Details
| Original language | English |
|---|---|
| Article number | 113669 |
| Journal | Mechanical Systems and Signal Processing |
| Volume | 243 |
| Early online date | 28 Nov 2025 |
| Publication status | Published - 15 Jan 2026 |
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
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- Signal Processing
- Engineering(all)
- Civil and Structural Engineering
- Engineering(all)
- Aerospace Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
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In: Mechanical Systems and Signal Processing, Vol. 243, 113669, 15.01.2026.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Constitutive modeling and reliability evaluation of interfacial slip damage in three-dimensional stacked micro/nano-scale through-silicon vias
AU - Zhang, Yuming
AU - Zheng, Xiaojing
AU - Ma, Juan
AU - Wriggers, Peter
AU - Phutphalla, Kong
N1 - Publisher Copyright: © 2025 Elsevier Ltd
PY - 2026/1/15
Y1 - 2026/1/15
N2 - 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.
AB - 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.
KW - BSVR
KW - Constitutive
KW - Cross entropy
KW - Reliability
KW - TSV
UR - http://www.scopus.com/inward/record.url?scp=105024871464&partnerID=8YFLogxK
U2 - 10.1016/j.ymssp.2025.113669
DO - 10.1016/j.ymssp.2025.113669
M3 - Article
AN - SCOPUS:105024871464
VL - 243
JO - Mechanical Systems and Signal Processing
JF - Mechanical Systems and Signal Processing
SN - 0888-3270
M1 - 113669
ER -