Hygro-thermal buckling of a thin PBGA package

In this present paper, the stability equations foe the PBGA package's warpage without the solder balls subjected to hygro-thermal loading, by modeled as an initial perfect composite plate, have been developed. The analytical closed-form solutions are found and used to compute not only the critical moisture contents but also the warpage before reaching the critical loads. The buckling of the PBGA packages, at the solder reflow peak temperature, occurs, when the theoretical moisture contents reach 0.259-0.283%w. These theoretically critical moisture contents accurately predict the experimental critical moisture contents 0.25-0.30%w from our previous work. However, the buckling occurs theoretically in the initial perfect package's structures at room temperature, but not occur practically. The structures of the PBGA package before buckling become stress-free at the moisture content 0.077%w and at the room temperature during moisture conditioning.