Scaling and universality in electrical failure of thin films

We describe the electrical failure of thin films as a percolation in two-dimensional random resistor networks. We show that the resistance evolution follows a sealing relation expressed as R similar to epsilon(-mu) where epsilon = (1 - t/tau). tau is the time of electrical failure of the film, and mu is the same critical exponent appearing in the scaling relation between R and the defect concentration. For uniform degradation the value of mu is universal. The validity of this scaling relation in the case of nonuniform degradation is proved by discussing the case in which the failure is due to a filamentary defect growth. The existence of tills relation allows predictions of failure times from early time measurements of the resistance.