Three dimensional finite element computations are used to predict the formation of quantum dot arrays in a strained epitaxial thin film system. The film is idealized as an initially planar, isotropic elastic layer with isotropic surface energy, which is coherently bonded to an elastic, lattice mismatched substrate. A small, doubly sinusoidal variation in film thickness, intended to represent the dominant wavelength of surface roughness, is introduced to trigger island formation. The film continues to roughen due to strain induced surface diffusion and eventually breaks up into arrays of discrete islands. The conditions necessary for island formation are identified, and are shown to differ significantly from the conditions necessary for spontaneous roughening of a strained layer. A detailed parametric study is conducted to determine the influence of the properties of film and substrate, film thickness, and surface roughness on the resulting island morphologies. In particular, our simulations show that there exists a critical range of surface roughness wavelength which leads to the formation of perfectly periodic island arrays. Finally, our predictions are compared with existing experimental measurements.
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