  Using the non-linear Ginzburg-Landau (GL) theory, we obtain the possible
vortex configurations in superconducting thin films containing a square lattice
of antidots. The equilibrium structural phase diagram is constructed which
gives the different ground-state vortex configurations as function of the size
and periodicity of the antidots for a given effective GL parameter
$\kappa^{*}$. Giant-vortex states, combination of giant- and multi-vortex
states, as well as symmetry imposed vortex-antivortex states are found to be
the ground state for particular geometrical parameters of the sample. The
antidot occupation number $n_o$ is calculated as a function of related
parameters and comparison with existing expressions for the saturation number
$n_s$ and with experimental results is given. For a small radius of antidots a
triangular vortex lattice is obtained, where some of the vortices are pinned by
the antidots and some of them are located between them. Transition between the
square pinned and triangular vortex lattices is given for different values of
the applied field. The enhanced critical current at integer and rational
matching fields is found, where the level of enhancement at given magnetic
field directly depends on the vortex-occupation number of the antidots. For
certain parameters of the antidot lattice and/or temperature the critical
current is found to be larger for higher magnetic fields.
Superconducting/normal $H-T$ phase boundary exhibits different regimes as
antidots are made larger, and we transit from a plain superconducting film to a
thin-wire superconducting network. Presented results are in good agreement with
available experiments and suggest possible new experiments.
