Since the late 1960s, several models have been proposed to describe electromigration. Mathematical modeling can significantly contribute to the understanding of EM failure mechanisms. It is an important tool for explaining several experimental observations and, ultimately, it can provide an improved basis for design and fabrication of reliable metallizations. The main problem is that EM is influenced by a wide diversity of physical phenomena and depends on a large number of intrinsic and extrinsic effects. Moreover, the complex interconnect geometries and technological process related features of modern interconnects, such as a typical dual-damascene line, make modeling even more challenging.
Several of the available models are based on simplifying assumptions, so that analytical solutions can be obtained. However, as the development and improvement of different experimental techniques has allowed a deeper analysis of the EM failure, the complexity of the models has gradually increased, in order to be able to reproduce these experimental observations. Such complex models cannot be analytically solved and, therefore, numerical solutions are now required. At the same time, the development of computational methods and resources has allowed to model complex systems and carry out numerical simulations in an efficient way. Thus, the use of TCAD (Technology Computer-Aided Design) tools for EM simulation in interconnect lines has become more popular.
As already mentioned, EM failures can normally be described by a void nucleation and a void evolution phase. Since each of these phases are related to different physical phenomena, it is convenient to treat them separately. A schematic design of such a TCAD tool for EM simulation is then shown in Figure 1.6.