Inverse Blech Length Phenomenon in Thin-Film Stripes

For decades, thin-film interconnects have been designed considering that the electric-current-induced mass transport or electromigration in thin films decreases with the reduction in the length of the film. This phenomenon is often called the Blech length effect, which dictates the seizure of electromigration if the product of the current density and the film length is smaller than a critical value. We report a phenomenon in Cu film stripes fabricated as per Blech configuration, where we observe that the electric-current-driven mass transport at the cathode increases as the sample length is reduced. We call this phenomenon the "inverse Blech length effect." Furthermore, the mass transport at the cathode in Cu film increases linearly with the inverse of the sample length. Finite-element analysis reveals an increase in the self-induced temperature gradients, which are very large to induce thermomigration in Cu, at the ends of Cu film with a decrease in the sample length. Therefore, the contribution of thermomigration increases in the overall mass transport at the cathode as the sample length is decreased. The ensuing electromigration-thermomigration coupling is used to qualitatively explain the observation of the inverse Blech length phenomenon. The findings in this work open avenues for the design of device-level interconnects in microelectronic devices.