Wandering and Bunching Instabilities of Steps Described By Nonlinear Evolution Equations

We study wandering and bunching instabilities of steps in a surface diffusion field with a direct electric field applied perpendicular to the steps. The drift of adatoms induced by the electric field modifies the surface diffusion length in the upper terrace and that in the lower terrace. This asymmetry causes wandering instability of an isolated step when the drift is opposite to the step motion. Near the critical point the time evolution of a step obeys the Kuramoto–Sivashinsky equation, which gives rise to spatiotemporal chaos. The asymmetry also causes bunching instability of an array of repulsive straight steps. The instability near the critical point is an amplification of density large wavelength. The step density after the instability obeys the Benney equation, which shows a stable array of solitons corresponding to the formation of stable bunches.