spectrometer-on-a-chip for millimeter and
submillimeter wavelength astronomy. Its very small size, wide spectral
bandwidth, and highly multiplexed readout will enable construction of powerful
multibeam spectrometers for high-redshift observations. The spectrometer
consists of a horn-coupled microstrip feedline, a bank of narrow-band
superconducting resonator filters that provide spectral selectivity, and
Kinetic Inductance Detectors (KIDs) that detect the power admitted by each
filter resonator. The design is realized using thin-film lithographic
structures on a silicon wafer. The mm-wave microstrip feedline and spectral
filters of the first prototype are designed to operate in the band from 195-310
GHz and are fabricated from niobium with at Tc of 9.2K. The KIDs are designed
to operate at hundreds of MHz and are fabricated from titanium nitride with a
Tc of 2K. Radiation incident on the horn travels along the mm-wave microstrip,
passes through the frequency-selective filter, and is finally absorbed by the
corresponding KID where it causes a measurable shift in the resonant frequency.
In this proceedings, we present the design of the KIDs employed in SuperSpec
and the results of initial laboratory testing of a prototype device. We will
also briefly describe the ongoing development of a demonstration instrument
that will consist of two 500-channel, R=700 spectrometers, one operating in the
1-mm atmospheric window and the other covering the 650 and 850 micron bands.
