应力诱发多种机制下沿晶微裂纹的演化

Evolution of Intergranular Microcracks Under Multiple Mechanisms Induced by Stress Migration

基于表面扩散和蒸发-凝结两种机制的经典理论,建立有限元法,对由应力诱发的两种机制共同作用下金属内连导线中沿晶微裂纹的演化进行数值模拟。采用机制比K衡量两种机制竞争的强弱,当K1时,可将模型视作仅受表面扩散机制的影响。结果表明:随着K的增大,微裂纹的演化呈现三个阶段,即表面扩散占据优势、两种机制竞争激烈和蒸发-凝结机制占据优势;微裂纹分节时面积整体呈增大趋势,增幅在两种机制竞争激烈时有所放缓;分节时间整体呈减小趋势,随着机制比增大,降幅有所减小;临界形态比则先增大后减小。

Based on the classical theory of two mechanisms including surface diffusion and evaporationcondensation,a finite element program was developed to simulate the evolution of intergranular microcracks in metal interconnects due to the two mechanisms induced by stress migration. The ratio K was used to evaluate the competitive strength of the two mechanisms. When K is much smaller than 1, the surface diffusion is the only affecting factor for the model. The results show that,with the increase of K,the evolution of intergranular microcracks can be divided into three stages,i. e., the surface-diffusiondominated stage, the competition stage and the evaporation-condensation-dominated stage. When the microcrack splits, the area tends to increase while the growth slows down in the middle stage. The splitting time tends to decrease and the decline reduces along with the increase of K. We also find out that the critical value of aspect ratio increases first and then decreases.