Phase field simulation of healing and growth of voids in interconnects under electric field-induced interface migration

Abstract

The micro-damage such as voids, inclusions, or cracks in interconnects of integrated circuits (IC) will evolve dramatically under different mass flow transport mechanisms driven by a variety of external physical fields, which will lead to the decrease of the reliability of the interconnects and the occurrence of failure in severe cases. Based on the microstructure evolution theory of solid materials, a phase field model under the mechanism of electric field-induced interface migration is constructed in this paper. The compatibility between the phase field model and the sharp interface model is proved by the asymptotic analysis. The modified theoretical solution of two-dimensional intragranular void in interconnects is derived, and the reliability of the finite element algorithm is verified by checking with the numerical results. Numerical simulation is carried out to discuss the effects of the electric field intensity χ, the initial morphological ratio β0, and the free energy density difference between the vapor-solid phase Δg˜ on the morphological evolution of the void. The results indicate that the external electric field drives the void to drift in the direction of the electric field, which is widely known as electromigration, and the morphology of the void becomes cylindrization gradually under the action of interface energy. With the increase of the external electric field, there are three morphological evolution trends of the void, including growth, equilibrium, and healing. The electric field critical value χcr, representing the equilibrium state of the void, is used to distinguish different evolution trends. The increase of β0 or the decrease of Δg˜ will lead to the acceleration of void drift velocity, the delay of cylindrization time, and the decrease of critical value, which aggravates the reliability problem of interconnects. Therefore, we should focus on the control of parameters such as χ, β0, and Δg˜, so that the current density of the interconnects is under the condition of χ<χcr. It can cause the intragranular void to shrink and even heal, effectively improving the reliability of IC and prolonging its service life.