  In X-ray observations, estimation of the particle-induced background is
important especially for faint and/or diffuse sources. Although software exists
to generate total (sky and detector) background data suitable for a given
Chandra ACIS observation, no public software exists to model the
particle-induced background separately. We aim to understand the spatial and
temporal variations of the particle-induced background of Chandra ACIS obtained
in the two data modes, VFAINT and FAINT. Observations performed with ACIS in
the stowed position shielded from the sky and the Chandra Deep Field South data
sets are used. The spectra are modeled with a combination of the instrumental
lines of Al, Si, Ni, and Au and continuum components. Similar spatial
variations of the spectral shape are found in VFAINT and FAINT data, which are
mainly due to inappropriate correction of charge transfer inefficiency for
events that convert in the frame-store regions as explained by Bartalucci et
al. 2014. Temporal variation of the spectral hardness ratio is found to be
$\sim 10\%$ at maximum, which seems to be largely due to solar activity. We
model this variation by modifying the spectral hardnesses according to the
total count rate. Incorporating these properties, we have developed a tool
``mkacispback'' to generate the particle-induced background spectral model
corresponding to an arbitrary celestial observation. As an example application,
we use the background spectrum produced by the mkacispback tool in an analysis
of the Cosmic X-ray Background in the CDF-S observations. We find an intensity
of 3.10 (2.98--$3.21)\times 10^{-12}$ erg s$^{-1}$ cm$^{-2}$ deg$^{-2}$ in the
2--8 keV band, consistent with or lower than previous estimates. The tool
mkacispback is available at https://github.com/hiromasasuzuki/mkacispback.
