Biased percolation and electrical breakdown

Abstract

To analyse the degradation of a thin-film conductor we have extended the biased percolation model to the case of electrical breakdown associated with a systematic decrease of the resistance. As relevant indicators of the degradation process we have chosen the damage pattern, the current and temperature distributions, the change of resistance, the lifetime, the relative resistance fluctuations and its power spectrum associated with 1/f noise. Our results are in a satisfactory agreement with available experiments, exhibiting several features which take place close to the abrupt failure of a thin-film device, and confirm the usefulness of the biased percolation model as a tool to investigate degradation processes. Analogies and differences between the two opposite situations when degradation occurs with a systematic increase or decrease of the resistance are discussed.