Electromigration and the local transport field in mesoscopic systems

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Abstract
An analysis is presented for the local field and electromigration driving force in mesoscopic systems, i.e., systems in which the dimension along the transport direction is smaller than the electron mean free path due to inelastic scattering. The electromigration driving force is a measure of the microscopic electric field acting on an impurity, and, in general, consists of two contributions, namely, the ‘‘electron-wind force’’ and the ‘‘direct force.’’ The local transport field also consists of electron-wind and direct contributions. Detailed analyses are presented for the local fields, forces, and resistivities in the following mesoscopic systems: (i) one-dimensional (1D) disordered conductors; (ii) an impurity-layer or grain boundary sandwiched between reservoirs; and (iii) an impurity in the vicinity of a point contact. For the first two systems, the direct force and the associated direct field vanish, whereas in the point-contact system the wind and direct contributions are comparable. The net electromigration force on a 1D conductor is a measure of the true potential drop across the disordered region, and is proportional to the Landauer resistivity. In the case of an isotropically scattering impurity near a point contact, the wind force is proportional to the impurity-induced change in the contact resistivity. Inconsistencies are pointed out in the use of linear-response formalism based upon the existence of an external field in mesoscopic systems.

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