Investigation and prediction of solder joint failure analysis for ball grid array package subject to mechanical bending environment
Authors: Wu Mei-Ling , Lan Jia-Shen 
Published: April 2017

Purpose
The purpose of this study was to investigate the changes in solder joint stress when subjected to mechanical bending. The analytical theory pertaining to the stresses in the solder joint between the components (including the molding compound, the chip and the substrate) was described, and the printed circuit board (PCB) with a discontinuity function when the PCB assembly is subjected to mechanical bending was developed. Thus, the findings reported here may lead to a better understanding of the solder joint failure based on the Physics of Failure model.

Design/methodology/approach
This paper discusses the analytical model for calculating the stress in solder joints, as well as presents a simulation model that can be used for calculating the strain energy density of solder joint. First, the multilayer plate theory is used in discussing the composite material for the component, including the molding compound, the silicon chip and the substrate, or the PCB, including the copper layers, the fiber and the epoxy. Finally, the complete structure of the analytical model developed as a part of this current work is presented.

Findings
For the analytical model of multilayer structures in which the interconnection layer is discrete, mechanical bending has been modeled with respect to varying silicon chip length. The analytical model that describes the stress of the outermost solder joint experiences is chosen, as this is the typical solder joint failure. The analytical model can be applied to discrete solder joints, which are evaluated by calculating the matrix form. Owing to its use of the matrix equation, the analytical model can be highly combinatorial and thus more capable of calculating the solution.

Research limitations/implications
The analytical solution based on a simple concept was presented and validated using the finite element model for the stress experienced by solder joints subjected to mechanical bending. To verify that the simulation represents a real PCB case, the authors use the finite element method (FEM) to compare their case with the multilayer plate theory. Owing to the good agreement between the theory and simulation results, the authors conclude that the multilayer plate theory can be correctly applied in multilayer PCB and be used in an analytical model for the PCB assembly subjected to mechanical bending.

Practical implications
Owing to the good agreement between the theory and simulation results, the authors conclude that the multilayer plate theory can be correctly applied in multilayer PCB and be used in an analytical model for the PCB assembly subjected to mechanical bending.

Social implications
The analytical model is validated with the FEM model and provides the way to physically examine the solder joint failure mechanism. In this paper, the analytical model is developed as a means to assess the solder joint stress subjected to mechanical bending.

Originality/value
The analytical model treats the solder joint as discrete and has been successfully validated against the finite element model. The complete structure model (the second analytical model) is presented to discuss the effects of varying silicon chip length on the normal stress in solder joints. When the silicon chip length exceeds to 80 per cent of the total package length, the stress of the outermost solder joint increases rapidly. The design analysis findings have suggested that the failure of the outermost solder joint subjected to mechanical bending on the PCB assembly can be reduced by analyzing the analytical model.