The analysis of heat transfer in the contact-film-substrate system under conditions when the heat removal from the sample to the substrate is insufficient to ensure that the sample is not overheated. For low temperatures, a method is proposed for increasing the heat removal from thin-film samples by passing a high-density electric current through them. The property of an anomalously high thermal conductivity of copper at temperatures from 5 to 50 K was used as the main factor in enhancing heat removal. The heat equation for the film-substrate system was numerically solved under the condition of additional heat transfer to potential contacts. It has been shown that beryllium bronze contacts can provide efficient heat removal from samples of superconducting films in a resistive state under conditions of strong Joule heat release.

Using time sweeps of the current through a sample of a superconducting film, the effect of the current sweep rate on the process of heat propagation from current contacts is investigated. The samples used were NbN films located below and above the transition temperature to the superconducting state. A method for determining the critical heating of key zones of the sample is proposed. The propagation velocities of the resistive front and normal domain in a superconductor are estimated at different temperatures.

A sequence of inhomogeneous differential equations for reconstructing the derivative of the nonlinear current–voltage characteristic is studied. The right-hand side of these equations is the experimentally determined dependence of the first-harmonic voltage on direct current. Such voltage arises, e.g., at the output of a nonlinear semiconductor structure simultaneously exposed to alternating and direct current. Based on numerical solutions of differential equations, the developed technique is applied to reconstruct the derivative of the current–voltage characteristic of two antiparallel connected p – n junctions.