A combined analytical and computational method was developed in order to study the mechanics of strained epitaxial island growth in typical semiconductor systems. It was recalled that, under certain growth conditions in systems with a film/substrate lattice mismatch, the deposited material aggregated into island-like shapes with geometries that had arc-shaped cross-sections. A 2-dimensional model, which assumed linear elastic behavior, was used to analyze an isolated arc-shaped island which had elastic properties that were similar to those of the substrate. The latter was assumed to be much larger than the island. Finite-element analysis showed that, in order to minimize the total energy (which comprised strain energy, surface energy, and film/substrate interface energy), a coherent island would adopt a particular height/width aspect ratio that was a function of the island volume alone. It was then shown that, for an island whose volume was greater than a critical size, the inclusion of a mismatch strain-relieving edge dislocation was favorable. The criterion for the critical size was based upon a comparison of the configurational forces which acted on the edge of the island in the presence of an edge dislocation. A finite-element calculation, combined with an analytical treatment of the singular dislocation fields, was used to determine the minimum-energy island aspect ratio for the dislocated island/substrate system. A combination of minimum-energy morphology studies, for coherent and dislocated systems, with dislocation nucleation criteria furnished a complete model for strained epitaxial island growth.

H.T.Johnson, L.B.Freund: Journal of Applied Physics, 1997, 81[9], 6081-90