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A numerical calculation of the evolution of the temperature distribution in the longitudinal section of a niobium nitride membrane when it is heated by an electric current pulse is performed. Mathematical modeling was carried out on the basis of a two-dimensional initial-boundary value problem for an inhomogeneous heat equation. In the initial boundary value problem, it was taken into account that current and potential contacts to the membrane serve simultaneously as contacts for heat removal. The case was considered for the third from the left and the first from the right initial-boundary value problem. Analysis of the numerical solution showed that effective heat removal from the membrane can be provided by current-carrying and potential clamping contacts made, for example, of beryllium bronze. This makes it possible to study the current-voltage characteristics of superconducting membranes near the critical temperature of the transition to the superconducting state by currents close to the critical density without significant heating.

Mathematical modeling of heat transfer in the film-substrate-thermostat system with a pulsed flow of high-density current through an electrically conductive film has been carried out. On the basis of the simulation, the analysis of the heating of a niobium nitride film with a high resistivity near the critical temperature of the transition to the superconducting state is made. The inhomogeneous heat conduction equation which is solved numerically, simulates heat transfer in the film-substrate-thermostat system for the third on the left and the first on the right initial boundary value problem. Using the symmetry of the problem, the parameter H is determined, which is equal to the ratio of the heat transfer of the film surface to its thermal conductivity; this parameter is necessary for effective heat removal. It is shown that effective heat removal from films can be provided by current-carrying and potential clamping contacts made, for example, of beryllium bronze. This makes possible to study the current-voltage characteristics of superconductors near the critical transition temperature to the superconducting state with high-density currents (104−105A/cm2) without significant heating of the samples.