In the scope of this work, the focus is put on the development of a fully three-dimensional continuum EM model which is suitable for implementation in a TCAD tool and for numerical simulations. In this way, it is possible to study the EM behavior in realistic three-dimensional interconnect structures. This demands a careful study of the available models, so that their main strengths and, at the same time, their main shortcomings can be identified. Based on this analysis, one is able to extend and further improve these models by taking into account the most relevant effects for EM simulation.
In Chapter 2 the physical phenomena related to electromigration are discussed, starting with a basic derivation of the EM driving force based on a quantum mechanical theory. Next, a general description of the available material transport paths along an interconnect line is given. Then, a detailed analysis of several EM models is presented. First, the simple one-dimensional models are presented, which are followed by more advanced models as their complexity gradually increases. Then, the void nucleation condition followed by a void evolution model is discussed.
In Chapter 3 the developed EM model is presented. First, the calculation of the electric potential and temperature distribution in an interconnect line is described. This is followed by a discussion of the material transport equations, where emphasis is put on the importance of fast diffusivity paths on the EM induced transport. Also, a detailed derivation of the influence of mechanical stress on the vacancy diffusivity is presented. Next, the connection between EM induced transport and production of mechanical stress is discussed, which is followed by the derivation of a new grain boundary and interface model. The mechanical deformation equations are then presented. Finally, an overview of the complete set of equations, which composes the EM model, is given.
Chapter 4 is devoted to the description of the numerical discretization of the physical model. It starts with the presentation of basic concepts of the finite element method and gives a general formulation for discretization of a three-dimensional domain with tetrahedrons. Then, the numerical discretization of the set of equations which form the EM model derived in Chapter 3 is presented in some detail. This is followed by the description of the TCAD tool developed for EM simulations. Here, the implementation of the algebraic system of equations is described, and all calculations are presented, which are performed during the assembly process of the system of equations for each set of equations composing the model.
In Chapter 5 several simulation studies of electromigration are carried out, starting with the presention of the set of material and simulation parameters which are required in the simulation examples. The developed model and its implementation is verified by simulating the EM transport in a simple interconnect line and comparing it with some of the analytical solution of the models described in Chapter 2. This is then repeated with the inclusion of mechanical stress into the calculations. Next, an original study of the effect of the mechanical stress on the vacancy diffusivity and its effect on the total EM transport is performed. This is followed by a discussion of the importance of fast diffusivity paths regarding the EM failure development. Here, emphasis is put on the role of material interfaces as fast paths for diffusion. Following, the effect of redundant vias in dual-damascene interconnect structures is analyzed. Then, a detail discussion of the impact of the microstructure on EM failure is given.
Finally, conclusions and suggestions for future works are presented in Chapter 6.