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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.
The copper-based conductor leads to electromigration, which is dominated by thermal diffusion. According to the widely used one-dimensional electromigration-induced reflow model and the concept of atomic flux divergence, a conventional linear stress evolution equation can be obtained. The surface free energy of the surface crystal material is included in the influence of strain energy density, and the nonlinear stress evolution equation suitable for copper conductor is deduced. The transient stress distribution in copper conductor is solved numerically for bounded and semi-unbounded boundary conditions. After the influence of the strain energy density, the tensile stress in the wire evolves more slowly than the linear stress evolution equation to a steady state, the tensile stress value is smaller than that of the linear equation, and the compressive stress is just the opposite. Of the critical length effect.Considering the influence of strain energy, the internal stress of the wire is asymmetric distribution, and this trend is more obvious when the wire length is reduced.The results of the paper will be integrated circuit design and copper interconnect material preparation Provide technical reference.