Residual-resistivity dipole in electron transport and electromigration

Abstract

The structure of Landauer's residual-resistivity dipole is investigated using expressions which have been recently derived from linear-response theory. We calculate the local field and charge density near an impurity in a current-carrying metal. The impurity is assumed to be an isotropic scatterer and is described by an $s$-wave phase shift. We find that the long-range average field of the residual-resistivity dipole is exactly as obtained by Landauer in a semiclassical picture; i.e., the dipoles give the macroscopic field which drives the current past the scatterers. The charge distribution is not strongly localized, but has important Friedel oscillations extending far from the impurity. Our results are applied to the calculation of the electromigration driving force on a weak scatterer due to the presence of an $s$-wave scatterer in its vicinity. When the $s$-wave scatterer is strong, the residual-resistivity dipole contributes substantially to the force on the weak scatterer. Such contributions have not been previously considered in explicit calculations of scattering interference effects in electromigration.