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 td 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
.