应力诱发界面迁移下晶内孔洞的演化

THE EVOLUTION OF INTRAGRANULAR VOIDS UNDER INTERFACE MIGRATION INDUCED BY STRESS MIGRATION

随着微电子技术的迅猛发展,集成电路中内连导线的失效问题引起广泛关注.内连导线内部孔洞萌生、长大、漂移和失稳变形成狭长裂纹,从而导致电路的开路失效.这是内连导线失效的常见形式.而界面迁移是导致微结构形态演化的主要机制之一.本文基于界面迁移下微结构演化的经典理论和弱解描述,建立了应力诱发界面迁移下微结构演化的有限单元法,并验证了算法的可靠性.对铜内连导线中晶内孔洞的演化进行了数值模拟,详细分析了应力、线宽及形态比对晶内孔洞演化的影响.研究结果表明,椭圆形晶内孔洞存在生长和收缩两种演化分叉趋势.通过大量数值分析得到了晶内孔洞演化的临界应力?σ_c、临界线宽?h_c和临界形态比β_c.当?σ≥?σ_c,?h≤?h_c或β≥β_c时,晶内孔洞会沿长轴长大;反之,晶内孔洞会收缩甚至愈合.此外,应力?σ越大、线宽?h越小或形态比β越大,晶内孔洞越易发生长大,且孔洞面积增大速度越快;?σ越小、?h越大或β越小,晶内孔洞越易发生收缩,且孔洞面积减小速度越快.

With the rapid development of microelectronics technology, the failure of interconnects in the integrated circuit raises wide attention. The interconnects inevitably exist some drawbacks, such as voids and cracks. If the drawbacks nucleate, grow and change their shape to form crack-like slits oriented perpendicular to an interconnect line, an open circuit could result. This is a common form of interconnects failure. And interface migration is one of the main mechanisms leading to the evolution of microstructure. Based on the classic theory and weak statement of interface migration, a finiteelement method is developed to simulate the evolution of intragranular voids in copper interconnects caused by interface migration induced by stress migration. The validity of the method is confirmed by the agreement of the numerically simulated the undulating surface with that predicted theoretically. Through a large number of numerical simulations, we find that the evolution of the intragranular voids has two trends, namely, void growth and void shrinkage. And the shape of the void is governed by the stress, σ, the linewidth, h, and the initial aspect ratio of the intragranular void, β, and there exist critical values for these parameters（ σc,hc and βc）. When σ≥σc,h≤hc or β≥βc, the intragranular void will grow along the major axis; otherwise, the intragranular void will shrink into a cylinder. The increase of the stress, or the aspect ratio, or the decrease of the linewidth is beneficial to void growth. And the area of void growth will increase faster with bigger σ, smaller h or bigger β. But, the decrease of the stress or the aspect ratio, or increase the linewidth accelerates void shrinkage and the shrinkage area will decrease faster with smaller σ, bigger h or smaller β.