The Li multiplication method for the driving force induced particle migration equation was proposed to solve numerically the stress and electric fields induced vacancy migration equation. On the basis of this method, vacancy migration behaviours were found to be predicted under the competitive relationship between stress and electric field. When a residual stress was dominant, vacancies concentrate around the maximum hydrostatic stress region, such as elastic–plastic boundary. On the other hand, when the electric field was dominant, vacancies did not concentrate around the maximum hydrostatic stress region, but move from the cathode end to the anode end. An in situ observation of electromigration on AlCuSi interconnect was conducted to verify the simulation results. A void nucleated and grew at the tip of a notch on an AlCuSi line without passivation film, while many voids appeared and grew in cathode side in a line with passivation film. Greater hydrostatic stress gradient was considered to occur in the line without passivation film, owing to a small scale of yielding, and this leads to concentrate void formation at the tip of the notch. These results indicate that numerical analysis of electromigration was valid to represent the experimental result. Based on results mentioned above, various failure modes in interconnects cased by electromigration were predictable by the proposed Li multiplication method.

Numerical Analysis of Vacancy Transport by Residual Stress in Electromigration on LSI Interconnects. T.Nemoto, T.A.Yokobori, T.Murakawa, H.Miura: Japanese. Journal of Applied Physics, 2010, 49[2], 024301