Smoluchowski ripening and random percolation in epitaxial Si1-xGex/Si(001) islands - art. no. 045315

摘要

Island size distributions of ripened Si1-xGex/Si(001) (x = 0.3 - 0.7) islands exhibit a slow decay at small island sizes and an asymmetric bell-shaped distribution peaked at a large size. We explain the ripening process in Si1-xGex/Si(001) islands by proposing a model based on random percolation and Smoluchowski ripening. Drawing an analogy with percolation theory, we use a shifted average height to represent the time variable, which is also applicable in the Smoluchowski ripening model; this shifted average height is used to analyze size distributions and correlation functions. Critical exponents derived from the site percolation model at d = 3 agree with our measurements, Island diffusion Dproportional tos(-alpha) leading to coalescence events, shows a weak dependence on size s: alpha = 0.28 +/- 0.20, attributable to the inverse process of sequential incorporation of atoms at step edges due to the high stress concentration at island terrace perimeters. While random percolation dominates for small sizes regime, Smoluchowski ripening controls the distribution peak at large island sizes. Good agreement is obtained between the model and the measured island size distributions. [References: 35]