Stability of the warpage in a PBGA package subjected to hygro-thermal loading

The CTE and CHE mismatch between materials in a thin PBGA package is primarily attributed to the warpage which occurs when the package is being mounted on to a PCB, especially when the moisture content reaches a specified value. In this paper, the stability equations for the warpage in a PBGA package without the solder balls being subjected to hygro-thermal loading, by modeling it as an initially perfect/imperfect composite plate, have been developed. The analytical closed-form solutions are found and used to compute not only the critical moisture content but also the warpage occurring before the critical loads are reached. The buckling of the PBGA package, at the solder reflow peak temperature, occurs when the theoretical moisture content reaches 0.259–0.283 wt.%. This theoretical critical moisture content accurately predicts the experimental critical moisture content (0.25–0.30 wt.%) derived from our previous work. The results, from comparison between theoretical and experimental critical moisture content, indirectly indicate that the PBGA package has little imperfection. However, the large initial imperfect structure of the package does not easily reach the buckling stage because of moisture absorption. In addition to this, the structure of the PBGA package before buckling become stress-free at the moisture level of 0.077 wt.% and at room temperature during moisture conditioning.