Electromigration modeling and simulation

Abstract

Electromigration induced failure is one of the main reliability issues for the microelectronics industry. The continuous scaling of the interconnect dimensions leads to higher operating current densities and temperatures, which accentuates the electromigration failure. As a consequence, electromigration still poses challenges for the development of the new technological nodes.<br />Mathematical modeling can significantly contribute to the understanding of the electromigration failure mechanisms. It has become an important tool for explaining several experimental observations and, ultimately, can provide a stronger basis for design and fabrication of reliable metallizations. In the scope of this work the focus is put on the development of a fully three-dimensional electromigration model which is suitable for numerical simulations. To accomplish this task, a detailed study of previous models is carried out, and their main strengths and shortcomings are identified. Based on this study, a complete model which connects electromigration induced material transport with the electro-themal and the mechanical problem in a general framework has been developed. Material interfaces and grain boundaries are treated as independent fast diffusivity paths. A careful analysis of the vacancy dynamics in grain boundaries is performed, and a new grain boundary model is proposed. The model equations are numerically solved using the finite element method. Their discretization is presented in detail, and the implementation of the corresponding system of algebraic equations in a software tool is described in a systematic way.<br />Electromigration simulations are carried out in realistic three-dimensional copper dual-damascene interconnect structures. The correctness of the implementation is verified by comparing the simulation results with the available analytical solutions. The effect of mechanical stress on electromigration induced material transport is presented, and its impact on the lifetime extrapolation is discussed.<br />Since the microstructure has a major influence on the electromigration failure, its effect on the electromigration lifetimes' distribution is analyzed. Several simulations are carried out in order to obtain the statistical properties of the electromigration lifetimes as a function of the the copper grain size statistics. The introduction of fast diffusivity paths and microstructure into the modeling framework represents a significant improvement of the model capabilities. The simulations results show that the proposed model is able to explain and reproduce some of the most common experimental observations of electromigration induced voiding, and demonstrate the predictive capability of the developed tool.