  Transit spectroscopy is the most promising path toward characterizing nearby
terrestrial planets at mid-infrared wavelengths in the next 20 years. The
Spitzer Space telescope has achieved moderately good mid-infrared photometric
precision in observations of transiting planets, but the intrinsic photometric
stability of mid-IR detectors themselves has not been reported in the
scientific or technical literature. Here, we evaluated the photometric
precision of a JWST MIRI prototype mid-infrared Si:As impurity band conduction
detector, using time-series data taken under flood illumination. These
measurements of photometric precision were conducted over periods of 10 hours,
representative of the time required to observe an exoplanet transit. After
selecting multiple sub-regions with a size of 10x10 pixels and compensating for
a gain change caused by our warm detector control electronics for the selected
sub-regions, we found that the photometric precision was limited to 26.3ppm at
high co-added signal levels due to a gain variation caused by our warm detector
control electronics. The photometric precision was improved up to 12.8ppm after
correcting for the gain drift. We also translated the photometric precision to
the expected spectro-photometric precision, assuming that an optimized
densified pupil spectrograph is used in transit observations. We found that the
spectro-photometric precision of an optimized densified pupil spectrograph when
used in transit observations is expected to be improved by the square root of
the number of pixels per a spectral resolution element. At the high co-added
signal levels, the total noise could be reduced down to 7ppm, which was larger
by a factor of 1.3 than the ideal performance that was limited by the Poisson
noise and readout noise. The systematic noise hidden behind the simulated
transit spectroscopy was 1.7ppm.
