Diffusional attractions between voids on a Si(111)7×7 surface

Ostwald ripening or coarsening is a term which describes the growth of large domains at the expanse of small ones in the final stages of any phase separation process. Several theories were developed in order to explain this process. All of them are based on the Lifshitz, Slyozov, and Wagner (LSW) model which predicts an increase in the average radius of domains r̄(t) ∞ t^1/3 and a reduction of the number density of domains as a function of time N(t) ∞ f^-1. The LSW model assumes static and circular domains, which are distributed at random. These assumptions were found to be incorrect by many experiments. And more advanced theories were necessary to explain these observations. In our work, we study the coarsening of voids formed in a Si(111)7×7 surface covered by 0.8 bilayers (BL). Besides the expected increase in the diameter of voids and the decrease in the number density, very strong attractions and rapid motion of voids towards each other were clearly observed. The result of the attraction between the voids is coagulation of voids and an increase in the spatial correlations between voids, as the coarsening process progresses, as we indeed observed. This is contradictory to the "ideal gas" picture which is the basis of the LSW model. Basically, this can be explained by a concentration gradient which develops between two voids of different size and the growth of voids in the direction of the larger concentration. However, this model cannot explain the large diffusional motions observed in our experiments. It is proposed that an amplification mechanism exists, whereby the arrival of a diffusing vacancy to the boundary of the void causes the release of several adatoms from the boundary. This process causes a much larger motion than expected by a single vacancy absorption. This picture, which is consistent with the structure of the steps, demonstrates how the microscopic details might have a significant affect on the global coarsening process.