A multi-phase-field model of void crossing grain boundary under electromigration-induced anisotropic surface diffusion in interconnects

Abstract

Under the external electric field, the voids in polycrystalline interconnect lines will exhibit different morphology evolution when crossing grain boundary. Predicting the void crossing process caused by electromigration is an important aspect to improve the reliability of miniaturized integrated circuits. Based on the basic theoretical framework of microstructural evolution in solid materials, a new multi-phase-field model is established in this paper to simulate the process of void crossing grain boundary under anisotropic surface diffusion caused by electromigration in bicrystal interconnect line. Through asymptotic analysis, the compatibility of the multi-phase-field model with the sharp interface model in the limit case is proven. The corresponding finite-element program is developed and the reliability of the model is verified by comparing the numerical simulation with the theoretical solution. The results indicate that the process of void crossing grain boundary is governed by the crystal orientation and the misorientation difference of two adjacent grains. Under different misorientation differences, the void in (110) crystal orientation has two evolutional bifurcation trends: void splitting and tilting drift, while the void in (100) and (111) crystal orientation always remains as a whole and drifts along the direction of the electric field. The void in (111) crystal orientation is the easiest to cross the grain boundary, the fastest to cross the grain boundary, and the influence of the misorientation difference is minimal. This can prevent the void from being pinned by the grain boundary and extending along the grain boundary to cause failure, so as to effectively improve the reliability of the interconnects and extend the service life of the integrated circuit.