Estimating the maximum heating of low temperature NbN film with a current pulse: calculations by heat conduction equation

The process of heat transfer in NbN film while applying a pulse of current is considered using the 2D inhomogeneous heat equation. The boundary value problem is solved for a longitudinal cross section in the film; the heat transfer problem is solved for a system "contacts-film-substrate-thermostat". The temperature evolution for the film cross section since the pulse start till the temperature relaxation is visualized. The maximum film heating is evaluated. It was shown that the contact material (beryllium copper BeCu) ensures the effective heat drainage from a superconductive film existing in the resistance mode while passing a heavy current through the film. The developed simulation method and the material for the contacts can be used for other types of metallic or semiconductor films.