Scaling relations and universality in electrical failure processes of thinfilms: 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 cas es by the degradation of metallic interconnects (thin films) which, because of several phenomena, lose their conducting properties. Here the electrica l failure of thin films is described in terms of a percolation in two-dimen sional random resistor networks. We show that the resistance evolution foll ows a scaling relation expressed as R similar to epsilon (-mu) where epsilo n = (I - t/tau). tau is the time of electrical failure of the film and mu i s the exponent characterizing the critical behavior of the resistance as a function of the defect concentration. For the special case of uniform degra dation the value of mu is universal and known from standard percolation the ory. In the case of nonuniform degradation the validity of this scaling rel ation is proved by discussing the case in which the failure is due to a fil amentary growth of defects. The implications of this scaling relation on th e possibility of predicting failure times of thin films are then discussed. (C) 2001 Elsevier Science B.V. All rights reserved.