Dynamics of Step Bunching Induced by DC Resistive Heating of Si Wafer

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Abstract
Step dynamics has been studied through numerical integration of the equations of motion of the steps at a vicinal surface during evaporation with dc resistive heating. The equations have been derived under the assumption that the surface processes involve drift of the adatoms in the dc direction perpendicular to the steps, in accordance with the hypothesis for Si adatom electromigration on Si surfaces. The calculated trajectories of the steps show bunching in the step-up direction of the drift velocity of adatoms when the interstep distance is at least two times longer than the mean diffusion distance. The formation of slow-moving pairs of steps is a key process in the electromigration-induced instability of vicinal surfaces. These pairs move at a rate which is lower than the rate of motion of the steps involved in bunching. As a result, steps detach from the bunch trail and the resulting pairs cross the terraces to attach to the front edge of the next bunch. The time evolution of the step array manifests a new kind of repulsive interaction between the moving steps, originating from the interplay of the surface transport and kinetics at the steps. The numerical analysis predicts that the instability develops rather slowly and evaporation of thousands of monolayer is necessary for detection of step bunching.