Theoretical Considerations of Critical Layer Thickness for Elastic Coherency Breakdown in Epitaxial Growth

Elastic coherency breakdown of epitaxial films is generally accompanied by the introduction of misfit dislocations (MD) at the film/substrate interface. Several theoretical models for predicting the critical layer thickness use the energy balance between the pure elastic distortion in the film and the misfit dislocation energy. The well-known theory of van der Merwe predicts the critical thickness reasonably well for metal/metal epitaxy, but underestimates it for semiconductor materials. It is generally accepted that this disagreement is due to the lack of MD sources and partly due to metastability in the state of elastic coherency in semiconductors. We reexamined these theoretical models and found that the van der Merwe theory starts deviating more significantly from experiments with decreasing misfit. This indicates that the MD energy for low misfit is not appropriate. We improved the calculation by using different boundary conditions in his original formulations.