This paper presented a comprehensive experimental and simulation study for thermomigration (TM) accompanying electromigration (EM) at elevated current densities. Both Blech and standard wafer-level electromigration acceleration test (SWEAT)-like test structures, with aluminum (Al) as a carrier, were used for testing and analysis. In Part I of our study (Cui et al., 2023a), the experimental and numerical results with the current density of 1 MA/cm² were presented. We observed that Al stripes with a SWEAT structure did not show damage in the entire length, while Blech structures showed void and hillock formations only at the cathode and anode, respectively. The temperature gradient owing to Joule heating was neglected in our previous simulations, and the predicted results agreed well with the experimental observations. However, we have not theoretically verified the effect of the temperature gradient. In this paper, we first reported the new experimental data under the elevated current densities of 3 and 5 MA/cm². In both Blech and SWEAT structures, the spreading of voids in the middle region of conductors was observed. Moreover, in Blech structures, voiding in the middle region occurred after a period of time when voids/hillocks were formed at the cathode and anode, while the SWEAT structures did not show damage at the two ends. Next, based on the coupled 3D theory (Cui et al., 2023a), new analytical one-dimensional (1D) solutions were derived for the Blech and SWEAT structures in the un-passivated configuration considering TM. We found that TM played a significant role in the EM development in the middle of conductors under the elevated current density. The numerical results were in excellent agreement with the experimental data with the consideration of TM. We further established new EM failure's threshold criteria for the SWEAT structures in the form of the product of current density and square of conductor length. This is a major departure from the original Blech's theory in which only mechanical stress gradient was considered. We also studied the acceleration factor of the current density exponent and presented an insight into failure mechanisms associated with TM.

本文介绍了在高电流密度下伴随电迁移 (EM) 的热迁移 (TM) 的综合实验和模拟研究。以铝 (Al) 为载体的 Blech 和标准晶圆级电迁移加速测试 (SWEAT) 类测试结构均用于测试和分析。^{在我们研究的第一部分 (Cui et al., 2023a)，电流密度为 1 MA/cm 2}的实验和数值结果被提出。我们观察到具有 SWEAT 结构的 Al 条纹在整个长度上没有显示出损坏，而 Blech 结构分别仅在阴极和阳极处显示出空隙和小丘形成。在我们之前的模拟中忽略了焦耳加热引起的温度梯度，预测结果与实验观察结果吻合良好。但是，我们还没有从理论上验证温度梯度的影响。在本文中，我们首先报告了在 3 和 5 MA/cm ^{2的高电流密度下的新实验数据}. 在 Blech 和 SWEAT 结构中，观察到导体中间区域的空隙扩散。此外，在 Blech 结构中，中间区域的空洞发生在阴极和阳极处形成空隙/小丘一段时间后，而 SWEAT 结构在两端没有显示出损坏。接下来，基于耦合 3D 理论（Cui 等人，2023a），针对未钝化配置中考虑 TM 的 Blech 和 SWEAT 结构推导出了新的解析一维 (1D) 解。我们发现在高电流密度下，TM 在导体中间的 EM 发展中发挥了重要作用。在考虑 TM 的情况下，数值结果与实验数据非常吻合。我们进一步建立了新的 EM 失败' SWEAT 结构的阈值标准，形式为电流密度和导体长度平方的乘积。这与仅考虑机械应力梯度的原始 Blech 理论大相径庭。我们还研究了电流密度指数的加速因子，并深入了解与 TM 相关的故障机制。