1.4.6 Electromigration Modeling

The extensive methodology of electromigration testing, presented in the previous sections, leads to a qualitative understanding of the factors which affect the electromigration reliability of interconnects, especially when the results are extrapolated to real operating conditions. The underlying mechanisms which are interacting during the degradation process, initiated by the electromigration test, are often difficult to identify. Furthermore, the times needed to perform the experimental tests are extremely long. The most viable solution for the recognition of the dominant failure mechanisms of electromigration and their relationship with the interconnect structure and its materials is to employ simulations using physical models. For this purpose, the use of technology computer aided design (TCAD) becomes necessary. It comprises physical modeling, numerical implementation of these models, simulations, and analysis and post-processing of the simulation results with the scope to relate them to experimental observations. TCAD is a useful tool which provides designers with additional information to better understanding the causes and speed of electromigration-induced failure. Models are implemented using the finite element method (FEM), which allows to obtain numerical solutions representing the physical process of degradation of interconnect structures [148]. With the help of FEM, the understanding of the electromigration failure mechanism and the explanation of experimental observations are provided in order to improve design and manufacture of more reliable interconnects. The use of FEM-based tools for electromigration modeling and simulation is therefore a must for a more thorough analysis of the electromigration wear-out failure.

A general electromigration model should be able to reproduce experimental observations of the electromigration failure. As already mentioned, electromigration failure goes through two distinct phases, namely void nucleation and void evolution phase. Each phase is based on different physical phenomena and exhibits a different influence on the operating features of the interconnect [29]. The development of the electromigration model is therefore related to the contribution of each phase on the electromigration-induced failure and requires an analysis in two parts. The goal of electromigration modeling is to determine the interconnect lifetime from the simulation results as the sum of the void nucleation time and the void evolution time, as presented in equation (1.3). These results are related to those obtained from the reliability experimental tests, in order to verify the assumptions made for the simulation of the electromigration failure in the interconnect.