  We analyze the occurrence of the Beresinkii-Kosterlitz-Thouless transition in
thin films of NbN at various film thickness, by probing the effect of vortex
fluctuations on the temperature dependence of the superfluid density below
$T_{BKT}$ and of the resistivity above $T_{BKT}$. By direct comparison between
the experimental data and the theory we show the crucial role played by the
vortex-core energy in determining the characteristic signatures of the BKT
physics, and we estimate its dependence on the disorder level. Our work
provides a paradigmatic example of BKT physics in a quasi-two-dimensional
superconductor.
