Phonon Escape Time Deduced From the Time of Nucleation of Hot Spots in Superconducting Niobium Filaments

We have observed the voltage response of superconducting niobium strips to overcritical $(I > I_{c})$ step pulses of electrical current. The resistive response appears after a certain delay time $t_{d}$ function of the temperature and of the ratio $I/I_{c}(T)$ , which can be analyzed through a time-dependent Ginzburg–Landau equation, along the method introduced by Tinkham. The experimental data can be fitted by using an effective gap relaxation time of a few nanoseconds, independently of the sample widths and of the temperature. Assuming proportionality to sample thickness, this indicates a phonon escape time of about 8 ps per nanometer of thickness for a Nb film dc sputtered on polished crystalline Al 2 O 3 .