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在线弹性断裂力学中,根据驱动力与裂纹扩展之间的内在关系可将裂纹划分为张开型裂纹、滑开型裂纹和撕开型裂纹,如图1所示。其中张开型裂纹扩展的特征为:拉应力垂直于裂纹面,裂纹扩展方向和拉应力垂直;滑开型裂纹扩展的特征为:剪应力位于裂纹面内,并与裂纹扩展方向平行;撕开型裂纹扩展的特征为:剪应力位于裂纹面内,并与裂纹扩展方向垂直。在因热失配引起的层状结构局部失效中,不会出现撕开型裂纹扩展模式,因此在文中只考虑张开型和滑开型裂纹扩展模式。
Figure 1. Schematic diagram of three typical crack expanding mode. (a) Mode I crack(opening mode); (b) Mode II crack(sliding mode); (c) Mode III crack(tearing type)
在描述裂纹的萌生与扩展时,以计算精度和成本为判据,通常认为双线性模型在众多本构关系模型中性能最佳,故文中采用由Aifanoh和Crisfield [8]建立的双线性牵引-分离内聚力模型。这里以张开型裂纹扩展为例介绍内聚力模型的参数设置,模型中运用的牵引-分离法则如图2所示:右下角的横坐标代表界面在法向拉应力作用下发生的分离量δ,纵坐标表示界面法向拉应力σ。当界面法向拉应力从0增加到σmax的过程中,界面之间的位移线性增加而不发生分层,法向拉应力一旦越过σmax,开始萌生界面局部分层,局部分层萌生后施加于界面上的法向拉应力则线性降低,当界面法向拉应力从σmax减小到0时,界面完全脱开,界面分层完成,此时对应的界面间距为δn。
在双线性内聚力模型中,张开型模式下的σmax和δn与滑开型模式下的τmax和δt是内聚力模型设置的重要参数。文中着重研究InSb芯片和底充胶(Underfill)之间的界面脱粘开裂过程,故而内聚力模型中参数的设置由界面断裂能决定。Xu等[9]对复合材料结构粘接破坏的统一内聚力模型及其参数识别进行研究,实验测得双线性内聚力模型下界面断裂能为0.873 N/mm。周清春等[10]对衬底界面粘接力学特性进行研究,实验测得胶粘剂与衬底之间I型界面断裂能普遍在0.9 N/mm。Guo等[11]通过实验测得胶粘剂与粘接界面之间I型和II型断裂能分别为0.3 N/mm和0.6 N/mm。Bellali等[12]通过内聚力模型和有限元分析法预测复合材料对铝缺口增强板损伤的补偿特性,测得用胶粘剂AV138粘接界面时的I型和II型断裂能分别为0.2 N/mm和0.38 N/mm。在上述粘接结构脱粘开裂的研究中,I型和II型断裂能值普遍分布在0.1~1 N/mm,故而笔者选取Underfill与InSb芯片脱粘时I型和II型断裂能应介于0.1~1 N/mm之间。在研究胶粘剂与衬底之间的分层实验中,测得的分层位移大多在毫米量级,故此文中选取1 mm作为Underfill与InSb芯片脱粘时的临界位移分离量。
考虑到器件局部分层主要发生在界面处,张开型和滑开型裂纹扩展混合模态比可从纯滑开型(0: 10)演变到纯张开型(10: 0)。当张开型和滑开型混合模态比设置为4: 6时,模拟结果与实测结果高度吻合。此时设置的张开型与滑开型界面断裂能分别为0.292 N/mm和0.441 N/mm,对应的法向粘接力和切向粘接力分别为882.6 kPa和583.5 kPa。笔者注意到Chen等[13]在研究Underfill材料对倒装焊结构可靠性影响时,测得的Underfill与芯片之间的界面粘接强度普遍介于122~851 kPa之间,这间接证实了文中参数选取的合理性。内聚力参数的选取如表1所示。
Mixed-mode
ratios, ωNormal cohesive traction Normal displacement jump Tangential cohesive traction Tangential displacement jump σ0/kPa δI0/mm τ0/kPa δII0/mm 9∶1 116.7 1 1050 1 8∶2 257.2 1 1029 1 7∶3 414 1 975 1 6∶4 583.5 1 882.6 1 5∶5 750 1 750 1 4∶6 882.6 1 583.5 1 3∶7 975 1 414 1 2∶8 1029 1 257.2 1 1∶9 1050 1 116.7 1 Table 1. Parameter setting of cohesive zone modeling under different mixed-mode ratios
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InSb IRFPAs通常由三层材料堆叠而成,采用倒装技术将最上面的InSb光敏元芯片与最下面的Silicon ROIC(Readout Integrated Circuits)通过铟柱阵列进行互连,铟柱阵列和Underfill相间排列构成中间层,这里Underfill呈网状结构环绕着铟柱阵列。在铟柱阵列和Underfill的相间排列区域,铟柱阵列的体积通常不超过整个中间层体积的16%,在局部分层易发生区域,铟柱更少。为便于分析,文中暂且忽略铟柱对局部分层的影响。考虑到InSb IRFPAs结构的对称性,选取整个探测器结构的1/2进行建模。在建立的模型[14-15]中,InSb芯片、Underfill、和Silicon ROIC的厚度分别为10 µm,10 µm和300 µm,其中Underfill边缘部分的厚度为20 µm,呈fillet结构包围着InSb芯片,这源于器件加工过程中的底充胶填充固化后,通常包围着InSb芯片的缘故。模型中InSb芯片、固化后的Underfill和Silicon ROIC都视为线弹性材料,其具体材料参数如表2所示。网格单元采用PLANE182,在InSb芯片与Underfill的界面处全部覆盖上接触单元CONTA172,目标单元选用TARGE169,接触算法设置为增强拉格朗日算法,接触模式为Bonded(多数),用于实现界面分层。二维结构模型示意如图3所示。
