Electron energy relaxation in disordered superconducting NbN films

We report on the energy relaxation of electrons studied by means of magnetoconductance and photoresponse in a series of superconducting NbN film with thickness in the range from 3 to 33 nm. The inelastic scattering rate of electrons on phonons obeys T^n temperature dependence where the exponent is in the range n = 3.2 - 3.8 and shows no systematically dependence on the degree of disorder. At 11 K electron-phonon scattering times are in the range 11.9 - 17.5 ps. We show that in the studied NbN films the Debye temperature and the density of phonon states are both reduced with respect to bulk material. In the thinnest studied films reduced density of states along with the phonon trapping slows down the energy relaxation of electrons by a factor of 4 as compared to the prediction of the tree dimensional phonon model.