The strain-relaxation phenomena during the early stages of plasma-assisted molecular-beam epitaxy growth of lattice-mismatched wurtzite (0001) AlN/GaN heterostructures have been studied by real-time recording of the in situ reflection high-energy electron diffraction (RHEED), ex situ transmission electron microscopy (TEM), and atomic-force microscopy. A pseudo-two-dimensional layer-by-layer growth is observed at substrate temperatures of 640--660 \ifmmode^\circ\else\textdegree\fi{}C, as evidenced by RHEED and TEM. However, the variation of the in-plane lattice parameter during growth and after growth has been found to be complex. Three steps have been seen during the deposition of lattice-mismatched AlN and GaN layers: they were interpreted as the succession of the formation of flat platelets, 3--6 monolayers high (0.8--1.5 nm) and 10--20 nm in diameter, their partial coalescence, and gradual dislocation introduction. Platelet formation leads to elastic relaxation as high as 1.8%, i.e., a considerable part of the AlN/GaN lattice mismatch of 2.4%, and can be reversible. Platelets are always observed during the initial stages of growth and are almost insensitive to the metal/N ratio. In contrast, platelet coalescence and dislocation introduction are very dependent on the metal/N ratio: no coalescence occurs and the dislocation introduction rate is higher under N-rich conditions. In all cases, the misfit dislocation density, as measured by the irreversible relaxation, is initially of the order of $7\ifmmode\times\else\texttimes\fi{}{10}^{11}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ and decreases exponentially with the layer thickness. These results are interpreted in the framework of a model that emphasizes the important role of the flat platelets for dislocation nucleation.
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