Constitutive modeling and reliability evaluation of interfacial slip damage in three-dimensional stacked micro/nano-scale through-silicon vias

verfasst von: Yuming Zhang, Xiaojing Zheng, Juan Ma, Peter Wriggers, Kong Phutphalla
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.
Organisationseinheit(en): Institut für Kontinuumsmechanik
Externe Organisation(en): Ministry of Education of the People's Republic of China (MOE)
Xidian University
Cambodia Academy of Digital Technology (CADT)
Typ: Artikel
Journal: Mechanical Systems and Signal Processing
Band: 243
ISSN: 0888-3270
Publikationsdatum: 15.01.2026
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Steuerungs- und Systemtechnik, Signalverarbeitung, Tief- und Ingenieurbau, Luft- und Raumfahrttechnik, Maschinenbau, Angewandte Informatik
Elektronische Version(en): https://doi.org/10.1016/j.ymssp.2025.113669 (Zugang: Geschlossen)
: Details im Forschungsportal „Research@Leibniz University“

BibTeX

@article{86abe2ad7240464291665d4795a9b891,
title = "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.",
keywords = "BSVR, Constitutive, Cross entropy, Reliability, TSV",
author = "Yuming Zhang and Xiaojing Zheng and Juan Ma and Peter Wriggers and Kong Phutphalla",
note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Ltd",
year = "2026",
month = jan,
day = "15",
doi = "10.1016/j.ymssp.2025.113669",
language = "English",
volume = "243",
journal = "Mechanical Systems and Signal Processing",
issn = "0888-3270",
publisher = "Academic Press",
}