Physically based models of electromigration: From Black’s equation to modern TCAD models

Electromigration failure is a major reliability concern for integrated circuits. The continuous shrinking of metal line dimensions together with the interconnect structure arranged in many levels of wiring with thousands of interlevel connections, such as vias, make the metallization structure more susceptible to failure. Mathematical modeling of electromigration has become an important tool for understanding the electromigration failure mechanisms. Therefore, in this work we review several electromigration models which have been proposed over the years. Starting from the early derivation of Black’s equation, we present the development of the models in a somewhat chronological order, until the recent developments for fully three-dimensional simulation models. We focus on the most well known, continuum physically based models which have been suitable for comprehensive TCAD analysis.