Mechanics of coherent and dislocated island morphologies in strained epitaxial material systems

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Abstract
A combined analytical and computational model is developed to study the mechanics of strained epitaxial island growth in typical semiconductor systems. Under certain growth conditions in systems with a film/substrate lattice mismatch, deposited material is known to aggregate into islandlike shapes with geometries having arc shaped cross-sections. A two-dimensional model assuming linear elastic behavior is used to analyze an isolated arc shaped island with elastic properties similar to those of the substrate. The substrate is assumed to be much larger than the island. Finite element analysis shows that in order to minimize the total energy, which consists of strain energy, surface energy, and film/substrate interface energy, a coherent island will adopt a particular height-to-width aspect ratio that is a function of only the island volume. It is then shown that for an island with volume greater than a certain critical size, the inclusion of a mismatch strain relieving edge dislocation is favorable. The criterion for the critical size is based on a comparison of the configurational forces acting on the edge of the island in the presence of an edge dislocation. Finally, a finite element calculation combined with an analytical treatment of the singular dislocation fields is used to determine the minimum energy island aspect ratio for the dislocated island/substrate system. The combination of the minimum energy morphology studies for the coherent and dislocated systems with the dislocation nucleation criterion gives a complete model for strained epitaxial island growth which can serve as a basis for interpretation of experiments.