A theoretical analysis to current exponent variation regularity and electromigration-induced failure

The electric current exponent, typically with j⁻ⁿ form, is a key parameter to predict electromigration-induced failure lifetime. It is experimentally observed that the current exponent depends on different damage mechanisms. In the current research, the physical mechanisms including void initiation, void growth, and joule heating effect are all taken into account to investigate the current exponent variation regularity. Furthermore, a physically based model to predict the mean time to failure is developed and the traditional Black's equation is improved with clear physical meaning. It is found that the solution to the resulting void initiation and growth equation yields a current exponent of 2 and 1, respectively. On the other hand, joule heating plays an important role in failure time prediction and will induce the current exponent n > 2 based on the traditional semi-empirical model. The predictions are in agreement with the experimental results.