Influence of the source arrangement on shell growth around GaN nanowires in molecular beam epitaxy

In a combined experimental and theoretical study, we investigate the influence of the material source arrangement in a molecular beam epitaxy system on the growth of nanowire (NW) core-shell structures. In particular, we study the shell growth of GaN around GaN template NWs under the boundary condition that Ga and N do not impinge on a given sidewall facet at the same time. Our experiments with different V/III ratios and substrate temperatures show that obtaining shells with homogeneous thickness along the whole NW length is not straightforward. Analyzing in detail the shell morphology with and without substrate rotation, we find that the different azimuthal angles of the sources have a major impact on the Ga adatom kinetics and the final shell morphology. In general, growth is possible only under directly impinging N, and Ga adatoms diffuse between the sidewalls and the top facet as well as the substrate, but not between adjacent sidewall facets. On the basis of these experimental results, we develop a diffusion model which takes into account different NW facets and the substrate. The model allows to describe well the experimental shell profiles and predicts that homogeneous shell growth can be achieved if the Ga and N sources are arranged next to each other or for very high rotation speeds. Moreover, the modeling reveals that the growth on a given side facet can be categorized within one rotation in four different phases: the Ga wetting phase, the metal-rich growth phase, the N-rich growth phase, and the dissociation phase. The striking difference to growth processes on planar samples is that, in our case, diffusion takes place between different regions, i.e. the sidewall vs the top facet and substrate, out of which on one N impinges not continuously, resulting in complex gradients in chemical potential that are modulated in time by substrate rotation. The comprehensiveness of our model provides a deep understanding of diffusion processes and the resulting adatom concentration, and could be applied to other three-dimensional structures and material systems.