Based on the weak formulation for combined surface diffusion and evaporation-condensation,a governing equation of the finite element is derived for simulating the evolution of intergranular microcracks in copper inter...Based on the weak formulation for combined surface diffusion and evaporation-condensation,a governing equation of the finite element is derived for simulating the evolution of intergranular microcracks in copper interconnects induced simultaneously by stressmigration,electromigration and thermomigration.Unlike previously published works,the effect of thermomigration is considered.The results show that thermomigration can contribute to the microcrack splitting and accelerate the drifting process along the direction of the electric field.The evolution of the intergranular microcracks depends on the mechanical stress field,the temperature gradient field,the electric field,the initial aspect ratio and the linewidth.And there exists a critical electric fieldχ_c,a critical stress field■,a critical aspect ratioβ_c and a critical linewidth■.When■or■,the intergranular microcrack will split into two or three small intergranular microcracks.Otherwise,the microcrack will evolve into a stable shape as it migrates along the interconnect line.The critical stress field,the critical electric field and the critical aspect ratio decrease with a decrease in the linewidth,and the critical linewidth increases with an increase in the electric field and the aspect ratio.The increase of the stress field,the electric field or the aspect ratio and the decrease of the linewidth are not only beneficial for the intergranular microcrack to split but also accelerate the microcrack splitting process.展开更多
基金supported by the Natural Science Foundation of Jiangsu Province of China (No.BK20141407)the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Based on the weak formulation for combined surface diffusion and evaporation-condensation,a governing equation of the finite element is derived for simulating the evolution of intergranular microcracks in copper interconnects induced simultaneously by stressmigration,electromigration and thermomigration.Unlike previously published works,the effect of thermomigration is considered.The results show that thermomigration can contribute to the microcrack splitting and accelerate the drifting process along the direction of the electric field.The evolution of the intergranular microcracks depends on the mechanical stress field,the temperature gradient field,the electric field,the initial aspect ratio and the linewidth.And there exists a critical electric fieldχ_c,a critical stress field■,a critical aspect ratioβ_c and a critical linewidth■.When■or■,the intergranular microcrack will split into two or three small intergranular microcracks.Otherwise,the microcrack will evolve into a stable shape as it migrates along the interconnect line.The critical stress field,the critical electric field and the critical aspect ratio decrease with a decrease in the linewidth,and the critical linewidth increases with an increase in the electric field and the aspect ratio.The increase of the stress field,the electric field or the aspect ratio and the decrease of the linewidth are not only beneficial for the intergranular microcrack to split but also accelerate the microcrack splitting process.
