Characteristic times for gap relaxation and heat escape in nanothin NbTi superconducting filaments: thickness dependence and effect of substrate

TL;DR

This study investigates how the gap relaxation and heat escape times in nanothin NbTi superconducting filaments depend on thickness and substrate, using voltage response measurements and theoretical modeling to inform superconducting device optimization.

Contribution

It provides a quantitative analysis of the thickness and substrate dependence of gap relaxation times in NbTi superconducting filaments using time-dependent Ginzburg-Landau theory.

Findings

Gap relaxation time scales linearly with film thickness.

Interfacial substrate interaction significantly affects relaxation times.

Measured relaxation times vary from 5.2 ns to 9 ns depending on substrate.

Abstract

We measured the temporal voltage response of NbTi superconducting filaments with varied nanoscale thicknesses to step current pulses that induce non-equilibrium superconducting states governed by a hot-spot mechanism. Such detected voltage emerges after a delay time td, which is intimately connected to the gap relaxation and heat escape times. By employing time-dependent Ginzburg-Landau theory to link the delay time to the applied current, we determined that the gap relaxation time depends linearly on film thickness, aligning with the acoustic mismatch theory for phonon transmission at the superconductor-substrate interface. We thereby find a gap relaxation time of 104 ps per nm of thickness for NbTi films on polished sapphire. We further show that interfacial interaction with the substrate significantly impacts the gap relaxation time, with observed values of 9 ns on SiOx, 6.8 ns on fused silica, and 5.2 ns on sapphire for a 50 nm thick NbTi strip at T = 5.75 K. These insights are valuable for optimizing superconducting sensing technologies, particularly the single-photon detectors that operate in the transient regime of nanothin superconducting bridges and filaments