Driving force in electromigration and the residual resistivity field

The mean force $\overrightarrow{\mathrm{F}}$ on the electron gas due to the scattering on impurities is shown to account for the residual-resistivity field which must be applied to a sample in order to keep a stationary current. The calculation of $\overrightarrow{\mathrm{F}}$ provides a means of estimating the driving force for the electromigration. It is also possible to obtain $\overrightarrow{\mathrm{F}}$ by calculating the net charge flux induced by the displacement of the impurity.