Parametric Optimization and Yield Probability Prediction of Package Warpage

This paper proposes a parametric modeling and simulation method to rank parameters, which affect warpage behaviors in a package of stacked die, in order of relevance. In addition, yield prediction with tolerance of epoxy mold compound (EMC) thickness and warpage optimization of the interaction between EMC thickness and die thickness have been achieved using ANSYS DesignXplorer (DX). It is well recognized that coefficient of thermal expansion (CTE) mismatch among packaging materials is intrinsic driving force for warpage. Moreover, package structure, including die size, substrate thickness, die thickness and EMC thickness, could play an important role. To attain better guidance for warpage control, finite element method (FEM) can be applied to set up parametric model in an economical and efficient way, and then to sort out major parameters through relevance analysis. After excluding insignificant parameters, design of experiment (DOE) can be conducted with fewer factors to search for optimal configuration with minimum warpage. Traditional fitting method has large gap between test points and fitting curve, while Neural Network, a machine learning method demonstrated in the paper, shows improvement in fitting performance. In practices, tolerances in various manufacturing steps are unavoidable. The manufacturing tolerances can affect warpage significantly and it is less taken into account in the past. With the method shown above, prediction of yield probability can be conducted to indicate sample percentage that has lower warpage than specification. Results show that EMC thickness, die thickness, substrate trace layer CTE, and EMC CTE are top relevant factors. Response surface showing warpage behavior with varying EMC and die thickness demonstrates a valley zone for lowest deformation, which indicates good performance of warpage within certain range of EMC and die thickness.