A model for electromigration and low-frequency noise in thin metal films

At stressing-current densities, low-frequency noise in thin-metal films has been known to have a 1/ƒγ component where γ is between 0.8 and 2. Although several experimental investigations have been made to measure electromigration parameters such as activation energy and lifetimes of metallization layers by low-frequency measurements, investigators so far have had to rely upon semi-empirical expressions for theory. In this paper we develop a theory connecting ion migration in metals to low-frequency noise. The model is based on the electron mobility fluctuations due to scattering from vacancies migrating along the grain boundaries. Through this model the shape of the experimentally observed low-frequency spectra, the current dependence of the noise magnitude and the frequency exponent γ, as well as the temperature dependence of γ can be accurately explained. Moreover, the model also yields the observed thermally activated form and the activation energies for the low-frequency noise magnitude.