Coupled Multiphysics Optimization of Ball Grid Array with Microchannel Heat Dissipation

Ball grid array (BGA) is widely used in chip packaging, and the thermo-mechanical performance of its solder joints significantly affects the performance of packaged devices. To investigate and improve the thermo-mechanical performance of BGA solder joints under steady-state conditions, a thermo-mechanical coupling model of a BGA packaging chip under microchannel-forced liquid cooling is established based on a method combining constructal theory and multiphysics field coupled numerical calculation, and a composite evaluation indicator of maximum temperature and maximum deformation is proposed for optimizing the solder joint design. With the total number and total volume of solder joints as constraints, and the long/short half-axis ratio of solder joints and the layout of the ball grid array as design variables, the maximum temperature, the maximum deformation, and their composite function are selected as performance indicators. The effects of solder joint shape and layout evolution on the thermo-mechanical performance of the device are systematically investigated. The results indicate that among the array, rectangular-ambulatory, and staggered layout types, the rectangular-ambulatory type consistently yields the lowest maximum temperature and maximum deformation for all long/short half-axis ratios, whereas the array type and staggered type each have their own advantages and disadvantages under different ratios. In the studied cases, the difference between the maximum and minimum values of the maximum temperature is 7.8 K, and the difference between the maximum and minimum values of the maximum deformation is 5.88 × 10−3 mm, with a maximum reduction ratio of 74.5%. Under the three BGA layouts, the maximum temperature increases monotonically with the long/short half-axis ratio, while the maximum deformation decreases monotonically. The variation in the composite function with the long-to-short half-axis ratio changes with the weighting-factor ratio, but the optimal BGA layout remains unchanged and is always the rectangular-loop layout. When the weighting factor ratio is 7:3, there exists an optimal long/short half-axis ratio that minimizes the composite function. The methods and results presented in this study can provide a theoretical basis for the thermo-mechanical design of BGA packaging chips.