  Disorder has different profound effects on superconducting thin films. For a
large variety of materials, increasing disorder reduces electronic screening
which enhances electron-electron repulsion. These fermionic effects lead to a
mechanism described by Finkelstein: when disorder combined to electron-electron
interactions increases, there is a global decrease of the superconducting
energy gap $\Delta$ and of the critical temperature $T_c$, the ratio
$\Delta$/$k_BT_c$ remaining roughly constant. In addition, in most films an
emergent granularity develops with increasing disorder and results in the
formation of inhomogeneous superconducting puddles. These gap inhomogeneities
are usually accompanied by the development of bosonic features: a pseudogap
develops above the critical temperature $T_c$ and the energy gap $\Delta$
starts decoupling from $T_c$. Thus the mechanism(s) driving the appearance of
these gap inhomogeneities could result from a complicated interplay between
fermionic and bosonic effects. By studying the local electronic properties of a
NbN film with scanning tunneling spectroscopy (STS) we show that the
inhomogeneous spatial distribution of $\Delta$ is locally strongly correlated
to a large depletion in the local density of states (LDOS) around the Fermi
level, associated to the Altshuler-Aronov effect induced by strong electronic
interactions. By modelling quantitatively the measured LDOS suppression, we
show that the latter can be interpreted as local variations of the film
resistivity. This local change in resistivity leads to a local variation of
$\Delta$ through a local Finkelstein mechanism. Our analysis furnishes a purely
fermionic scenario explaining quantitatively the emergent superconducting
inhomogeneities, while the precise origin of the latter remained unclear up to
now.
