An electro-thermo-mechanical coupling phase-field model of defect evolution induced by electromigration in interconnects

IF 7.1 1区 工程技术 Q1 ENGINEERING, MECHANICAL
Xin-Wei Wu, Mingyang Chen, Liao-Liang Ke
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Abstract

In this paper, the defect evolution caused by electromigration induced surface diffusion in interconnects is investigated using a newly-developed electro-thermo-mechanical coupling phase-field model. The Joule heat and its resulting thermomigration are included into the phase-field model. The governing equation of the phase-field is solved by semi-implicit spectral methods and the accompanied governing equations of applied physics fields are solved by finite volume methods. Comparative investigation into defect evolution with and without the influence of Joule heating is conducted. It is deduced that thermomigration facilitates local elongation of the defect in the “current crowding” region and exerts a substantial influence on the defect morphological evolution. Subsequently, the effect of the inclination angle of the electric field on the void morphology evolution and crack propagation is discussed. We find that the defect achieves the largest characteristic length when the electric field direction is perpendicular to the uniaxial tension direction, implying a higher threat to the circuit safety. This study may help to deepen people's understanding of how the thermal effect functions in electromigration process and sheds light on different modes of defect evolution in interconnects.

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互连器件中电迁移诱发缺陷演变的电-热-机械耦合相场模型
本文采用新开发的电-热-机械耦合相场模型,研究了互连器件中由电迁移引起的表面扩散所导致的缺陷演变。相场模型中包括焦耳热及其产生的热迁移。相场的控制方程采用半隐谱法求解,应用物理场的伴随控制方程采用有限体积法求解。对有焦耳加热影响和无焦耳加热影响的缺陷演变进行了比较研究。结果表明,热迁移促进了 "电流拥挤 "区域内缺陷的局部伸长,并对缺陷的形态演变产生了重大影响。随后,讨论了电场倾角对空隙形态演变和裂纹扩展的影响。我们发现,当电场方向垂直于单轴拉伸方向时,缺陷的特征长度最大,这意味着对电路安全的威胁更大。这项研究有助于加深人们对热效应如何在电迁移过程中发挥作用的理解,并揭示了互连器件中缺陷演化的不同模式。
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来源期刊
International Journal of Mechanical Sciences
International Journal of Mechanical Sciences 工程技术-工程:机械
CiteScore
12.80
自引率
17.80%
发文量
769
审稿时长
19 days
期刊介绍: The International Journal of Mechanical Sciences (IJMS) serves as a global platform for the publication and dissemination of original research that contributes to a deeper scientific understanding of the fundamental disciplines within mechanical, civil, and material engineering. The primary focus of IJMS is to showcase innovative and ground-breaking work that utilizes analytical and computational modeling techniques, such as Finite Element Method (FEM), Boundary Element Method (BEM), and mesh-free methods, among others. These modeling methods are applied to diverse fields including rigid-body mechanics (e.g., dynamics, vibration, stability), structural mechanics, metal forming, advanced materials (e.g., metals, composites, cellular, smart) behavior and applications, impact mechanics, strain localization, and other nonlinear effects (e.g., large deflections, plasticity, fracture). Additionally, IJMS covers the realms of fluid mechanics (both external and internal flows), tribology, thermodynamics, and materials processing. These subjects collectively form the core of the journal's content. In summary, IJMS provides a prestigious platform for researchers to present their original contributions, shedding light on analytical and computational modeling methods in various areas of mechanical engineering, as well as exploring the behavior and application of advanced materials, fluid mechanics, thermodynamics, and materials processing.
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