FEM Based Multiphysics Analysis of Electromigration Voiding Process in Nanometer Integrated Circuits
Failures introduced by the electromigration (EM) effect in copper interconnect is one of the top reliability issues in modern integrated circuits (ICs) in 10 nm technology and below. International Technology Roadmap for Semiconductors (ITRS) predicts that the required current density for driving a normal gate will exceed the EM current density limit in 2024 if the industry continues current technology scaling with existing interconnect materials and EM design rules based on current density.
Because of EM effect, under extreme current densities, copper interconnect is highly probable to fail over time, most of which is caused by void formation. The behavior of void in copper interconnect, which includes void generation, growth, migration, merging, and vanishing, interacting very tightly with mechanical hydrostatic stress, is critical to the EM reliability. Among the variety void behaviors, void growth and migration dominates the impact on the consequence of open-circuit failures. The analysis of void growth and migration and circuit failures thereby is considerably difficult because of the coupling of a variety physical systems (temperature, electrical current density, void shape, and hydrostatic stress).
In this work, a multi-physics finite element method (FEM) based analysis method for void growth simulation of confined copper interconnects is proposed. The purpose is to facilitate the analysis of void behavior and EM-induced copper interconnect failures. The proposed method for the first time considers four important physics simultaneously in the EM failure process and their time-varying interactions: the hydrostatic stress in the confined interconnect wire, the current density, copper-void boundary evolution, and Joule heating induced temperature. A solver based on finite element method is proposed to solve the coupled systems in time-dependent manner. The proposed work ranges from deriving the partial differential equations governing the interaction of the hydrostatic stress and copper-void boundary evolution, to their variational form derivation, and finally to a software implementation.
The experiment data acquired from the software matches well with the behavior observed in real silicon experiments, which are in the aspects of hydrostatic stress and void shape evolution, final hydrostatic stress distribution, and Joule heating effect.