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First-principles calculations of doped elements on electromigration of Bi
The first-principles calculations on the elemental doping in SnBi lead-free solders were performed, aiming to inhabit electromigration of Bi element during microelectronic packaging. Zn and Sb elements were theoretically added into SnBi system, and the diffusion barrier energy of Bi was calculated with nudged elastic band (NEB) methods. The results show that, after Sb doping, the diffusion barrier energy of Bi increases from 0.32 eV to 0.46 eV, and the diffusion activation energy of Bi increases from 1.14 eV to 1.18 eV. On the other hand, after Zn doping, the diffusion barrier energy of Bi increases from 0.32 eV to 0.48 eV, and the diffusion activation energy of Bi increases from 1.14 eV to 1.22 eV. Zn and Sb can inhabit the diffusion of Bi during electromigration. The density of states (DOS) analyses show that p-state curves of Sb and Bi almost completely overlap, which indicates that Sb and Bi has stronger covalent bonding than Sn-Bi, thereby increases the diffusion barrier energy of Bi. The calculated DOS of Zn and Bi is the same as that of Sb and Bi, which indicates that Zn—Bi also has stronger covalent bonding than Sn—Bi, hence, the addition of Zn also increases the barrier energy of Bi. In conclusion, Sb and Zn doping can inhibit Bi electromigration in SnBi solder.