  Using scanning tunneling spectroscopy (STS), we address the problem of the
superconductor-insulator phase transition (SIT) in homogeneously disordered
ultrathin (2-15 nm) films of NbN. Samples thicker than 8 nm, for which the
Ioffe-Regel parameter $k_F l \geq 5.6$, manifest a conventional
superconductivity : A spatially homogeneous BCS-like gap, vanishing at the
critical temperature, and a vortex lattice in magnetic field. Upon thickness
reduction, however, while $k_F l$ lowers, the STS revealed striking deviations
from the BCS scenario, among which a progressive decrease of the coherence peak
height and spatial inhomogeneities. The thinnest film (2.16 nm), while not
being exactly at the SIT ($T_C \approx 0.4 T_{C-bulk}$), showed astonishingly
vanishing coherence peaks and the absence of vortices. In the quasi-2D limit,
such clear signatures of the loss of long-range phase coherence strongly
suggest that, at the SIT the superconductivity is destroyed by phase
fluctuations.
