Abstract
A well-posed moving boundary-value problem, describing the dynamics of curved interfaces and surfaces associated with voids and/or cracks that are interacting with grain boundaries, is obtained. Extensive computer simulations are performed for void configuration evolution during intergranular motion, under the actions of capillary and electromigration forces in thin-film metallic interconnects with bamboo structures. The analysis of experimental data, utilizing the mean time to failure formulas derived in this paper, gives consistent values for the interface diffusion coefficients and enthalpies of voids. 5.85×10−5exp(−0.95eV∕kT)m2s−1 is the value obtained for voids that form in the interior of the copper interconnects avoiding any surface contamination. 1.80×10−4exp(−1.20eV∕kT)m2s−1 is obtained for those voids that nucleate either at triple junctions or at the grain-boundary technical surface intersections (grain-boundary groove), where the chemical impurities such as Si, O, S, and even C are segregated during the metallization and annealing processes and may act as trap centers for hopping vacancies.
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