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For an impurity in a bulk metal, the connection between electromigration and electric fields associated with dc conductivity is understood in terms of Landauer's residual resistivity dipole. This connection is examined, and appropriate generalizations are made for an impurity in a two-dimensional electron gas and for an impurity near a metal surface. The residual resistivity dipole field decays less rapidly with distance in a two-dimensional gas than in bulk, thus resulting in a larger voltage drop across an impurity in the system of lower dimensionality.
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