Experimental works have observed two distinct ElectroMigration (EM) failure modes in copper dual-damascene interconnects, namely, the late (strong) mode and the early (weak) mode. The late failure mode is characterized by the growth of a void spanning the line cross section. In turn, in the early failure mode, a slit void under the cathode via is typically observed. It has been shown that the late mode is dominated by the void growth kinetics, while the early mode is governed by the combination of the void nucleation and growth mechanisms. Since the reliability assessment of a given interconnect technology is primarily determined by its early failures, modeling and understanding the early failure mode becomes a necessity. We have developed a compact model for the early EM failures of copper dual-damascene interconnects. The model is based on analytical expressions obtained from the available solutions of electromigration stress build-up assuming slit void growth under the interconnect vias. Fully three-dimensional numerical simulations indicate that the stress development can be described by a linear relationship for lower stresses and by a square root model for higher stresses, as shown in Figure 1. Thus, the stress increase obtained with regard to physics of a rather complete model can be conveniently described by simple analytical solutions and the time to void nucleation is then readily obtained applying the square root model. Once a void is nucleated it grows under the via, so that the EM failure occurs as soon as the void reaches the size of the via. The EM lifetime is then estimated by the sum of the void nucleation and the void growth time, shown in Figure 2. The simulations yield a reasonable estimation for the early EM lifetimes in comparison to published experimental results.
To sum up, a model for estimation of the early EM lifetime distribution in copper dual-damascene interconnects has been proposed. A key feature of the model is that it consists of a physical model that provides a satisfactory description of the complex physics of EM phenomena. The model can take into account the statistical distribution of physical parameters and is thus able to deliver a distribution of EM lifetimes. Moreover, it accounts for both, the void formation and the void growth kinetics, which yields a more precise description of the EM damage and a better extrapolation methodology of the accelerated tests to use condition.