Experiments have shown that electromigration lifetimes for copper dual-damascene interconnects follow a lognormal distribution. Although the origin of such a distribution is not entirely clear, the microstructure has been considered as its major cause. The understanding of the electromigration lifetimes distribution is crucial for the extrapolation of the times to failure obtained empirically from accelerated tests to real operating conditions.
It has been shown that the microstructure plays a key role in the failure mechanisms in copper dual-damascene interconnects. Grain boundaries affect electromigration in different ways. They are natural locations of atomic flux divergence, they act as fast diffusivity paths for vacancy diffusion, and grain boundaries act as sites of annihilation and production of vacancies.
We have developed a continuum multi-physics electromigration model that incorporates the effects of grain boundaries and interfaces. Grain boundaries are treated as separate regions that can trap and/or release vacancies. The vacancies trapped at grain boundaries are responsible for the build-up of local tensile stress. When the grain boundaries are able to capture a high amount of vacancies, a high tensile stress develops and void nucleation occurs.
The electromigration model has been implemented in FEDOS (Finite Element Diffusion and Oxidation Simulator), a finite element based tool for three-dimensional problems. All important driving forces have been taken into account in the vacancy transport equation. Moreover, fast diffusivity paths for material transport, such as material interfaces, have also been considered.
The implemented model can satisfactorily explain the locations where voids are commonly observed to nucleate.