中文摘要：

铜互连导线导电后会产生由热扩散主导的电迁移现象,而根据广泛使用的一维电迁移引起的回流模型和原子通量散度的概念,可得到传统的线性应力演化方程.通过在表面晶体材料的表面自由能中计入应变能密度的影响,推导出适合铜导线的非线性应力演化方程.数值求解有界和半无界边界条件下铜导线中的瞬时应力分布.结果表明当考虑应变能密度影响后,导线中的拉应力演变较线性应力演化方程的解更缓趋于稳态,拉应力数值较线性方程应力解更小,而压应力则恰恰相反.同时还讨论了铜条的临界长度效应.计入应变能的影响后,导线内部的应力呈非对称分布,而这种趋势在导线长度减小时更加明显.文中的研究结果将为集成电路设计和铜互连材料的制备提供技术参考.

英文摘要：

Electromigration dominated by thermal diffusion would happen when electron passes through a copper line. Based on the widely used one-dimension electromigration-induced back flow model and the conception of atomic flux divergence, traditional linear stress evolution equation could be deduced. In this article, the effect of strain energy density was taken into account on the surface free energy of surface crystal structure, and nonlinear stress evolution equation for copper line was deduced. Transient stress distribution was numerically solved under finite and semi-infinite boundary conditions. Numerical results demonstrated that the value of tensile stress was smaller and reached the stationary distribution more slowly compared to the solution of linear equation, while compressive stress turned out just the opposite. Critical length of copper strip was also discussed. The unsymmetrical stress distribution became more visible as line length decreased. The results of this article would provide guidelines for intergrated circuit design and fabrications of copper interconnect.