电迁移诱发表面扩散下沿晶微裂纹的演化

随着微电子技术的快速发展，铜内连导线的失效问题日益受到关注。基于表面扩散和蒸发—凝结的经典理论及其弱解描述，建立描述电迁移下微结构演化的有限单元法，对铜材料内沿晶微裂纹在电迁移诱发表面扩散下的不稳定外形演化进行了有限元模拟。详细讨论了电场、形态比和晶界能与表面能比值对沿晶微裂纹演化的影响。结果表明：沿晶微裂纹在沿着晶界和电场方向发生漂移的过程中存在分节与不分节两种形貌演化分叉趋势，且裂腔分节存在临界形态比 和临界电场值 。当 或 时，沿晶微裂纹会沿着晶界分节成一大一小两个小沿晶微裂纹。沿晶微裂纹分节时间随形态比和电场的增大而减小，即形态比和电场的增大都使沿晶微裂纹加速分节。而临界电场值 随着形态比的增大而减小；临界形态比 随电场的增大而减小。也就是说形态比和电场的增大还将有助于沿晶微裂纹分节。此外，沿晶微裂纹分节时间要比晶内微裂纹的小，即晶界的存在有助于加速裂腔分节。

The EvolutionofIntergranular Microcracks due to Surface Diffusion Induced by Electromigration

With the rapid development of microelectronics technology, more attention has been paid to the major failure mode of Copper interconnects. Based on the classical theory of surface diffusion and evaporation-condensation and its weak statement, a finite-element method is developed for simulating the shape instability of intergranular microcracks in Copper caused by the electromigration-induced surface diffusion. A detailed discussion has been given about the impacts of the electric field , the aspect ratio , and the ratio of grain boundary energy to surface energy on the shape instability of intergranular microcracks. The results show that the evolution of the intergranular microcracks has two trends when they migrate along the electric field direction and the grain boundary: being a cylinder or splitting into two small intergranular microcracks (one is relatively larger than the other). There exist critical values of the aspect ratio and the electric field . When or , the intergranular microcrack will split into two smaller intergranular microcracks. The splitting time of the intergranular microcrack decreases with an increase in the electric field or the aspect ratio, indicating that the increase of electric field or aspect ratio accelerates microcrack splitting. The critical electric field decreases as the aspect ratio increases, and the critical aspect ratio decreases as the electric field increases. In other words, the increase of the electric field or the aspect ratio is beneficial to microcrack splitting. In addition, the splitting time of the intergranular microcracks is less than that of the intragranular microcracks. The existence of grain boundary accelerates microcrack splitting.