Dynamics and Scaling of One Dimensional Surface Structures

TL;DR

This paper investigates the long-term scaling behavior of one-dimensional step flow models in surface dynamics, revealing how different atom exchange mechanisms affect the scaling exponent and density functions.

Contribution

It introduces a scaling ansatz for step flow models, linking the scaling exponent to the atom exchange mechanism and validating the continuum approach against discrete simulations.

Findings

Scaling exponent b3=2 for global reservoir exchange

Scaling exponent b3=4 for local terrace exchange

Computed density functions match discrete system simulations

Abstract

We study several one dimensional step flow models. Numerical simulations show that the slope of the profile exhibits scaling in all cases. We apply a scaling ansatz to the various step flow models and investigate their long time evolution. This evolution is described in terms of a continuous step density function, which scales in time according to D(x,t)=F(xt^{-1/\gamma}). The value of the scaling exponent \gamma depends on the mass transport mechanism. When steps exchange atoms with a global reservoir the value of \gamma is 2. On the other hand, when the steps can only exchange atoms with neighboring terraces, \gamma=4. We compute the step density scaling function for three different profiles for both global and local exchange mechanisms. The computed density functions coincide with simulations of the discrete systems. These results are compared to those given by the continuum approach of Mullins.