Scaling relations and universality in electrical failure processes of thin films: is it possible to predict failure times?

The increasing level of miniaturization of electronic devices enhances the importance of degradation and failure processes. Failure occurs in many cases by the degradation of metallic interconnects (thin films) which, because of several phenomena, lose their conducting properties. Here the electrical failure of thin films is described in terms of a percolation in two-dimensional random resistor networks. We show that the resistance evolution follows a scaling relation expressed as R∼ϵ−μ where ϵ=(1−t/τ), τ is the time of electrical failure of the film and μ is the exponent characterizing the critical behavior of the resistance as a function of the defect concentration. For the special case of uniform degradation the value of μ is universal and known from standard percolation theory. In the case of nonuniform degradation the validity of this scaling relation is proved by discussing the case in which the failure is due to a filamentary growth of defects. The implications of this scaling relation on the possibility of predicting failure times of thin films are then discussed.