Critical behavior of epitaxial Si1−xGex/Si(001) islands

Island size distributions of three-dimensional Si1−xGex/Si(001) islands of varying Ge fractions (x=0.4–0.7) and thicknesses grown by ultrahigh vacuum chemical vapor deposition are studied. Size distributions for percolating islands obey the dynamic scaling hypothesis due to a random percolation process, only in the small island limit. Island morphologies strongly suggest the presence of Smoluchowski ripening, in which islands collide and ripen. Random percolation and Smoluchowski ripening are thus combined to analyze the size distributions. To understand the critical behavior of the islands, as exhibited by their size distributions, a mean-field theory for coherently strained island formation is formulated, by incorporating surface energy and strain relaxation. The resulting phase diagram shows that island formation in Si1−xGex/Si(001) occurs near the critical region. Order parameter fluctuations can be estimated by calculating the curvature energy for such a system, showing that the strain fluctuations a...