  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 $\tau$ which is dependent upon
the three energy scales in the problem: $k_{B}T$, the step stiffness, $\gamma$,
and the bias associated with adatom hopping under the influence of an
electromigration force, $\pm \Delta U$. For ($t < \tau$), the correlation
function evolves as a superposition of $t^{1/4}$ and $t^{3/4}$ power laws. For
$t \ge \tau$ 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.
