A Computational Framework to Predict the Maximum Possible Warpage Due to Package-to-Package Variations

Semiconductor package warpage is an important issue that must be accurately predicted early in the package development process. Typically, warpage predictions rely on average geometric dimensions and average measured material property of different package components. However, these simulations often overlook the impact of geometric dimension tolerances and material property scattering. The combined effect of these tolerances leads to package-to-package warpage variations. This approach may be effective when the warpage remains well below the critical limits such that even with these variations, the limits are not exceeded. However, with the advancement of new package technologies, the gap between the predicted average warpage and the critical threshold is reducing. As a result, during the high-volume manufacturing, some packages may exceed the critical warpage limit due to a combined effect of geometric dimension and material property variation even within the specified tolerances. Therefore, it becomes essential to assess the maximum possible warpage caused by these variations early in the development phase. In this paper, we propose a computational framework to predict the extreme potential warpage resulting from geometric tolerances and material property scattering. This approach involves running numerous simulations to generate a dataset within the defined tolerances. To facilitate this, the model was first optimized for computational efficiency through the use of symmetry, mesh optimization and material homogenization. Next, the model was calibrated to the measured warpage using the average material and geometry values. Subsequently, a design of experiment (DOE) algorithm was employed to create a dataset incorporating the geometric and material property input parameters. Finally, optimization was performed on the metamodel to predict the maximum potential warpage. This framework provides pathways to tighten specific geometry and material parameters tolerances, ultimately helping to prevent warpage issues during the highvolume manufacturing phase.