Electromigration-induced stress in a confined bamboo interconnect with randomly distributed grain sizes

Microfailure of thin film interconnects by electromigration (EM)-induced stress is one of primary causes of degradation of the reliability of microelectronic circuits. We describe a two-dimensional model to simulate EM-induced stress in a confined bamboo interconnect line with randomly distributed grain sizes. We find that the steady-state stress distribution along the line is linear, the stress gradient being solely dependent upon the applied electric field, independent of the grain distribution and the diffusion condition at the line ends. However, the grain boundary concentration produces a significant shift in the steady-state stress along the line. When the grain boundaries concentrate in the tensile (compressive) stress zone, the steady-state stress lines shift up (down). Accordingly, the maximum tensile stress increases (decreases). The more the grain boundaries are in the tensile (compressive) stress zone, the more the maximum tensile stress increases (decreases). Thus, the maximum stress achieved at steady state is not only dependent on the line length for given applied electric field, but is also dependent on the grain boundary distribution along the line. A line microstructure with more grains in the compressive stress zone is of benefit to reduce the maximum tensile stress in the line. The preset results not only interpret why the EM-induced failure observed in experiments is sensitive to the variation in the line microstructures, but also imply that designing a line with fine grains in the compressive stress zone (near anode end) may significantly reduce the maximum tensile stress in the line, which can cause inhibition of failure due to EM-induced microcracking and void nucleation.