  Flux pinning is still the main limiting factor for the critical current of
the high-temperature superconductors in high fields. In this paper we model the
field dependence of the critical current in thin films with columnar defects
aligned with the field. The characteristic shape of the critical current of the
BaZrO$_3$ doped YBa$_2$Cu$_3$O$_{6+x}$ thin films is reproduced and explained.
The model is based on solving the Ginzburg-Landau equations with columnar
defects present in the lattice. The size of the columnar defect is found to be
of key importance in explaining the rounded shape of the critical current of
the BaZrO$_3$ doped YBa$_2$Cu$_3$O$_{6+x}$ thin films. It is also found that
the size of the rod changes the long range order of the vortex lattice.
