Constitutive modeling and reliability evaluation of interfacial slip damage in three-dimensional stacked micro/nano-scale through-silicon vias
Abstract
Micro/nano-interconnect structures are critical components in three-dimensional high-density packaging, yet their reliability is critically constrained by the copper pumping effect induced by the thermal mismatch between copper and silicon. This study investigates interfacial failure at the copper/silicon interface in through-silicon via (TSV) composite structures. Based on continuum damage mechanics, a constitutive relation for interfacial slip is established using energy dissipation as a damage indicator. The reliability under thermoelectrical coupling is evaluated, and the model is further applied to analyze thermal residual stress and strain in common liner materials. A Bayesian support vector regression (BSVR) model is integrated into a cross-entropy-based framework for failure probability assessment. Within this framework, importance sampling is employed to optimize BSVR hyperparameter selection, while BSVR serves as a surrogate to reduce computational cost in constitutive simulations. To address the analytical intractability of the marginal likelihood integral in BSVR, a simulation-based sampling method is proposed as an alternative to Laplace approximation. The proposed computational framework effectively combines the advantages of cross-entropy methods and BSVR surrogate modeling in handling high-dimensional problems with small failure probabilities, thereby mitigating efficiency degradation caused by data sparsity and complex failure domains.
Details
- Organisation(s)
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Institute of Continuum Mechanics
- External Organisation(s)
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Ministry of Education of the People's Republic of China (MOE)
Xidian University
Cambodia Academy of Digital Technology (CADT)
- Type
- Article
- Journal
- Mechanical Systems and Signal Processing
- Volume
- 243
- ISSN
- 0888-3270
- Publication date
- 15.01.2026
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Control and Systems Engineering, Signal Processing, Civil and Structural Engineering, Aerospace Engineering, Mechanical Engineering, Computer Science Applications
- Electronic version(s)
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https://doi.org/10.1016/j.ymssp.2025.113669 (Access:
Closed
)
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Details in the research portal "Research@Leibniz University"
