Numerical simulation of the heating process of an NbN film by a current pulse at low temperatures based on the two-dimensional heat-conduction equation

Abstract

The simulation of the process of heat propagation in the NbN film during the passage of a current pulse through it was carried out on the basis of an inhomogeneous two-dimensional equation of heat conduction. The initial-boundary value problem for longitudinal section of the film is solved numerically, and the analysis of heat transport in the system contacts-film-substrate-thermostat is carried out. The temperature evolution of the film cross section from the onset of the pulse to temperature leveling is visualized. It is shown that the contact material (beryllium bronze) provides efficient heat removal from a superconducting film in a resistive state when a high-density current flows through it. The proposed modeling method and contact material can be used to study other metal or semiconductor films.