Self-Heated Hotspots in Superconducting Nanowires Cooled by Phonon Black-Body Radiation

Heat transfer in nanostructures is of fundamental and practical interest. Sufficient cooling is critical for the operation of superconducting nanowire single photon-detectors (SNSPDs), which can support large current densities (~5 MA/cm²) just prior to being switched into a high resistivity (~250 μΩ*cm) normal state by an incident photon, leading to substantial local heating. The thermal boundary conductance (TBC) between the nanowire and the substrate determines the cooling rate, and hence the reset time, and potentially impacts the quantum efficiency of SNSPSDs. Despite the TBC’s importance, open questions remain about its correct description in few-nm thick films, and little experimental data exists on patterned nanowire devices.

Here, we show that simple DC electrical measurements can be used to estimate the TBC between the nanowire and the substrate. Our results suggest that the heat transfer from these devices is well-described by phonon black-body radiation into the substrate, with a phonon-emissivity that depends on the acoustic properties of the wire and substrate. Calculations using the acoustic mismatch model assuming two semi-infinite elastic media match the phonon-emissivity extracted from measurements. One-dimensional numerical simulations validate our approach.