Machine learning for board-level drop response of BGA packaging structure

Board-level drop responses are critical to evaluate the mechanical reliability of solder joints to serve as electrical and mechanical connections in electronic devices to resist failure due to drop impact. A machine learning (ML) model based on the back propagation (BP) method is proposed for predicting three-dimensional board-level drop responses of the ball grid array (BGA) packaging structures. Compared with conventional finite element (FE) simulations with solid elements, the proposed approach with a deep neural network is more than three orders of magnitude faster in terms of computational efficiency. More importantly, detailed stress and strain of all solder joints and also the warpage of the printed circuit board (PCB) can be accurately predicted throughout the drop process. According to the contact type between BGA packaging structure and rigid ground, the drop conditions are divided into three types: surface contact, line contact and point contact. After training the ML model, the obtained nonlinear mapping relation can well predict the mechanical response of solder joints in BGA packaging structures. To significantly extend the application scope, the trained ML model could reasonably predict the dynamic responses of BGA structures with the drop angles which are beyond the training samples. Compared with FE results, the prediction accuracy of the proposed ML model is objectively measured by the Pearson correlation coefficient which is found to be above 0.95 after estimating the stress, strain and energy density of solder joints and PCB warpage. Except for those stress, train and energy density values close to 0, the prediction errors are mostly less than 10% compared with the finite element simulation values. Therefore, it is affirmed that the computational efficiency and accuracy of the proposed ML method are satisfactory to replace the traditional time-consuming FE modeling for predicting the dynamic responses of board-level BGA packaging structures even under more extreme and complicated loading conditions.