MODELING OF ELECTROMIGRATION FAILURE PREDICTING FOR FCBGA SOLDER BUMP UNDER MULTI-PHYSICAL FIELD LOADS
ZhangYuanxiang1, LiangLihua2,*,, ZhangJicheng2, ChenJunjun2, ShengYufeng2 1 College of Mechanical Engineering, Quzhou University, Quzhou 324000, Zhejiang, China2 College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310014, China 中图分类号:O346,TN406 文献标识码:A
关键词:电迁移;电-热-结构耦合分析;互连焊点;失效寿命;空洞演化 Abstract With the rapid development of microelectronics packaging technology, more attention has been paid to the electromigration (EM) failure on solder bump. The electric-thermal-structural multi-physical coupled analysis for flip chip ball grid array (FCBGA) packaging is performed in this paper based on FEM and submodeling technique. The simplified method of package model is introduced in detail. The current density distribution, temperature distribution and stress distribution of the key solder bump is investigated. It is found that the current crowding effect is easily generated at the location where electrons enter the bump from Cu metal layer, and the temperature gradient of the whole key solder bump is small. This paper presents the atomic density integral (ADI) method which considers four driving forces for electromigration such as electron wind force, stress gradient, temperature gradient and atomic density gradient. According to ADI method and the failure rule on void formation and diffusion, the electromigration void evolution process of the key solder bump is simulated with different mesh density. In can be found that the ADI method is stable and almost independent on the mesh density. The EM void location and time to failure (TTF) of key solder bump in FCBGA package is also simulated in the real service condition by ADI method. And the effect of solder material and Cu metal layer on EM failure is investigated in detail. We can see that the TTF of lead-free solder (Sn3.5Ag) is about 2.5 times than leaded solder (63Sn37Pb) because the TTF is determined to increase exponentially with the activation energy. And the EM failure is also influenced by the effective charge number. The adjustment of Cu metal layer structure will change the current flow direction and the stress distribution of the solder bump, which will affect the time to failure of solder bump.
Keywords:electromigration;electric-thermal-structural coupled analysis;solder bump;time to failure;void evolution -->0 PDF (24128KB)元数据多维度评价相关文章收藏文章 本文引用格式导出EndNoteRisBibtex收藏本文--> 张元祥, 梁利华, 张继成, 陈俊俊, 盛玉峰. 多物理场下FCBGA焊点电迁移失效预测的数值模拟研究[J]. 力学学报, 2018, 50(3): 487-496 https://doi.org/10.6052/0459-1879-18-077 ZhangYuanxiang, LiangLihua, ZhangJicheng, ChenJunjun, ShengYufeng. MODELING OF ELECTROMIGRATION FAILURE PREDICTING FOR FCBGA SOLDER BUMP UNDER MULTI-PHYSICAL FIELD LOADS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 487-496 https://doi.org/10.6052/0459-1879-18-077
