A thermodynamic model for electrical current induced damage

Electromigration induced damage, which is in principal an irreversible mass diffusion under high current density, has been a concern for VLSI design for a long time. Miniaturization of electronic device sizes down to nano-scale will make electromigration a concern for all conducting components. This paper uses thermodynamics, statistical mechanics and mass transport (diffusion) principals to propose a model for electromigration process and a damage evolution model to quantify the degradation in microelectronics (and Micro Electro Mechanical System) solder joints subjected to high current densities. Entropy production in the system is used as a damage metric. The irreversible thermodynamic damage model utilized in this work has previously been successfully applied to thermomechanical fatigue of microelectronic solder joints. In this paper we extend this model to electromigration-induced degradation. Electromigration process is modeled by the atomic vacancy flux (mass diffusion) process. The proposed unified model is compared with several existing analytical and empirical models. A comparison of the damage evolution model proposed in here agrees well with empirical models proposed in the literature.