Drift Of Adatoms Research Articles

Hierarchical Bunching of Steps in a Conserved System

We study the growth law of step bunches formed by the drift of adatoms in a one-dimensional step model with conservation of atoms. The simulation result shows that the terrace size between bunches grows as a power of time L ∼ t β with β=1/2 irrespective of the step interaction. The exponent agrees with experiment on Si(111) surface. The average step distance in a bunch is also related to the step interaction potential. A simple theoretical picture, based on a hierarchical bunching of steps, explains these results.

Simple model for anisotropic step growth

We consider a simple model for the growth of isolated steps on a vicinal crystal surface. It incorporates diffusion and drift of adatoms on the terrace, and strong step and kink edge barriers. Using a combination of analytic methods and Monte Carlo simulations, we study the morphology of growing steps in detail. In particular, under typical molecular beam epitaxy conditions the step morphology is linearly unstable in the model and develops fingers separated by deep cracks. The vertical roughness of the step grows linearly in time, while horizontally the fingers coarsen proportional to ${t}^{0.33}$. We develop scaling arguments to study the saturation of the ledge morphology for a finite width and length of the terrace.

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.

Wandering Instability of an Isolated Step with Direct Electric Current

We study wandering instability of an isolated step in a surface diffusion field with a direct electric current applied perpendicular to the step. The drift of adatoms caused by the electric current modifies the surface diffusion length. In sublimation the difference between the modified surface diffusion length in the upper terrace and that in the lower terrace causes an instability with respect to fluctuation along the step. This instability occurs when the drift is opposite to the step motion and its strength is within a limited range. Near the lower critical current the step obeys the Kuramoto-Sivashinsky equation, which gives rise to spatiotemporal chaos.

Nonlinear Effect in Step Bunching Caused by Electric Current

We study nonlinear effects in step bunching in a surface diffusion field with a direct electric current. Linear stability analysis shows that the bunching instability occurs in sublimation at long wavelength if the step distance is smaller than the surface diffusion length and the drift of adatoms induced by the electric current is in the step down direction. When we take account of the nonlinear effect, the density of steps obeys the Benney equation, which shows an array of step bunches or spatiotemporal chaos. This feature is similar to the step bunching caused by the asymmetry of step kinetics except that the surface profile may change with the sign of the dispersion term.