晶体相场法研究金属微互连结构形变过程对界面Kirkendall空洞生长的抑制机理

doi:10.19596/j.cnki.1001-246x.8618

计算物理 ›› 2023, Vol. 40 ›› Issue (4): 416-424.DOI: 10.19596/j.cnki.1001-246x.8618

晶体相场法研究金属微互连结构形变过程对界面Kirkendall空洞生长的抑制机理

马文婧¹^,²^,³(), 王进¹^,²^,³^,*(), 郭慧¹^,²^,³, 吕美妮¹^,²^,³, 张宏泽¹^,²^,³, 李冬德¹^,²^,³

1. 广西机器视觉与智能控制重点实验室, 广西梧州 543002
2. 广西高校图像处理与智能信息系统重点实验室, 广西梧州 543002
3. 梧州学院电子与信息工程学院, 广西梧州 543002

收稿日期:2022-08-16 出版日期:2023-07-25 发布日期:2023-10-13
通讯作者: 王进
作者简介:
马文婧(1984-), 女, 讲师, 博士, 研究方向为金属和陶瓷材料微观组织计算机模拟, E-mail: mercury1204@126.com
基金资助:
国家自然科学基金(62162054); 中央引导地方科技发展资金项目; 广西科技基地和人才专项(桂科AD20238053); 广西自然科学基金(2021JJB170060); 广西高校中青年教师科研基础能力提升项目(2019KY0691); 广西高校中青年教师科研基础能力提升项目(2020KY17010); 梧州学院重大项目(2017A004); 梧州学院重大项目(2017A005)

Phase Field Crystal Method Study on Inhibitory Mechanism of the Growth of Kirkendall Voids During Deformation Process at the Interface of Metal Micro Interconnect Structures

Wenjing MA¹^,²^,³(), Jin WANG¹^,²^,³^,*(), Hui GUO¹^,²^,³, Meini LYU¹^,²^,³, Hongze ZHANG¹^,²^,³, Dongde LI¹^,²^,³

1. Guangxi Key Laboratory of Machine Vision and Intelligent Control, Wuzhou, Guangxi 543002, China
2. Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System, Wuzhou, Guangxi 543002, China
3. School of Electronic and Information Engineering, University, Wuzhou, Guangxi 543002, China

Received:2022-08-16 Online:2023-07-25 Published:2023-10-13
Contact: Jin WANG

摘要/Abstract

摘要：

应用晶体相场方法模拟研究金属微互连结构形变过程对界面Kirkendall空洞生长的抑制作用。主要研究在金属微互连结构对称界面不同取向差的情况下, 双向恒定速率应变对Kirkendall空洞微观组织及生长动力学的影响。研究结果表明: 金属微互连结构界面在双向恒定速率应变作用下有非晶化趋势, 界面原子错配度和缺陷密度增大, 进而抑制Kirkendall空洞的生长; 双向恒定速率应变不改变Kirkendall空洞在对称界面取向差情况下的形核方式, Kirkendall空洞的形核方式为体系形核点饱和后的晶界形核; Kirkendall空洞在金属微互连结构小角度对称和大角度对称界面皆为均匀分布; 随着演化时间的延长Kirkendall空洞平均尺寸和面积均逐渐增大; 随着小角度对称界面取向差的增大Kirkendall空洞平均尺寸、面积和生长指数均逐渐降低; 随着大角度对称界面取向差的增加, Kirkendall空洞平均尺寸和面积逐渐减小, 而生长指数逐渐增大。双向恒定速率应变可有效减小Kirkendall空洞生长尺寸和面积, 抑制Kirkendall空洞的生长, 进而提升金属微互连结构的可靠性。

关键词: Kirkendall空洞, 金属微互连, 抑制生长, 晶体相场法, 生长动力学, 形变

Abstract:

In this paper, the phase field crystal method is employed to simulate and study the inhibition effect of the growth of Kirkendall voids at the interface of metal micro interconnection structures during the deformation process. The effect of bidirectional constant rate of strain on the microstructure evolution and growth kinetics of Kirkendall voids with different orientation differences at the symmetric interface of metal micro interconnects is mainly studied. The research results show that the interface of the metal micro interconnect structure has a tendency of amorphization under the action of bidirectional constant rate of strain, and the atomic mismatch and defect density of the interface increase, thereby inhibiting the growth of Kirkendall voids. The bidirectional constant rate of strain does not change the nucleation mode of Kirkendall voids in the case of symmetric interface orientation, and the nucleation modes of Kirkendall voids are all grain boundary nucleation after the system nucleation point is saturated. The Kirkendall voids are uniformly distributed at the small-angle symmetrical and large-angle symmetrical interfaces of the metal micro interconnect structure. The average size and area of Kirkendall voids increase with evolution time. The average size, area and growth index of Kirkendall voids gradually decrease with the increase of the misorientation of the small-angle symmetric interface. The average size and area of Kirkendall voids gradually decrease with the increase of the misorientation of the large-angle symmetric interface, while the growth index increases. The bidirectional constant rate of strain can effectively reduce the growth size and area of Kirkendall voids, inhibit the growth of Kirkendall voids, and improve the reliability of metal micro interconnect structures.

