  A future mission in medium-energy gamma-ray astrophysics would allow for many
scientific advancements, e.g. a possible explanation for the excess positron
emission from the Galactic Center, a better understanding of nucleosynthesis
and explosion mechanisms in Type Ia supernovae, and a look at the physical
forces at play in compact objects such as black holes and neutron stars.
Additionally, further observation in this energy regime would significantly
extend the search parameter space for low-mass dark matter. In order to achieve
these objectives, an instrument with good energy resolution, good angular
resolution, and high sensitivity is required. In this paper we present the
design and simulation of a Compton telescope consisting of cubic-centimeter
Cadmium Zinc Telluride (CdZnTe) detectors as absorbers behind a silicon tracker
with the addition of a passive coded mask. The goal of the design was to create
a very sensitive instrument that is capable of high angular resolution. The
simulated telescope showed achievable energy resolutions of 1.68$\%$ FWHM at
511 keV and 1.11$\%$ at 1809 keV, on-axis angular resolutions in Compton mode
of 2.63$^{\circ}$ FWHM at 511 keV and 1.30$^{\circ}$ FWHM at 1809 keV, and is
capable of resolving sources to at least 0.2$^{\circ}$ at lower energies with
the use of the coded mask. An initial assessment of the instrument in Compton
imaging mode yields an effective area of 183 cm$^{2}$ at 511 keV and an
anticipated all-sky sensitivity of 3.6 x 10$^{-6}$ photons cm$^{-2}$ s$^{-1}$
for a broadened 511 keV source over a 2-year observation time. Additionally,
combining a coded mask with a Compton imager to improve point source
localization for positron detection has been demonstrated.
