Theory of surface electromigration on metals: application to self-electromigration on Cu(111)

Abstract

We present a calculation of the force, due to electron scattering, acting upon an adatom at the surface of a current-carrying metal, i.e., the so-called “wind” force in surface electromigration. The force is calculated from the Feynman-Hellmann theorem in which the electron scattering states are computed with full multiple scattering corrections by a layer-KKR method. In contrast to previous jellium models, this approach allows the proper treatment of electron scattering by both the surface barrier and the substrate and its effect upon the current-carrying states at the surface. The electron scattering force is computed for the self-electromigration of Cu adatoms on Cu(111). At room temperature, the effective valence of the adatom is found to be ≈ −21. We conclude that surface electromigration of Cu on Cu(111) is dominated by the electron scattering force and that any direct force originating from charge transfer to the adatom is likely to be unimportant in this case. The implications of the computed value of the wind force for the mass transport at a current-carrying metal surface are discussed.