多物理场下金属微互连结构的电迁移失效及数值模拟研究
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摘要
随着电子产品不断向微型化和高性能化发展,导致金属微互连结构的电流密度急剧增加,极易引起电迁移诱致失效的可靠性问题。本文针对金属微互连结构的电迁移失效问题,提出考虑“电子风力”、温度梯度、应力梯度和原子浓度梯度共同作用下的多物理场耦合计算模型,并结合电迁移试验,揭示微互连结构在多场载荷交互作用下的迁移特性和失效特征,为金属微互连结构的设计和可靠性评价提供必要的理论和数值分析基础。
本文首先基于电迁移的基本理论,分析引起电迁移失效的驱动机制;对基于互连引线电迁移失效提出的传统原子通量散度有限元法进行改进,并分析和讨论该方法的适用性及存在的问题。
其次,综合考虑“电子风力”、温度梯度、应力梯度和原子浓度梯度等驱动机制,通过加权余量法对电迁移演化方程进行求解,导出原子浓度重分布迭代方程;通过ANSYS电-热-结构耦合分析获得模型的电流密度分布、温度分布和应力分布,基于FORTRAN编写的原子浓度重分布算法获得不同时刻的原子浓度,依据空洞/小丘形成和扩展失效准则电迁移动态空洞演化进行模拟并获得失效寿命。将该算法分别应用于SWEAT结构和CSP结构,并将模拟结果与试验结果进行比较,验证了算法的可靠性和精度;研究原子浓度梯度对电迁移失效的影响,发现其对电迁移起抑制作用,不考虑原子浓度梯度项将会低估电迁移的失效寿命;建立电迁移灵敏度分析方程及其相应的数值算法,考虑设计变量为激活能、初始自扩散系数和材料力学性能参数等对互连焊球结构进行电迁移灵敏度分析,结果表明,互连焊球的电迁移对激活能非常敏感,材料力学性能参数对电迁移影响最小。
进一步,分别对0.18μm功率器件工艺的Al互连直线结构和Al互连通孔结构在不同温度和不同电流条件下进行标准晶圆级电迁移加速试验和封装级电迁移试验,获得电迁移失效寿命;并通过扫描电镜观察其电迁移失效后的微观形貌,分析其失效机理;基于提出的原子浓度积分算法分别对试验结构进行数值模拟和寿命预测,并将数值结果与试验结果进行比较。结果表明:原子浓度积分算法可以准确预测出空洞失效的位置,并预测出合理的失效时间;通过电迁移试验和数值模拟均证实化学机械抛光技术和扩散阻挡层厚度对Al互连直线结构的电迁移失效寿命有重要影响。
As the electronic products continue to push for miniaturization and high performance, the current densities in IC metal interconnects increase dramatically, which may cause electromigration (EM) failure. This thesis studies the electromigration failure of metal micro-interconnects, and presents a coupled multi-physics model for simulating such a failure. The present model considers four driving forces including the electron wind force, stress gradient, temperature gradient, as well as atomic concentration gradient induced forces. The coupled multi-physics modeling is combined with electromigration test to investigate the electromigration induced failure mechanisms of metal interconnects, which will provide us a theoretical and numerical analysis foundation for guiding the design and reliability evaluation of metal micro-interconnects.
Firstly, according to the basic EM theory, the driving mechanisms of EM are summarized. The improved Atomic Flux Divergence (AFD) method is introduced and the existed problems of AFD method are discussed.
Secondly, the atomic concentration redistribution equation is derived from EM evolution equation by a weighted residual method with considering a variety of EM driving mechanisms which includes the electron wind force, stress gradient, temperature gradient and atomic concentration gradient. The electric-thermal-structural coupled analysis based on ANSYS multi-physical simulation platform is performed to obtain the current density, temperature and stress distribution of the studied model. An EM atomic concentration redistribution algorithm is developed using FORTRAN code to get atomic concentration distribution of different time. The dynamic simulation of EM void evolution is performed to get TTF (Time to Failure) based on the criterion of void/hillock incubation and propagation. The simulated results based on SWEAT and CSP structures show good agreement with experimental observations, which verify the correction of the present developed algorithm. The impact of atomic concentration gradient on EM is studied and it shows that the atomic concentration will be retarded by considering the atomic concentration gradient item in the time-dependent EM evolution equation. Without consideration of the atomic concentration gradient, the TTF will be underestimated. The sensitivity analysis equations with considering EM parameters and mechanical properties of material as design variables are derived for EM sensitivity analysis. The results show that the EM is very sensitive to the activation energy of material and the mechanical properties of material have the minimal impact on EM.
