Quantitative description for the growth rate of self-induced GaN nanowires

We determine with high precision the growth rate of self-induced GaN nanowires grown by molecular beam epitaxy under various conditions from scanning electron micrographs by taking into account in situ measurements of the initial incubation time, which is needed before the nanowire growth starts. In order to quantitatively describe the dependence of the growth rate on growth time, gallium flux, and growth temperature, we develop a detailed theoretical model of diffusion-induced nanowire growth specifically for the self-induced approach, i.e., without any droplet at the nanowire top. The theoretical fits are in excellent agreement with the experimental data and allow us to deduce important kinetic parameters of the self-induced GaN nanowire growth. The gallium adatom effective diffusion length on the nanowire sidewalls composed of m-plane facets is only 45 nm, which is consistent with our experimental finding that the growth rate initially decreases drastically as the contribution from the adatoms on the planar substrate surface rapidly vanishes. In contrast, the gallium adatom effective diffusion length on the amorphous silicon nitride substrate surface reaches about 100 nm. Furthermore, the nucleation energy on the nanowire sidewalls is found to be 5.44 eV and is larger than on their top facet accounting for the nanowire elongation.