Measurement of the gap relaxation time of superconducting NbTi strips on a sapphire substrate

We report on the study of the transient voltage response of superconducting NbTi strips to an over-critical current pulse (I> I_c, where I_c is the pair-breaking current). In this experiment, a localized normal spot appeared for a current amplitude larger than the critical current. The induced metastable superconducting state was identified as either a hotspot or phase-slip center. These two dissipative modes share the feature of the voltage response occurring after a delay time t_d, a solution of the time-dependent Ginzburg–Landau (TDGL) theory developed by M. Tinkham. The gap relaxation time was subsequently deduced from fitting the experimental data with the TDGL theory. An agreement was found by choosing an effective gap relaxation time τΔ=4.75ns for a thickness of 50 nm. Assuming the proportionality to sample thickness, this indicates a thermal relaxation time of 96 ps/nm for a NbTi film sputtered at room temperature on polished crystalline Al ₂O ₃. If we assume that the electron and the phonon specific heats have the same ratio as for pure Nb, then it results in a phonon heat escape time τes/d=32ps/nm.