  Thickness uniformity is regarded as an important parameter in designing thin
film devices. However, some applications based on films with non-uniform
thickness have recently emerged, such as gas sensors and optimized materials
based on the gradual change of film composition. This work deals with
superconducting Pb thin films with a thickness gradient prepared with the aid
of a diffuse stencil mask. Atomic Force Microscopy and Energy-Dispersive X-ray
Spectroscopy show variations ranging from 90~nm to 154~nm. Quantitative
magneto-optical images reveal interesting features during both the abrupt and
the smooth penetration regimes of magnetic flux, as well as the
thickness-dependent critical current density ($J_c$). In addition, we observe a
gradual superconducting transition as the upper critical field is progressively
reached for certain thicknesses. Furthermore, the hysteresis observed for
triggering flux avalanches when increasing and decreasing magnetic fields is
also accounted for by the $J_c$ profile evolution along the thickness gradient.
Numerical simulations based on the Thermomagnetic Model are in fair agreement
with the experimental data. These findings demonstrate that wedge-shaped films
are a viable approach to investigate, in a continuous fashion,
thickness-dependent properties of a superconducting materials.

Superconductivity;Mesoscale and Nanoscale Physics;Materials Science