Numerical model for predicting warpage of wafer with back-end-of-line layers: A comparison investigation

The wafer warpage caused by unbalanced thermal stress among various materials in back-end-of-line (BEOL) layers poses challenges to the manufacturing process. In addition, the diversity of materials and the complexity of metal constitutive models are crucial problems for predicting wafer warpage. This article presents a novel method to predict the wafer warpage with BEOL layers by the equivalent plastic model to during thermal cycling. Regarding the applicability of the equivalent material model, two different models based on the representative volume element (RVE) are discussed, including the equivalent elastic model and equivalent plastic model. To verify the validity of two equivalent models, the warpage during thermal cycling is measured and compared with simulated warpage. The wafer model based on equivalent plastic properties can predict wafer warpage and characterize the plastic characteristics of warpage deformation during thermal cycling. The error between the simulated warpage and the measured warpage is less than 5%. In conclusion, this research provides a novel insight into solving the problem of wafer warpage prediction caused by complex structures such as BEOL and redistribution layer (RDL).