Prediction of Electromigration Critical Current Density in Passivated Arbitrary-Configuration Interconnect
Prediction of Electromigration Critical Current Density in Passivated Arbitrary-Configuration Interconnect
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DOI：
10.1115/1.4042980
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发表时间：
2019-06
影响因子：
1.6
通讯作者：
Y. Kimura;M. Saka
中科院分区：
文献类型：
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作者：
Y. Kimura;M. Saka
为了将互连中的电迁移（EM）损伤降至最低，人们对临界电流密度进行了研究，临界电流密度是互连中抗电迁移能力的一个标准，当电流密度高于此值时，电迁移损伤就会产生。一般来说，尽管临界电流密度对结构特性很敏感，但对临界电流密度的评估仅限于被称为布莱希（Blech）试样的直连线。这项工作提出了一种利用原子密度和电势之间的类比来预测任意结构互连的临界电流密度的方法。在将直连线和桶状连线作为现代倒装芯片技术中典型的焊料凸点的模型中，通过所提出的公式计算电势，并基于有限元分析（FEA）进行模拟，从而预测临界电流密度。通过实验得到的直连线的临界电流密度可用于数值计算临界电势，该临界电势与互连结构无关。临界电势对应于临界原子密度，在该密度以下原子会发生聚集。计算出的临界电势确定了包括电流拥挤效应在内的任意结构互连的临界电流密度。这一发现可以预测实际任意结构模型的临界电流密度，并为球栅阵列和C4倒装芯片焊料凸点等封装设计的应用提供见解。
A critical current density, a criterion of electromigration (EM) resistance in interconnects, above which EM damages initiate has been studied to minimize EM damages of interconnects. In general, the assessment of a critical current density is confined to straight interconnect called as Blech specimen, although the critical current density is sensitive to structural characteristic. This work proposes a procedure of predicting a critical current density for any arbitrary-configuration interconnect by using the analogy between atomic density and electrical potential. In the models of straight and barrel interconnects as the typical solder bumps in modern flip-chip technology, the critical current density is predicted through calculating electrical potential by proposed formulation and simulation based on the finite element analysis (FEA). The critical current density for straight interconnect obtained by experiment leads to numerically calculate the critical electrical potential, which is independent of interconnect configuration. The critical potential corresponds to the critical atomic density, below which the accumulation of atoms allows. The calculated critical electrical potential determines a critical current density for arbitrary-configuration interconnect including current crowding effect. This finding can predict a critical current density for actual arbitrary-configuration model and provide an insight for the applying to the packaging design such as ball grid array and C4 flip-chip solder bumps.