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Using the Green's function of the 3D heat equation, we develop an analyticalaccount of the thermal behaviour of superconducting films subjected toelectrical currents larger than their critical current in the absence of anapplied magnetic field. Our model assumes homogeneity of films and currentdensity, and besides thermal coefficients employs parameters obtained byfitting to experimental electrical field - current density characteristics atconstant bath temperature. We derive both a tractable dynamic equation for thereal temperature of the film up to the supercritical current density J^\ast(the lowest current density inducing transition to the normal state), and athermal stability criterion that allows prediction of J^\ast . For two typicalYBCO films, J^\ast predictions agree with observations to within 5%. Thesefindings strongly support the hypothesis that a current-induced thermalinstability is generally the origin of the breakdown of superconductivity underhigh electrical current densities, at least at temperatures not too far fromTc.

An analytical approach to the thermal instability of superconducting films under high current densities