3. Modeling Electromigration Using TCAD

In the previous chapter a description of the various physical phenomena related to the electromigration failure mechanism were described. The different physical models proposed allow to obtain analytical solutions and may only be applied to investigate simple structures. Since the scope of this thesis is to analyze complex interconnect geometries, the derivation of analytical solutions does not provide appropriate results. For this purpose, the development of an electromigration model, adapted for the implementation in a technology computer aided design (TCAD) tool, is necessary in order to simulate complicated interconnect structures. Since different physical effects are responsible for electromigration failure, modeling electromigration constitutes a multiphysics analysis which can be divided into different blocks. Initially a description of the electro-thermal problem allows to determine the distributions of electric potential, current density, and temperature inside the structure. Then, the vacancy balance equation is solved, which takes into account all the various driving forces for vacancy transport and the effects of the different fast diffusivity paths. This is followed by the determination of the distribution of the electromigration-induced stress build-up in the structure obtained from solid mechanics modeling. Reaching of a threshold stress implies void nucleation and the beginning of the second phase of failure. The different methodologies adopted for modeling the void evolution mechanism are fully described in this chapter. Finally, an overview of the model blocks, which must be solved numerically with the TCAD tool, is briefly presented.