井亚彬, 黄佩珍. 弹性模量比对界面迁移下夹杂演化的影响[J]. 工程力学, 2020, 37(7): 8-16. DOI: 10.6052/j.issn.1000-4750.2019.08.0444
引用本文: 井亚彬, 黄佩珍. 弹性模量比对界面迁移下夹杂演化的影响[J]. 工程力学, 2020, 37(7): 8-16. DOI: 10.6052/j.issn.1000-4750.2019.08.0444
JING Ya-bin, HUANG Pei-zhen. THE EFFECT OF ELASTIC MODULUS RATIO ON INCLUSION EVOLUTION BY INTERFACE MIGRATION[J]. Engineering Mechanics, 2020, 37(7): 8-16. DOI: 10.6052/j.issn.1000-4750.2019.08.0444
Citation: JING Ya-bin, HUANG Pei-zhen. THE EFFECT OF ELASTIC MODULUS RATIO ON INCLUSION EVOLUTION BY INTERFACE MIGRATION[J]. Engineering Mechanics, 2020, 37(7): 8-16. DOI: 10.6052/j.issn.1000-4750.2019.08.0444

弹性模量比对界面迁移下夹杂演化的影响

THE EFFECT OF ELASTIC MODULUS RATIO ON INCLUSION EVOLUTION BY INTERFACE MIGRATION

  • 摘要: 集成电路的导线内不可避免存在夹杂等缺陷。在各种内在机制以及外界环境作用下夹杂会出现形态演化从而影响内连导线的各种性能。该文基于界面迁移机制下微结构演化理论,推导了应力诱发固-固界面迁移的单元控制方程,数值模拟了夹杂-基体弹性模量比对夹杂形态演化的影响。结果表明:不同模量比下夹杂的形态演化存在两种分叉趋势,并且存在着临界应力\widetilde \sigma _\rmc、临界形态比\beta _\rmc、临界线宽\widetilde h_\rmc。当\widetilde \sigma > \widetilde \sigma _\rmc\beta > \beta _\rmc\widetilde h < \widetilde h_\rmc 时,夹杂长大;反之收缩。随着模量比的增加,临界应力、临界形态比随之增大,而临界线宽会减小。并且,当夹杂与基体的弹性模量比\alpha > 0.6时,模量比对于临界应力和临界形态比的影响可忽略。

     

    Abstract: Defects such as inclusions are inevitably presented in the wires of integrated circuit. Under the effect of various internal mechanisms and external environment, the morphology evolution of the inclusions will affect the performance of the interconnects. Based on the weak statement of microstructure evolution for the interface migration, the governing equations of stress-induced solid-solid interface migration are derived, and the effects of the Young's modulus ratio of the inclusion and the matrix on the morphology evolution of inclusion are numerically simulated. The results show that: there are two kinds of bifurcation trends in the morphology evolution of the inclusions, and exist the critical stress \widetilde \sigma _\rmc, the critical aspect ratio \beta _\rmc and the critical line width \widetilde h_\rmc. When \widetilde \sigma > \widetilde \sigma _\rmc, \beta > \beta _\rmc or \widetilde h < \widetilde h_\rmc , the inclusion grows. Otherwise, the inclusion will shrink. As the modulus ratio increases, the critical stress or the critical aspect ratio increases, and the critical linewidth decreases. Also, when the Young's modulus ratio of the inclusion to the matrix \alpha > 0.6, the effect of the modulus ratio on the critical stress and the critical aspect ratio can be ignored.

     

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