Equilibrium current density balancing two atomic flows in coupled problems of electromigration and thermomigration in unpassivated gold film
Equilibrium current density balancing two atomic flows in coupled problems of electromigration and thermomigration in unpassivated gold film
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DOI：
10.1063/5.0011417
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发表时间：
2020-08
期刊：
影响因子：
1.6
通讯作者：
Y. Kimura;Y. Ju
中科院分区：
文献类型：
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作者：
Y. Kimura;Y. Ju
本工作研究耦合问题的电迁移（EM）和热迁移（TM）诱导的异常原子流通过实验证明EM和TM测试和理论公式描述的原子行为。一个二维的未钝化的Au互连，有一个突出的鼻子区域，原子积累，用于观察小丘形成下的电流应力和加热的基板。小丘的形成位置取决于实验条件，包括电流密度和温度与EM和TM的驱动力。通过实验观察到的小丘形成位置和平衡电流密度的命题之间的耦合EM和TM诱导的驱动力之间的关系进行了澄清。考虑到EM和TM引起的驱动力的大小关系，证明了存在平衡电流密度，低于或高于该平衡电流密度，EM或TM分别占主导地位。提出了理论平衡电流密度的计算公式，用以估计电磁场和电磁铁的平衡状态，并由此推导出电磁场和电磁铁的成丘行为。在较低电流密度和较高温度的情况下，由于电磁感应的前向流动，在前缘形成小丘。相反，在较高的电流密度和较低的温度下，由于TM诱导的回流，在稍微远离鼻端的区域形成小丘。
This work studies the coupled problems of electromigration (EM)- and thermomigration (TM)-induced anomalous atomic flows through experiments for demonstrating EM and TM tests and the theoretical formulation describing the atomic behavior. A two-dimensional unpassivated Au interconnect, having a protrusion nose area where atoms are accumulated, was used for observing hillock formation under current stressing and heating of the substrates. The hillock formation locations depend on the experimental conditions, including current density and temperature involved with the driving forces of EM and TM. The relationship between coupling the EM- and TM-induced driving forces was clarified through the experimental observation of the hillock formation location and the proposition of the equilibrium current density. Considering the magnitude relationship of the EM- and TM-induced driving forces, it was proved that an equilibrium current density, below or above which EM or TM is dominant, respectively, exists. The theoretical equilibrium current density was formulated to estimate the equilibrium state of EM and TM, deducing the behavior of hillock formations by EM and TM. Hillocks form at the nose edge due to EM-induced forward flow in the case of lower current density and higher temperature. Conversely, hillocks form at an area slightly away from the nose end due to TM-induced backward flow in the case of higher current density and lower temperature.