Rapid PCB warpage modeling through automated copper pattern classification and classical lamination Theory-Driven anisotropic viscoelastic homogenization

Abstract

In the pursuit of enhancing reliability and manufacturability in semiconductor packages, warpage prediction is critical due to its impact on performance and assembly processes. This study presents an automated pattern classification-based finite element simulation model designed to predict warpage in semiconductor packages. This model focuses on the anisotropic and viscoelastic properties of complex copper (Cu) patterns, such as trace, circle, grid, and square shapes, alongside polymer-based dielectric materials. Python-based image processing techniques, including histogram of oriented gradients (HOG), black-white ratio analysis, and canny edge detection, are utilized to classify the orientation, shape, and volume fraction of Cu circuits. HOG analysis identifies the orientation of Cu patterns, while the volume fraction is calculated through grayscale image processing, distinguishing Cu traces in white from dielectric materials in black. By integrating these data, a comprehensive matrix was created to account for orientation, pattern type and trace/space ratios. This matrix is used as the mechanical property value of each layer, which has anisotropic viscoelastic properties based on a composite classical lamination theory. The proposed simulation method enabled fast and accurate warpage prediction, and experimental verification demonstrated a noteworthy accuracy of 96.8%. These results demonstrate a strong correlation between the equivalent simulation model and experimental data, confirming the model's accuracy in predicting warpage during the reflow process and highlighting its potential as a reliable tool.