Decay of one dimensional surface modulations

Details Decay of one dimensional surface modulations Decay of one dimensional surface modulations

2000-06-12

arxiv.org/abs/cond-mat/0006191v1

Physics

Condensed Matter

Materials Science

18 pages, 6 figures in 9 eps files

Scientific paper

10.1103/PhysRevB.62.13707

The relaxation process of one dimensional surface modulations is re-examined. Surface evolution is described in terms of a standard step flow model. Numerical evidence that the surface slope, D(x,t), obeys the scaling ansatz D(x,t)=alpha(t)F(x) is provided. We use the scaling ansatz to transform the discrete step model into a continuum model for surface dynamics. The model consists of differential equations for the functions alpha(t) and F(x). The solutions of these equations agree with simulation results of the discrete step model. We identify two types of possible scaling solutions. Solutions of the first type have facets at the extremum points, while in solutions of the second type the facets are replaced by cusps. Interactions between steps of opposite signs determine whether a system is of the first or second type. Finally, we relate our model to an actual experiment and find good agreement between a measured AFM snapshot and a solution of our continuum model.

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