由于传统Sn-Pb焊料中Pb对人体和环境有极大危害,无铅焊料正在逐步取代传统的Sn-Pb焊料. 图10为考虑焊点为无铅焊料Sn3.5Ag时的 电流密度矢量和静水应力分布. 与图5比较可以发现,焊点材料为Sn3.5Ag的电流密度最大值较63Sn37Pb的高,这主要是由于Sn3.5Ag焊料的电阻 率较63Sn37Pb焊料低,导电性能较好导致的. 由于Sn3.5Ag的焊料热传导率较63Sn37Pb的大,热传导速度较快,因此,焊点材料为Sn3.5Ag的温度梯度较小. 从图10(b)可以发现,虽然Sn3.5Ag焊料与包裹它的填充树脂之间的热膨胀系数更接近,降低了材料间的热不匹配 现象,但由于Sn3.5Ag的热膨胀系数变大增大了焊点与铜金属层以及铜引线的热应力,因此Sn3.5Ag焊点的静水应力有所增大. 显示原图|下载原图ZIP|生成PPT 图10无铅焊点的电流密度矢量和静水应力分布 -->Fig. 10Current density and hydrostatical stress distribution of Pb free solder bump -->
通过电迁移失效寿命计算,无铅焊料关键焊点的预测寿命约为有铅焊点的2.5倍,失效寿命提高显著. 这主要是因为焊料Sn3.5Ag相 对63Sn37Pb激活能增加了0.06 eV. 激活能是原子克服势垒发生迁移所需要的最小能量. 激活能越大,发生电迁移所需的能量也就越大,即越难发生电迁移. 之前的研究表明[21,22],电迁移失效寿命对激活能非常敏感,随着激活能的增加,电迁移失效寿命将呈指数级增加. 研究还发现,有效电荷数 对电迁移失效寿命也有一定的影响. 图11为有效电荷数对Sn3.5Ag焊点电迁移失效寿命的影响,可以看出,与激活能对电迁移失效寿命 的影响结果相反,电迁移失效寿命随着有效电荷数绝对值的增大而减小. 利用灵敏度分析发现[21,22],互连焊点的电迁移失效寿命对激活能要比有效电荷数敏感得多. 显示原图|下载原图ZIP|生成PPT 图11有效电荷数对电迁移失效寿命的影响 -->Fig. 11The effect of effective charge number on TTF -->
4.2 铜金属层结构对电迁移失效的影响
铜金属层结构既是焊点的支撑,同时也作为电信号的连接. 由于其层数较多且结构复杂,铜金属层结构的优化设计是高密度封装 技术发展的重要内容. 事实上,改变铜金属层结构可以调整电流的流向进而影响电迁移失效. 以无铅焊点为例,图12为改进后的铜金属层结构及电流流向,与图3比较可以发现,原先结构中关键焊点VSSA直接与L1层相连,而改进 后的结构增加了两个通孔再与L1层相连,因此电流走向与原先存在很大的不同. 图13为改进后铜金属层结构下无铅焊点的电流密度矢量和静水应力分布. 与图10比较可以看出,虽然电流流向发生明显改变,但VSSA焊点的电流密度几乎没什么变化,而焊点的应力却明显增大. 显示原图|下载原图ZIP|生成PPT 图12改进后的铜金属层结构 -->Fig. 12Modified Cu metal layer -->
显示原图|下载原图ZIP|生成PPT 图13改进铜金属层结构后VSSA的电流密度矢量和静水应力分布 -->Fig. 13Current density and hydrostatical stress distribution of VSSA solder bump for modified copper trace structure -->
图14比较了不同铜金属层结构对VSSA焊点 方向应力梯度的影响,可以发现,两种结构焊点左侧均呈现压应力,但改进铜金属层结 构后焊点的最大应力梯度比原始结构大很多. 一般而言,压应力将抑制电迁移失效,拉应力将加剧电迁移失效[4,23]. 因此,改进铜金属层结构后无铅焊点预测寿命约为原先结构的1.5倍,失效寿命提高显著,这为电迁移的防治提供了一种途径,对 高密度电子封装结构的设计具有重要的指导作用. 事实上,应力对电迁移失效的影响非常复杂, 由应力梯度诱致的正则化迁移通量计算公式为 ${\pmb q}_{\rm S} = - \dfrac{cD}{k_{\rm B} T}\varOmega \nabla \sigma _{\rm H} (10)$ 因此,由应力梯度引起的原子通量散度为 $ {\rm div}\left( {{\pmb q}_{\rm S} } \right) = - \dfrac{\varOmega D}{k_{\rm B} T} \Bigg\{ c \Bigg[ \left( {\dfrac{E_{\rm a} }{k_{\rm B} T^2} -\dfrac{1}{T}} \right)\nabla \sigma _{\rm H} \cdot \nabla T + \\ \nabla ^2\sigma _{\rm H} \Bigg] + \nabla\sigma _{\rm H} \cdot \nabla c \Bigg \} (11)$ 显示原图|下载原图ZIP|生成PPT 图14铜金属层结构对VSSA焊点方向应力梯度的影响 -->Fig. 14Effect of Cu metal layer on stress gradient along direction for VSSA solder bump -->
本文对真实服役工况下的某型号FCBGA封装结构进行了热-电-结构多物理场仿真模拟,并基于原子 密度积分法对关键焊点进行了电迁移失效预测,研究表明: (1)原子密度积分算法稳定,不依懒于网格密度,可实现电迁移动态演化模拟并获得失效寿命,能够比较准确地预测真实服役工 况下焊点电迁移空洞的形成位置. (2)激活能对电迁移失效寿命影响非常大,由于无铅焊点的激活能比有铅焊点高,无铅焊点的电迁移失效寿命显著提高. 电迁移 失效寿命随着有效电荷数绝对值的增大而减小. (3)铜金属层结构的改变会影响电流的流向,虽然对电流密度几乎没有影响,但由于提高了焊点的压应力从而增加电迁移失效寿 命. 但是,压应力并非总是抑制电迁移现象,还和应力梯度相关,因此需要结合应力梯度综合评估. The authors have declared that no competing interests exist.
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