1.5 Outline of the Thesis

The purpose of the work described in this document is to develop a physical model for the investigation of the electromigration problem in interconnects which takes into account all the most relevant effects related to electromigration degradation. The model treats the two phases of failure separately in order to extract essential information from a detailed analysis of each phase. Since the model is influenced by a wide variety of physical phenomena, it is convenient to implement it into a FEM-based simulation tool such as COMSOL Multiphysics^® [38], which provides numerical solutions and contributes to the analysis of the results obtained for both failure phases. Moreover, the simulation software provides the ability to design the complex interconnect geometry on which the analysis must be performed. In this way, it is possible to investigate the electromigration failure in a variety of interconnect structures required for a better understanding of reliability in 3D integration technology, such as open copper TSVs and solder bumps.

The body of the thesis is arranged into six chapters as follows. Chapter 2 treats the history and the evolution on the studies of electromigration from early to modern times. Then, a detailed derivation of the driving force governing the electromigration failure and its action on the transport of metal atoms along the available diffusion paths over the interconnect are presented. This is followed by an overview of the state of the art for electromigration modeling, where the impact of the stress build-up due to electromigration, the derivation of the void nucleation condition, and several approaches for void evolution analysis are described.

Chapter 3 presents in detail the full continuum electromigration model, which includes all the mechanisms related to electromigration failure. Since electromigration modeling requires a multiphysics approach, it is most conveniently separated into submodels. The submodels are comprised of the electro-thermal problem, vacancy dynamics problem, and solid mechanics model. The latter permits to determine the void nucleation condition and it therefore represents the beginning of the second phase of failure, the void evolution. The description of three different approaches to model the void evolution mechanism in interconnects is included in this chapter.

In Chapter 4, the numerical implementation of the physical model in a FEM-based tool is described. First, the chapter presents a basic introduction to FEM and gives an example of finite element analysis for a simple problem. Then, the general description of the capabilities of the simulation tool employed for electromigration simulations is introduced, followed by the presentation of a schematic procedure flow for electromigration studies.

Chapter 5 deals with the simulation studies of electromigration, carried out for different interconnect structures. Case studies of particular interest are open through silicon vias and flip-chip solder bumps. Furthermore, a newsworthy comparative study regarding the impact of geometry and microstructure on the electromigration failure development in standard interconnect lines is presented.

Finally, in Chapter 6 the work is summarized and possible further improvements concerning electromigration investigations are presented.