It has been shown that the microstructure plays a key role regarding the failure mechanisms in copper dual-damascene interconnects [71]. It affects electromigration in different ways. Grain boundaries are natural locations of atomic flux divergence, they act as fast diffusivity paths for vacancy diffusion [168], and they act as sites of annihilation and production of vacancies [148].
Electromigration data have been described by lognormal distributions [22]. Although the origin of the lognormal distribution of electromigration lifetimes is not entirely clear, it has been argued that the diffusion process in connection with the effect of microstructure on electromigration provides the basis for the lognormal distribution [20]. In copper dual-damascene interconnects the main diffusivity path is along the copper/capping layer interface. This interfacial diffusion is affected by the orientation of the grains. As the copper grain sizes seem to follow lognormal distributions in typical dual-damascene process technology [20], and due to the influence of microstructure on the electromigration process, the lognormal distribution has been used as the underlying statistics for electromigration lifetimes.
Understanding the electromigration lifetime distribution is crucial for the extrapolation of the times to failure obtained empirically from accelerated tests to real operating conditions, as performed by equation (1.23). Therefore, in this section the statistical distribution of electromigration times to failure as a function of the distribution of copper grain sizes is investigated. The discussion is focused on the impact that the variation of the standard deviation of the grain size distribution has on the electromigration lifetimes, and the consequences of the latter for reliability assessment of interconnects.