Key words: Kirkendall voids, micro-scale metal interconnect, inhibitory mechanism, phase field crystal method, growth kinetics, deformation

马文婧, 王进, 郭慧, 吕美妮, 张宏泽, 李冬德. 晶体相场法研究金属微互连结构形变过程对界面Kirkendall空洞生长的抑制机理[J]. 计算物理, 2023, 40(4): 416-424.

Wenjing MA, Jin WANG, Hui GUO, Meini LYU, Hongze ZHANG, Dongde LI. Phase Field Crystal Method Study on Inhibitory Mechanism of the Growth of Kirkendall Voids During Deformation Process at the Interface of Metal Micro Interconnect Structures[J]. Chinese Journal of Computational Physics, 2023, 40(4): 416-424.

图/表 10

图1 初始模拟区域

Fig.1 Initial simulation area

图2 HRTEM观察的晶界微观结构[21]

Fig.2 Grain boundary microstructure observed by HRTEM[21]

图3 对称界面取向差示意图(a) 对称界面；(b) 界面取向角

Fig.3 Schematic diagram of symmetry interface misorientations (a) symmetry interface; (b) interface orientation angle

图4 等体积形变

Fig.4 Isovolumetric deformation

图5 Kirkendall空洞微观组织结构图(a)~(c) θ=4.8°; (d)~(f) θ=8.2°; (g)~(i) θ=9.4°; (a)、(d)、(g) t=1.0×105; (b)、(e)、(h) t=3.6×105; (c)、(f)、(i) t=8.6×105

Fig.5 Microstructure and morphology of Kirkendall voids (a)~(c) θ=4.8°; (d)~(f) θ=8.2°; (g)~(i) θ=9.4°; (a), (d), (g) t=1.0×105; (b), (e), (h) t=3.6×105; (c), (f), (i) t=8.6×105

图6 Kirkendall空洞生长行为随时间的变化(a) 平均尺寸随时间的变化；(b)空洞面积随时间的变化

Fig.6 Growth behavior of Kirkendall voids vs time (a) average size of Kirkendall voids vs time; (b) area of Kirkendall voids vs time

表1 Kirkendall空洞生长指数

Table 1 The growth exponent of Kirkendall voids

	Y=K_tt^n_y
	K_t	n_y
4.8°	2.522 77	0.128 3
8.2°	2.894 74	0.126 57
9.4°	2.341 47	0.112 9

图7 Kirkendall空洞微观组织形貌图(a)~(c) θ=16.6°; (d)~(f) θ=18.4°; (g)~(i) θ=22.8°; (a), (d), (g) t=1.0×105; (b), (e), (h) t=3.6×105; (c), (f), (i) t=8.6×105

Fig.7 Microstructure and morphology of Kirkendall voids (a)~(c) θ=16.6°; (d)~(f) θ=18.4°; (g)~(i) θ=22.8°; (a), (d), (g) t=1.0×105; (b), (e), (h) t=3.6×105; (c), (f), (i) t=8.6×105

图8 Kirkendall空洞生长行为随时间的变化(a) 平均尺寸随时间的变化；(b)空洞面积随时间的变化

Fig.8 Growth behavior of Kirkendall voids vs time (a) average size of Kirkendall voids vs time; (b) area of Kirkendall voids vs time

表2 Kirkendall空洞生长指数

Table 2 The growth exponent of Kirkendall voids

	Y=K_tt^n_y
	K_t	n_y
16.6°	3.735 38	0.072 16
18.4°	3.347 04	0.087 37
22.8°	2.978 63	0.106 37

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晶体相场法研究金属微互连结构形变过程对界面Kirkendall空洞生长的抑制机理

Phase Field Crystal Method Study on Inhibitory Mechanism of the Growth of Kirkendall Voids During Deformation Process at the Interface of Metal Micro Interconnect Structures

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