Fig. 1.
(Color online) Comparison of the first 18 Zernike polynomial wafer distribution maps and the characteristic post-bonding residual distribution for a (100) silicon wafer.
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Journal of Semiconductors
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2026
> Accepted Manuscript
| Citation: |
Rui Wang, Sen Lu, Kaiming Yang, Yu Zhu. An extended overlay assessment model with process correlation analysis for sub-100-nm accuracy wafer bonding[J]. Journal of Semiconductors, 2026, In Press. doi: 10.1088/1674-4926/25120038
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R Wang, S Lu, K M Yang, and Y Zhu, An extended overlay assessment model with process correlation analysis for sub-100-nm accuracy wafer bonding[J]. J. Semicond., 2026, accepted doi: 10.1088/1674-4926/25120038
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An extended overlay assessment model with process correlation analysis for sub-100-nm accuracy wafer bonding
DOI: 10.1088/1674-4926/25120038
CSTR: 32376.14.1674-4926.25120038
More Information-
Rui Wang is studying for a Ph.D. in Mechanical Engineering in Tsinghua University. He received his BS degree in Mechanical Engineering from Tsinghua University in 2019. His main research direction is Accuracy Guarantee of Alignment and Bonding technology for Wafer Stacking Equipment -
Sen Lu is an assistant professor at the Department of Mechanical Engineering at Tsinghua University. He received his PhD in mechanical engineering from Tsinghua University in 2019. His current interests include ultra-precision measurement and control technology as well as 3D IC packaging technology -
Kaiming Yang is a professor at the Department of Mechanical Engineering at Tsinghua University. He received his BS and MS degrees in mechanical engineering from Zhengzhou University in 1995 and 1998, respectively, and his PhD in mechanical manufacturing and automation from Tsinghua University in 2005. His research areas include ultra-precision motion control, computerized numerical control, and mechatronic equipment control -
Yu Zhu graduated from the China University of Mining and Technology in 2001 with a doctoral degree. From July 2001 to September 2004, he worked as a postdoctoral fellow at Tsinghua University. He is the head of the Institute of Mechanical Electronics at the Department of Mechanical Engineering at Tsinghua University and a leader in the field of IC equipment at Tsinghua University. His research interests include dynamical system design and analysis theory for ultra-precision systems, displacement measurement and motion control technology for nano-precision systems, and development strategies for IC manufacturing equipment - Corresponding author: yangkm@tsinghua.edu.cn
- Revised Date: 2026-01-21 Available Online: 2026-03-02
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Abstract
To address the urgent demand for sub-100-nm overlay accuracy in wafer bonding for three-dimensional integration, this study systematically investigates and proposes an extended overlay assessment model that integrates physical mechanisms with data-driven approaches, along with a methodology for analyzing its correlation with process parameters. Conventional rigid-body transformation models fail to effectively characterize systematic deformations induced by crystalline anisotropy and process stresses. To overcome this limitation, this paper constructs an extended overlay model based on Zernike polynomials. By incorporating systematic deformation terms with clear physical significance, the model achieves precise description of non-uniform wafer deformation. Furthermore, an innovative Zernike term selection strategy is proposed, which combines physics-guided pre-screening with stepwise regression optimized by the Akaike Information Criterion (AIC). This strategy effectively resolves issues of model overfitting and underfitting, significantly enhancing the model's generalizability and interpretability while maintaining accuracy. Experimental validation using Patterned Wafer Geometry (PWG) data demonstrates that the proposed model achieves a goodness-of-fit R2 greater than 0.70 for both the net deformation introduced by the bonding process and the lithography-compensable component, showcasing excellent deformation decomposition capability. Further correlation analysis based on multiple sets of process experimental data quantitatively reveals strong correlations (|r| > 0.85) between key process parameters, such as the peak bonding head force, and specific Zernike deformation modes. This provides direct evidence for actively suppressing detrimental deformations through process optimization. This research establishes a complete technical framework encompassing theory, algorithm, experimental verification, and process traceability, laying a crucial theoretical and technical foundation for mechanism diagnosis, predictive compensation, and closed-loop control in high-precision wafer bonding. -
References
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