Decay of isolated surface features driven by the Gibbs-Thomson effect in an analytic model and a simulation

A theory based on the thermodynamic Gibbs-Thomson relation is presented that provides the framework for understanding the time evolution of isolated nanoscale features (i.e., islands and pits) on surfaces. Two limiting cases are predicted, in which either diffusion or interface transfer is the limiting process. These cases correspond to similar regimes considered in previous works addressing the Ostwald ripening of ensembles of features. A third possible limiting case is noted for the special geometry of ``stacked'' islands. In these limiting cases, isolated features are predicted to decay in size with a power-law scaling in time: A∝(${\mathrm{t}}_0$-t${)}^{\mathrm{n}}$, where A is the area of the feature, ${\mathrm{t}}_0$ is the time at which the feature disappears, and n=2/3 or 1. The constant of proportionality is related to parameters describing both the kinetic and equilibrium properties of the surface. A continuous-time Monte Carlo simulation is used to test the application of this theory to generic surfaces with atomic scale features. A method is described to obtain macroscopic kinetic parameters describing interfaces in such simulations. Simulation and analytic theory are compared directly, using measurements of the simulation to determine the constants of the analytic theory. Agreement between the two is very good over a range of surface parameters, suggesting that the analytic theory properly captures the necessary physics. It is anticipated that the simulation will be useful in modeling complex surface geometries often seen in experiments on physical surfaces, for which application of the analytic model is not straightforward.