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Analysis of Electromigration-Driven Interactions between Voids in Metallic Thin Films

Jaeseol Cho, M. Rauf Gungor, and Dimitrios Maroudas. Department of Chemical Engineering, University of Massachusetts, 686 N. Pleasant Street, Amherst, MA 01003

Electromigration-induced void dynamics in metallic thin films has been studied extensively due to its significance as an interconnect reliability problem in microelectronics and as an intriguing nonlinear dynamical phenomenon of driven mass transport and microstructural evolution in conducting materials. Theoretical analysis of void dynamics has focused mostly on the driven evolution of a single (isolated) void confined in a metallic thin film. The interactions between two morphologically evolving voids in a metallic thin film of finite width may lead to stable or unstable void morphologies (through, e.g., void coalescence) that can cause drastic changes in the film's electrical properties. This presentation addresses systematically the current-driven morphological evolution of two interacting voids taking into account surface diffusional anisotropy and current crowding effects.

Our analysis focuses on the electromigration-induced interactions between two voids that, if isolated, they would be morphologically stable migrating at constant speed along the metallic thin film driven by the electric current. The analysis is based on self-consistent numerical simulations of current-induced migration and morphological evolution of void surfaces in metallic thin films, which accounts rigorously for current crowding effects that become particularly significant in narrow metallic films, as well as surface curvature effects that can be particularly strong due to the strong anisotropy of adatom diffusion on void surfaces. The mass transport problem on the void surfaces is solved self-consistently coupled with the electric field distribution in the conducting film that contains the morphologically evolving voids. A two-dimensional (2D) implementation is followed in the plane of an infinitely long metallic film of finite width, based on the assumption that the voids extend throughout the film thickness, which is consistent with experimental observations. Parameters and initial conditions are chosen so that the two voids do not interact initially and until they reach their stable steady states as if they were isolated in the film. Driven continuously by the electric current, the two voids eventually approach and start interacting with each other; as a result, their shapes change and reach other stable or unstable configurations depending on the electromigration conditions (electric field strength, strength of diffusional anisotropy, etc.), as well as their sizes.

Our simulations reveal an extremely broad class of phenomena, governed by void-void interactions in the finite-width interconnect lines under consideration, through the perturbation of the electric-field distribution around the void surface created by the presence in close proximity of the other void. Specifically, the analysis predicts stable steady or time-periodic states that can be reached by two voids migrating in the same direction mediated by their interactions, including coalescence and breakup phenomena, as well as film failure caused by such void-void interactions. Contrary to the conventional wisdom, it is demonstrated that a trailing larger void can approach a leading smaller one. More interestingly, two voids may coalesce or not depending on how the electric field distributions around the voids are perturbed by each other. It is demonstrated that void coalescence can cause sudden changes in the electrical resistance evolution of interconnect lines, which are in excellent qualitative agreement with electrical resistance measurements from accelerated electromigration testing experiments. It is also demonstrated that void-void interactions in the metallic thin film can lead to film failure through formation of thin slits emanating from the surface of one of the voids or to wave propagation on one of the void surfaces, in cases where neither void would evolve into such states if isolated in the film. Furthermore, some intriguing phenomena are predicted under certain electromigration conditions: these include void breakup following void coalescence and current-driven interactions leading to voids passing each other as they migrate along the film.