Influence of strain on the indium incorporation in (0001) GaN

The incorporation of indium in GaN (0001) surfaces in dependence of strain is investigated by combining molecular-beam epitaxy (MBE) growth, quantitative transmission electron microscopy, and density-functional theory (DFT) calculations. Growth experiments were conducted on GaN, as well as on $30%\ifmmode\pm\else\textpm\fi{}2%$ partially relaxed $\mathrm{I}{\mathrm{n}}_{0.19}\mathrm{G}{\mathrm{a}}_{0.81}\mathrm{N}$ buffer layers, serving as substrates. Despite the only $0.6%$ larger in-plane lattice constant of GaN provided by the buffer layer, our experiments reveal that the In incorporation increases by more than a factor of two for growth on the $\mathrm{I}{\mathrm{n}}_{0.19}\mathrm{G}{\mathrm{a}}_{0.81}\mathrm{N}$ buffer, as compared to growth on GaN. DFT calculations reveal that the decreasing chemical potential due to the reduced lattice mismatch stabilizes the In--N bond at the surface. Depending on the growth conditions (metal rich or N rich), this promotes the incorporation of higher In contents into a coherently strained layer. Nevertheless, the effect of strain is highly nonlinear. As a consequence of the different surface reconstructions, growth on relaxed $\mathrm{I}{\mathrm{n}}_{x}\mathrm{G}{\mathrm{a}}_{1\ensuremath{-}x}\mathrm{N}$ buffers appears more suitable for metal-rich MBE growth conditions with regard to achieving higher In compositions.