DECAY OF ISOLATED SURFACE-FEATURES DRIVEN BY THE GIBBS-THOMSON EFFECTIN AN ANALYTIC MODEL AND A SIMULATION

A theory based on the thermodynamic Gibbs-Thomson relation is presente d 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 t ransfer is the limiting process. These cases correspond to similar reg imes considered in previous works addressing the Ostwald ripening of e nsembles of features. A third possible limiting case is noted for the special geometry of ''stacked'' islands. In these limiting cases, isol ated features are predicted to decay in size with a power-law scaling in time: A proportional to(t(0)-t)(n), where A is the area of the feat ure, 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 continu ous-time Monte Carlo simulation is used to test the application of thi s theory to generic surfaces with atomic scale features. A method is d escribed to obtain macroscopic kinetic parameters describing interface s in such simulations. Simulation and analytic theory are compared dir ectly, 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 prop erly captures the necessary physics. It is anticipated that the simula tion will be useful in modeling complex surface geometries often seen in experiments on physical surfaces, for which application of the anal ytic model is not straightforward.