  Migration of halogen vacancies is one of the primary sources of phase
segregation and material degradation in lead-halide perovskites. Here we use
first principles density functional theory to compare migration energy barriers
and paths of bromine vacancies in the bulk and at a (001) surface of cubic
CsPbBr$_3$. Our calculations indicate that surfaces might facilitate bromine
vacancy migration in these perovskites, due to their soft structure that allows
for bond lengths variations larger than in the bulk. We calculate the migration
energy for axial-to-axial bromine vacancy migration at the surface to be only
half of the value in the bulk. Furthermore, we study the effect of modifying
the surface with four different alkali halide monolayers, finding an increase
of the migration barrier to almost the bulk value for the NaCl-passivated
system. Migration barriers are found to be correlated to the lattice mismatch
between the CsPbBr$_3$ surface and the alkali halide monolayer. Our
calculations suggest that surfaces might play a significant role in mediating
vacancy migration in halide perovskites, a result with relevance for perovskite
nanocrystals with large surface-to-volume ratios. Moreover, we propose viable
ways for suppressing this undesirable process through passivation with alkali
halide salts.