The standard wafer-level electromigration accelerated test and package level electromigration test are performed for metal line and via interconnect structures by using 0.18μm power technology respectively. The TTFs are obtained from the tests, at the same time, the microstructure evolution and damage mechanism are examined by scanning electron microscope (SEM) observation. The above mentioned algorithm is used to simulate the failure of these test structures and the results show that the predicted TTFs and EM failure location are well agreement with the test results. Both EM test and modeling results disclose the significant influence of chemical-mechanical planarization and barrier metal thickness on the EM failure life.
本文首先基于电迁移的基本理论,分析引起电迁移失效的驱动机制;对基于互连引线电迁移失效提出的传统原子通量散度有限元法进行改进,并分析和讨论该方法的适用性及存在的问题。
其次,综合考虑“电子风力”、温度梯度、应力梯度和原子浓度梯度等驱动机制,通过加权余量法对电迁移演化方程进行求解,导出原子浓度重分布迭代方程;通过ANSYS电-热-结构耦合分析获得模型的电流密度分布、温度分布和应力分布,基于FORTRAN编写的原子浓度重分布算法获得不同时刻的原子浓度,依据空洞/小丘形成和扩展失效准则电迁移动态空洞演化进行模拟并获得失效寿命。将该算法分别应用于SWEAT结构和CSP结构,并将模拟结果与试验结果进行比较,验证了算法的可靠性和精度;研究原子浓度梯度对电迁移失效的影响,发现其对电迁移起抑制作用,不考虑原子浓度梯度项将会低估电迁移的失效寿命;建立电迁移灵敏度分析方程及其相应的数值算法,考虑设计变量为激活能、初始自扩散系数和材料力学性能参数等对互连焊球结构进行电迁移灵敏度分析,结果表明,互连焊球的电迁移对激活能非常敏感,材料力学性能参数对电迁移影响最小。
进一步,分别对0.18μm功率器件工艺的Al互连直线结构和Al互连通孔结构在不同温度和不同电流条件下进行标准晶圆级电迁移加速试验和封装级电迁移试验,获得电迁移失效寿命;并通过扫描电镜观察其电迁移失效后的微观形貌,分析其失效机理;基于提出的原子浓度积分算法分别对试验结构进行数值模拟和寿命预测,并将数值结果与试验结果进行比较。结果表明:原子浓度积分算法可以准确预测出空洞失效的位置,并预测出合理的失效时间;通过电迁移试验和数值模拟均证实化学机械抛光技术和扩散阻挡层厚度对Al互连直线结构的电迁移失效寿命有重要影响。
As the electronic products continue to push for miniaturization and high performance, the current densities in IC metal interconnects increase dramatically, which may cause electromigration (EM) failure. This thesis studies the electromigration failure of metal micro-interconnects, and presents a coupled multi-physics model for simulating such a failure. The present model considers four driving forces including the electron wind force, stress gradient, temperature gradient, as well as atomic concentration gradient induced forces. The coupled multi-physics modeling is combined with electromigration test to investigate the electromigration induced failure mechanisms of metal interconnects, which will provide us a theoretical and numerical analysis foundation for guiding the design and reliability evaluation of metal micro-interconnects.
Firstly, according to the basic EM theory, the driving mechanisms of EM are summarized. The improved Atomic Flux Divergence (AFD) method is introduced and the existed problems of AFD method are discussed.
Secondly, the atomic concentration redistribution equation is derived from EM evolution equation by a weighted residual method with considering a variety of EM driving mechanisms which includes the electron wind force, stress gradient, temperature gradient and atomic concentration gradient. The electric-thermal-structural coupled analysis based on ANSYS multi-physical simulation platform is performed to obtain the current density, temperature and stress distribution of the studied model. An EM atomic concentration redistribution algorithm is developed using FORTRAN code to get atomic concentration distribution of different time. The dynamic simulation of EM void evolution is performed to get TTF (Time to Failure) based on the criterion of void/hillock incubation and propagation. The simulated results based on SWEAT and CSP structures show good agreement with experimental observations, which verify the correction of the present developed algorithm. The impact of atomic concentration gradient on EM is studied and it shows that the atomic concentration will be retarded by considering the atomic concentration gradient item in the time-dependent EM evolution equation. Without consideration of the atomic concentration gradient, the TTF will be underestimated. The sensitivity analysis equations with considering EM parameters and mechanical properties of material as design variables are derived for EM sensitivity analysis. The results show that the EM is very sensitive to the activation energy of material and the mechanical properties of material have the minimal impact on EM.
The standard wafer-level electromigration accelerated test and package level electromigration test are performed for metal line and via interconnect structures by using 0.18μm power technology respectively. The TTFs are obtained from the tests, at the same time, the microstructure evolution and damage mechanism are examined by scanning electron microscope (SEM) observation. The above mentioned algorithm is used to simulate the failure of these test structures and the results show that the predicted TTFs and EM failure location are well agreement with the test results. Both EM test and modeling results disclose the significant influence of chemical-mechanical planarization and barrier metal thickness on the EM failure life.
引文
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