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arXiv · 0704.0624

Temporal Evolution of Step-Edge Fluctuations Under Electromigration Conditions

P. J. Rous·T. W. Bole
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Abstract

The temporal evolution of step-edge fluctuations under electromigration conditions is analysed using a continuum Langevin model. If the electromigration driving force acts in the step up/down direction, and step-edge diffusion is the dominant mass-transport mechanism, we find that significant deviations from the usual $t^{1/4}$ scaling of the terrace-width correlation function occurs for a critical time $τ$ which is dependent upon the three energy scales in the problem: $k_{B}T$, the step stiffness, $γ$, and the bias associated with adatom hopping under the influence of an electromigration force, $\pm ΔU$. For ($t < τ$), the correlation function evolves as a superposition of $t^{1/4}$ and $t^{3/4}$ power laws. For $t \ge τ$ a closed form expression can be derived. This behavior is confirmed by a Monte-Carlo simulation using a discrete model of the step dynamics. It is proposed that the magnitude of the electromigration force acting upon an atom at a step-edge can by estimated by a careful analysis of the statistical properties of step-edge fluctuations on the appropriate time-scale.

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P. J. Rous, T. W. Bole. 2007-04-04. Temporal Evolution of Step-Edge Fluctuations Under Electromigration Conditions. https://doi.org/10.1103/physrevb.76.125435

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