Theoretical analysis on the element diffusion during thermomigration

With the miniaturization trend and functional demand in high-density microelectronic packaging, the thermomigration in flip chip solder joints due to the joule heating becomes a serious reliability issue in recent years. A majority of researches have been devoted to understanding the failure mechanism of the thermomigration accompanied by the electromigration behavior; and based on the microstructure observation, the thermomigration in eutectic SnPb and other lead free solders in terms of SnBi, SnCu and SnAgCu has been investigated and the dominate diffusion element in each solder bulk has been identified according to the microstructure evolution. However, only a few works are focused on the theoretical analysis for this novel migration process. In this study, according to our previous research of the thermomigration in the composite SnPb solder bump of the flip chip system at low ambient temperature, the tendency of the each diffusion element in this composite SnPb solder is certificated based on the diffusion theory. It is proved that both Sn and Pb atoms in the solder bulk tend to migrate from the hot side to the cold side during thermomigration, and the different microstructure phenomenon appeared in the other studies, such as Sn and Pb atoms are detected to be the dominate diffusion element when the ambient temperature is higher and lower than 100°C respectively, is mainly due to the different diffusion rate of them. Furthermore, this conclusion can be set up as the universal law for the diffusion process under a certain thermal gradient, which indicates that no matter what kind of atoms they are in the solder bulk, all of them have the tendency to move from the hot zone to the cold zone due to the asymmetrical temperature distribution. On the other hands, the important thermomigration parameter, the molar heat flux Q*of Sn atoms in the SnPb solder alloy is calculated to be 19.1 kJ/mole.