Data-Driven Stress/Warpage Analyses Based on Stoney Equation for Packaging Applications

Stress and warping analyses are frequently required in modern semiconductor and packaging processing. Accurately predicting the structural stress and warping topology is crucial for improving processing reliability. Simple analytic models and their revised forms are typically used for quick estimation. However, these revised analytical forms often rely on considering just a single modification factor, which may not align with practical semiconductor and electronic packaging scenarios and lack appropriate analytical solutions. Consequently, extensive and costly 3D finite element simulations are commonly conducted. In theory, machine learning could offer an effective gray-box estimation solution for such problems. Nevertheless, the performance and impact on parameter settings must be justified and evaluated. To address these concerns, we use typical substrate/film stress/warpage problems as examples to demonstrate the effectiveness of data-driven mechanics prediction. This approach integrates the Stoney equation as the kernel and utilizes an artificial neural network to predict the correction factor based on practical considerations. We apply this approach to three cases of substrate-film structures, including multi-layered film, thicker film, and viscoelastic film, to assess its feasibility and performance. Furthermore, we concurrently address all three practical concerns using the same artificial intelligence scheme. Our findings indicate that the machine-learning prediction can achieve a successful rate of up to 99% for accuracy better than 95%. With the feasibility demonstrated, we propose a scheme that combines this data-driven approach with Green’s function to address the warpage of substrates with discrete film segments. Additionally, we have developed a topology reconstruction method by extending the proposed machine-learning approach for general 3D warpage prediction in related packaging engineering applications.