Materials Elastic modulus, E/GPa Poison’s ratio, μ Temperatures, T/K InSb chip 409(in plane)
123(out of plane)0.35 77–300 Underfill 0.0002/α 0.30 77–300 Silicon ROIC 163 0.28 77–300 $\alpha = 22.46 \times {10^{ - 6}} + 5.04 \times {10^{ - 8}} \times {\rm{(}}T{\rm{ - }}273{\rm{)}}$, K是开式温度单位 Table 2. Related material parameters of InSb IRFPAs
Research on local delamination failure mechanism of InSb infrared focal plane arrays detector
doi: 10.3788/IRLA20210133
- Received Date: 2021-03-04
- Rev Recd Date: 2021-05-14
- Publish Date: 2022-04-07
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Key words:
- InSb IRFPAs /
- cohesive zone model(CZM) /
- local delamination /
- mixed-mode ratios
Abstract: Local delamination failure phenomena of indium antimonide infrared focal plane detectors (InSb IRFPAs) in their mass production have become a bottleneck restricting the improvement of their final yield. In order to determine the inducement of local delamination in InSb IRFPAs, the interface between the InSb chip and the underlying underfill with cohesion units was covered, and the specified parameters in cohesion model were optimized, finally the two-dimensional model of local delamination failure analysis of InSb IRFPAs was established. Simulation results are verified by the measured distribution characteristics of local delaminations, that is, (1) Most local delamination appears in the surrounding edges of InSb chip, and occupies a certain width; (2) Once the InSb chip is separated from the underlying underfill in the normal direction, the local delamination will expand gradually toward its both sides of the plane. In order to clarify the inducement of the local delamination, the evolution rule of the local delamination with different mixed-mode ratios is systematically analyzed under the jointed action of both the opening mode and sliding mode. The simulation results are highly consistent with the measured results when the mixed-mode ratio between the opening mode and the sliding mode is set to 4: 6. The local delamination of the InSb IRFPAs are ascribed to the jointed action of both the interfacial normal stress and the in-plane shear stress, is the typical mixed-mode local delamination mode, furthermore, the sliding local delamination mode is dominant.