Control of Chaotic Wandering of an Isolated Step by the Drift of Adatoms

Abstract

The drift of adatoms strongly influences the wandering pattern of an isolated step moving in a surface diffusion field. When the drift velocity has a component against the step motion and exceeds a critical value, the straight step becomes unstable with long wavelength fluctuations, and wanders. This wandering pattern can be controlled by changing the direction of the drift. When the drift has no component parallel to the step edge, the unstable step obeys the Kuramoto-Sivashinsky equation and shows a chaotic pattern. When the drift has a component parallel to the step edge, the step obeys the Benney equation. If the parallel component is sufficiently large, the step shows a regular pattern.[ S0031-9007(98)

Instabilities of steps induced by the drift of adatoms and effect of the step permeability

“…This type of nonlinear term is related to the velocity increment of the inclined straight step. 25,36 The normal velocity of the inclined step V n ( …”

“…31 and 32, except that the jump of adatoms over the step is allowed without an extra diffusion barrier to include the permeability of adatoms at step sites. 25,33 The uniform drift of adatoms is taken into account as a biased diffusion probability. This treatment is valid when the adatom density is low.…”

“…We use the standard step flow model with drift of adatoms 9,10,[14][15][16][17][18][19][20][21][22]24,25 for a mathematical analysis of the step motion. When the drift is perpendicular to the average orientation of steps, the diffusion equation of the adatom density c(r,t), on a terrace, is given by ‫ץ‬c ‫ץ‬t ϭD s ٌ 2 cϪv ‫ץ‬c ‫ץ‬y…”

“…Theoretically in a vicinal face two kinds of instabilities, step bunching and step wandering, 22,24,25 are possible. Recently Degawa et al observed both bunching and the wandering by using a cylindrical specimen.…”

Step bunching induced by flow in solution

“…If the chosen atom is an atom in a solution, we carry out a diffusion trial. The flow in a solution is expressed as bias in the diffusion probability [10,11]. When an atom at the site (i, j) is chosen, the atom moves to the sites (i, j ± 1) with the probability 1/4 and to the sites (i ± 1, j) with the probabilities arrives at the vicinal face after diffusion trials, solidification occurs with the probability [12] …”