Modeling one-dimensional island growth with mass-dependent detachment rates

Abstract

m+1 b , with constant b. A mapping onto a column problem shows that these systems are zero-range processes, whose steady state properties are exactly calculated under the assumption of independent column heights in the master equation. Simulation provides accurate island size distributions which confirm analytic reductions and are particularly useful whenever the analytical tools cannot provide results in closed form. The shape of island size distributions can be changed from monomodal to monotonically decreasing by tuning the temperature or changing the coverage onedimensional density . In all cases, small values of the scaling variable X �1 / 1� favor the monotonically decreasing ones. However, for large X, rapidly increasing rates m lead to distributions with peaks very close to m and rapidly decreasing tails, while slowly increasing m provide peaks close to m / 2 and fat right tails.