ElectroMigration (EM) lifetimes are commonly described by Black's equation. After fitting it to experimental data, Black's equation is used to extrapolate results from accelerated tests to operating conditions. This extrapolation methodology is based on the critical assumption that the parameters obtained from accelerated experiments are also valid at the lower temperature and the lower current density at normal operation. Thus, the failure mechanism, or more generally, the dominant physical effects during accelerated tests are considered to remain the same under use conditions. However, it has been shown that the parameters obtained from Black's equation fit are not directly applicable to lifetime extrapolation.
We have developed an approach for lifetime extrapolation based on a more rigorous physical model for EM failure of copper dual-damascene interconnects. Figure 1 shows the extrapolation of EM lifetimes for several current densities. The model was first calibrated for 1.33MA/cm². Then, using the same set of parameters, the lifetimes for other current densities were calculated. As figure 1 shows, the extrapolated (simulated) lifetimes are in good agreement with the experimental results. In particular, the simulations closely follow the experiments for all failure percentiles. Figure 2 shows the lifetime extrapolation to lower temperatures. The model was calibrated for 342°C. A very good agreement between simulation and experiment is obtained at higher temperatures, for all failure percentiles. However, at lower temperatures a significant lifetime difference is observed for small failure percentiles. The simulations predict a smaller standard deviation than the experimental one. The significant change of the standard deviation with temperature observed experimentally indicates that the EM failure mechanism has changed in such a way that the proposed model cannot completely describe it.
We observed that the approach applied above yielded better extrapolation results than the standard methodology based on Black's equation. This is a consequence of the more rigorous model we developed. Furthermore, the proposed approach requires a detailed analysis of the experimental data and associated failure mechanisms, which leads to a more suitable description of the problem and, consequently, to a more precise extrapolation.