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_2Cu_3O_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

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... he columnar defect is found to be of key importance in explaining the rounded shape of the critical current of the BaZrO_3 doped YBa_2Cu_3O_6+x thin films. It is also found that the size of the rod changes the long range order of the vortex lattice.