  CsSnI$_3$ is widely studied as an environmentally friendly Pb-free perovskite
material for optoelectronic device applications. To further improve material
and device performance, it is important to understand the surface structures of
CsSnI$_3$. We generate surface structures with various stoichiometries, perform
density functional theory calculations to create phase diagrams of the
CsSnI$_3$ (001), (110), and (100) surfaces, and determine the most stable
surfaces under a wide range of Cs, Sn, and I chemical potentials. Under I-rich
conditions, surfaces with Cs vacancies are stable, which lead to partially
occupied surface states above the valence band maximum. Under I-poor
conditions, we find the stoichiometric (100) surface to be stable under a wide
region of the phase diagram, which does not have any surface states and can
contribute to long charge carrier lifetimes. Consequently, the I-poor (Sn-rich)
conditions will be more beneficial to improve the device performance.
