  The hole spectral function of the t-J model on a two-dimensional
semi-infinite lattice is calculated using the spin-wave and noncrossing
approximations. In the case of small hole concentration and strong
correlations, $t\gg J$, several near-boundary site rows appear to be depleted
of holes. The reason for this depletion is a deformation of the magnon cloud,
which surrounds the hole, near the boundary. The hole depletion in the boundary
region leads to a more complicated spectral function in the boundary row in
comparison with its bulk shape.
