内连导线线宽对沿晶微裂纹演化的影响

基于应力诱发表面扩散的经典理论,用有限元法模拟了线宽对铜内连导线中沿晶微裂纹演化的影响。数值模拟结果表明:随着线宽的减小,椭圆形沿晶微裂纹存在分节与不分节两种演化分叉趋势,且演化分节存在临界线宽珔hc;当珔h≤珔hc时,沿晶微裂纹分节成3个新的沿晶微裂纹;当珔h珔hc时,沿晶微裂纹圆柱化。沿晶微裂纹分节时间^tf随线宽的减小而减小,即减小线宽会加速微裂纹分节。临界外载珋σc与临界形态比βc随线宽的减小而减小,即减小线宽有利于沿晶微裂纹分节。临界外载和临界形态比随晶界能与表面能比值的增大而减小,且沿晶微裂纹比晶内微裂纹更易发生分节。

Effect of Line Width on Intergranular Microcrack Evolution in Interconnects

Based on the classical theory of surface diffusion induced by stress migration, a finite element program is developed for simulating the evolution of intergranular microcracks in copper interconnects. The numerical results show that there exists a critical value of the line width under the biaxial tensile stress state. When the line width is equal or less than the critical value, the intergranular microcrack will grow and split into three small microcracks along the grain boundary. When the line width is greater than the critical value, the microcrack will directly evolve into a cylinder. The splitting time of the intergranular microcrack reduces with the line width decreasing, which means that the decrease of the line width will accelerate the splitting process. Both the critical value of the stress and that of the aspect ratio decrease when the line width decreases, that is, the decrease of the line width is beneficial to the microcrack splitting. The critical values of the stress and the aspect ratio decrease when the ratio of the grain-boundary energy to the surface energy increases. And it is easier for the intergranular microcrack to split than the intragranular microcrack.