The Ginzburg-Landau equations are solved for ideally periodic vortex lattices in superconducting films of arbitrary thickness in a perpendicular magnetic field. The order parameter, current density, magnetic moment, and the three-dimensional magnetic field inside and outside the film are obtained in the entire ranges of the applied magnetic field, Ginzburg-Landau parameter $\kappa$, and film thickness. The superconducting order parameter varies very little near the surface $(\approx 1\%)$ and the energy of the film surface is small. The shear modulus $c_{66}$ of the triangular vortex lattice in thin films coincides with the bulk $c_{66}$ taken at large $\kappa$. In thin type-I superconductor films with $\kappa <1∕\sqrt{2},c_{66}$ can be positive at low fields and negative at high fields. The magnetization of thin films at small applied fields is enhanced beyond its bulk value $-H_{c1}$ due to the energy of the magnetic stray field.

• Received 6 September 2004

DOI:https://doi.org/10.1103/PhysRevB.71.014521