Thermal-Torsion Coupling Loading Analysis and Optimization of 3-D PoP Assembly Solder Joints at Different Temperatures

A simulation analysis was conducted to investigate the stress distribution of package on package (PoP) assembly array solder joints subjected to thermal-torsional coupling loads, with the validity of the simulation confirmed through coupled loading stress-strain measurement experiments. The volume-weighted average method was employed to calculate the average equivalent stress (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \sigma $ </tex-math></inline-formula>) of the critical solder joint danger element layer within the PoP assembly array, using <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \sigma $ </tex-math></inline-formula> as the evaluation benchmark. The impact and sensitivity of structural parameters on the thermal-torsional coupling stress of solder joints were examined. A structural parameter sensitivity model was developed to facilitate the stability and optimization analysis of the structural parameter intervals. The results indicate that solder joints in the lower array of the PoP assembly experience higher thermal-torsional coupling stress, with the peak internal stress occurring at the interface between the solder joint and the copper pad. The variation in thermal-torsional coupling stress of the array solder joints is more pronounced in the low-temperature region compared to the high-temperature region, with maximum stress occurring at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$- 55~^{\circ }$ </tex-math></inline-formula>C and minimum stress observed at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$125~^{\circ }$ </tex-math></inline-formula>C. Within the structural parameter range, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \sigma $ </tex-math></inline-formula> value of the critical solder joint shows a negative correlation with solder joint height, solder joint diameter, and substrate thickness, and a positive correlation with PCB thickness. The sensitivity to structural parameters follows the order: solder joint diameter, solder joint height, PCB thickness, and substrate thickness. Finally, the optimal range of structural parameters was determined, and the stability of this range was assessed.