Predictive Modeling and Optimization of Wafer Warpage in FOPoP Packaging Using Element Birth and Death Technique

The fan-out package-on-package (FOPoP) process includes backside redistribution layer (RDL) formation, molding compound (MC) curing, and frontside RDL patterning, where thermal effects induce wafer warpage, leading to yield loss, stress, and fracture risks. Mitigation involves optimizing materials, refining processes, and improving inspections to ensure quality. Finite element analysis (FEA) using the element birth and death technique simulated warpage due to mismatched coefficients of thermal expansion (CTE) among materials. The model included 11 stages: a four-layer backside RDL, MC curing, and a six-layer frontside RDL. Warpage predictions were validated against experimental data, showing errors below 10%, confirming model accuracy. Parametric analysis identified positive correlations between the CTE of polyimide (PI), glass, and MC with warpage, while glass CTE and MC Young’s modulus showed negative correlations. No significant effect was observed for PI Young’s modulus or thickness. A one-factor-at-a-time approach combined with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{\text {k}}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3^{\text {k}}$ </tex-math></inline-formula> factorial designs identified key factors, with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3^{\text {k}}$ </tex-math></inline-formula> design demonstrating higher accuracy in capturing interactions. Analysis of variance (ANOVA) and response surface methodology (RSM) developed regression models for predicting FOPoP warpage, with a 0.4% error compared to experimental results. The optimized parameters reduced the wafer warpage by 29%, demonstrating effectiveness. These findings offer a robust approach for predicting and mitigating warpage, improving product quality and yield.