Dynamic fuse model for electromigration failure of polycrystalline metal films

We introduce a dynamic fuse model for the damage done to a current-carrying polycrystalline metal film by electromigration. For all initial densities of defects p, the mean failure time 〈${\mathit{T}}_{\mathit{f}}$〉 is, to an excellent approximation, proportional to the average length of the shortest path across the film in a certain metric. 〈${\mathit{T}}_{\mathit{f}}$〉 tends to zero as (${\mathit{p}}_{\mathit{c}}$-p${)}^{4/3}$ as the percolation threshold p=${\mathit{p}}_{\mathit{c}}$ is approached.