Electron energy relaxation in disordered superconducting NbN films

We report on the inelastic-scattering rate of electrons on phonons and relaxation of electron energy studied by means of magnetoconductance, and photoresponse, respectively, in a series of strongly disordered superconducting NbN films. The studied films with thicknesses in the range from 3 to 33 nm are characterized by different Ioffe-Regel parameters but an almost constant product q_Tl(q_T is the wave vector of thermal phonons and l is the elastic mean free path of electrons). In the temperature range 14-30 K, the electron-phonon scattering rates obey temperature dependencies close to the power law 1/\tau_{e-ph} \sim T^n with the exponents n = 3.2-3.8. We found that in this temperature range \tau_{e-ph} and n of studied films vary weakly with the thickness and square resistance. At 10 K electron-phonon scattering times are in the range 11.9-17.5 ps. The data extracted from magnetoconductance measurements were used to describe the experimental photoresponse with the two-temperature model. For thick films, the photoresponse is reasonably well described without fitting parameters, however, for thinner films, the fit requires a smaller heat capacity of phonons. We attribute this finding to the reduced density of phonon states in thin films at low temperatures. We also show that the estimated Debye temperature in the studied NbN films is noticeably smaller than in bulk material.