A new approach to calculate atomic flux divergence by electromigration

The atomic flux divergence obtained from current density and temperature in metal lines undamaged by electromigration is useful to predict the formation of initial void. In this study, a new method to calculate the atomic flux divergence used for predicting the formation of initial void is proposed considering two-dimensional distributions of current density and temperature and also simply considering the line structure not only of polycrystalline line but also of bamboo line. The flux divergence is formulated based on the Humington-Grone's equation and modeling of line structure. For the verification, electromigration phenomenon near the corner of an angled polycrystalline line, which results in two-dimensional distributions of current density and temperature, is treated as an example. The usefulness of the proposed method is discussed by comparison of the prediction of void formation near the corner with the experimental result.