  We analyze the influence of the magnetic field generated by the supercurrents
(self-field) on the current density distribution by numerical simulations. The
thickness of the superconducting film determines the self-field and
consequently the critical current density at zero applied field. We find an
equation, which derives the thickness dependence of the critical current
density from its dependence on the magnetic induction. Solutions of the
equation reproduce numerical simulations to great accuracy, thus enabling a
quantification of the dependence of the self-field critical current density
with increasing film thickness. This result is technologically relevant for the
development of coated conductors with thicker superconducting layers.
