Measurement of magnetic penetration depth and superconducting energy gap in very thin epitaxial NbN films

We report the evolution of the magnetic penetration depth (?) and superconducting energy gap (?) in epitaxial NbN films with thickness (d) varying between 51-3 nm. With decrease in film thickness Tc and ?(0) monotonically decreases, whereas ?(0) monotonically increases. Our results show that while the values of ?(0) and ?(0) are well described by Bardeen-Cooper-Schrieffer theory, at elevated temperatures, films with d ? 6.5 nm show sudden drop in superfluid density associated with the Kosterlitz-Thouless-Berezinski transition. We discuss the implication of these results on the time response of superconducting bolometers made out of ultrathin NbN films.