Temperature Dependence of the Phonon Escape Time Deduced from the Nucleation Time of Phase Slip Center in Superconducting NbTiN Thin Film

We have investigated the voltage response of superconducting NbTiN strips to a step-pulse of overcritical current in the range of temperatures 0.4 < T/T _c < 0.9, where the critical temperature, T_c, is 8.7 K. The current-induced destruction of the Cooper pairs leads to the nucleation of a phase-slip center. The response appears after a certain delay time t_d, which we analyze through a Time-Dependent Ginzburg-Landau (TDGL) theory according to Tinkham’s approach. The experimental findings can be fitted by inferring a film cooling time of about 1.8 ns for a 20-nm-thick film, very little dependent upon sample width and temperature. Assuming a definite ratio between the electron and phonon specific heats, one deduces an average phonon escape time of 90 ps per nm thickness of NbTiN film sputtered on sapphire.