Scaling and Universality in Electrical Failure of Thin Films

Abstract

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 scaling relation expressed as R approximately epsilon(-&mgr;) where epsilon = (1-t/tau), tau is the time of electrical failure of the film, and &mgr; is the same critical exponent appearing in the scaling relation between R and the defect concentration. For uniform degradation the value of &mgr; 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 this relation allows predictions of failure times from early time measurements of the resistance.