A well-known model for the rate of heterogeneous nucleation and growth of a second-phase precipitate in a solid matrix has successfully been applied to analyze the electromigration process in Al thin-film interconnects. The change of resistance is considered resulting mainly from the scattering of electrons by atoms around the vacancies or voids at grain boundaries. Free volume is introduced to describe the behavior of these atoms and to simplify the complicated scattering process by means of the effective scattering cross section of the free volume. The quantitative relation between the scattering cross section and the resistance change is established, and from which the resistance revolution can be characterized during different electromigration stages. Comparison of our simulation results with experimental data shows good agreement and our model can explain the previously unexplained abrupt resistance change phenomena.