We point out that the relationship between the adatom-induced surface resistivity, p s , and the lifetime of the parallel vibrational motion of adatoms, τ, recently derived by Persson can be recast to read as F∫/J∫ = n e el f p s /n a , where F∫, J∫, n e , l f , and n a are the damping force on the adatom, the apparent current density in the metal seen from the adatom, the electron density in the metal, the film thickness, and the 2-dimensional density of adatoms, respectively. This has essentially the same form as the relationship between p , and the indirect (electron-wind) force F w on the adatom located in a current density J W , i.e., F W /J W =n e el f p s /n a , which has been known for a long time in the theory of electromigration. Using a first-principles linear response approach, we show that both the equations hold true if the substrate is translationally invariant in the plane (flat jellium model). We derive a simple expression of the surface resistivity, p s , which can be evaluated from the scattering amplitudes of one-electron wave functions at the Fermi energy alone.
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