  We investigate evolution of the magnetic penetration depth and
superconducting energy gap in epitaxial NbN films using a low frequency mutual
inductance technique and tunneling spectroscopy using a low temperature
scanning tunneling microscope (STM). The superconducting transition temperature
(Tc) for films grown under optimal growth conditions decreases monotonically
from 15.87K to 9.16K as the film thickness is decreased from 50nm to 3nm. With
decrease in film thickness delta(0) monotonically decreases, whereas lambda(0)
monotonically increases. We observe that Tc, lambda(o) and delta(0) are well
described by Bardeen-Cooper-Schrieffer (BCS) theory in all films other than the
two thinnest ones where we see evidence of the Kosterlitz-Thouless-Berezinski
(KTB) transition close to Tc.
