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The thickness-composition phase diagrams of the growth modes were determined for the GaInN-on-GaN (GaInN/GaN) and the GaInN-on-AlN-on-GaN (GaInN/AlN/GaN) structures. For this determination, the strain energy was calculated by considering the stress relaxation due to introduction of misfit dislocations, the surface energy was estimated from bonding enthalpy of the nearest-neighbor bonds on the surface, and the interface energy was estimated by considering both effects of the dangling bonds due to lattice misfit and the abrupt transition of bonding species at the heterointerface. From these phase diagrams, it was found that the layer-by-layer growth such as the Frank–van der Merwe mode was very difficult to obtain for the epitaxial growth of GaInN on GaN when the InN fraction is large. The Volmer–Weber mode is dominant in the phase diagram of the GaInN/GaN structures. The influence of an AlN buffer layer with a larger surface energy was studied by introducing an AlN layer between the GaInN layer and the GaN substrate. It was known that the layer-by-layer growth could be more easily obtained if misfit dislocations were introduced and an AlN layer was used as a buffer. © 2001 American Institute of Physics.