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 i slands obey the dynamic scaling hypothesis due to a random percolation proc ess, only in the small island limit. Island morphologies strongly suggest t he presence of Smoluchowski ripening, in which islands collide and ripen. R andom percolation and Smoluchowski ripening are thus combined to analyze th e size distributions. To understand the critical behavior of the islands, a s exhibited by their size distributions, a mean-field theory for coherently strained island formation is formulated, by incorporating surface energy a nd strain relaxation. The resulting phase diagram shows that island formati on in Si1-xGex/Si(001) occurs near the critical region. Order parameter flu ctuations can be estimated by calculating the curvature energy for such a s ystem, showing that the strain fluctuations are relevant to properly descri be island formation in the Si1-xGex/Si(001) system. (C) 2001 American Vacuu m Society.