Temporal step fluctuations on a conductor surface: electromigration force, surface resistivity and low-frequency noise

Scattering of charge carriers from surface structures will become an increasing factor in the resistivity as the structure decreases in size to the nanoscale. The effects of scattering at the most basic surface defect, a kink in a step edge, are here analyzed using the continuum step model. Using a Langevin analysis, it has been shown that the electromigration force on the atoms at the step edge causes changes in the temporal evolution of the step-edge. For an electromigration force acting perpendicular to the average step edge and mass-transport dominated by step-edge diffusion, significant deviations from the usual t1/4 scaling of the displacement correlation function occur dependent on a critical time τ and the direction of the force relative to the step edge (i.e. uphill or downhill). Experimental observations of step fluctuations on Ag(111) show the predicted changes among step fluctuations without current, and with current in the up- and down-hill directions for a current density of order 105 A cm−2. The results yield the magnitude of the electromigration force acting on kinked sites at the step-edge. This in turn yields the contribution of the fluctuating steps to the surface resistivity, which exceeds 1% of the bulk resistivity as wire diameters decrease below 10s of nanometres. The temporal fluctuations of kink density can thus also be related to resistivity noise. Relating the known fluctuation spectrum of the step displacements to fluctuations in their lengths, the corresponding resistivity noise is predicted to show spectral signatures of ~f−1/2 for step fluctuations governed by random attachment/detachment, and ~f−3/4 for step fluctuations governed by step-edge diffusion.