Analytical description of the metal-assisted growth of III–V nanowires: Axial and radial growths

The growth of III–V nanowires from metal seed particles is described in an analytical manner within the framework of a material conservation model. Direct impingement of growth species on the particle, coupled to their diffusion from the sidewall and the substrate surface, are considered in the derivation of expressions for the time evolution of both axial and radial growths. Two regimes are distinguished: the structure originally grows in a purely axial manner until its length exceeds the diffusion length of adatoms incoming from the substrate, at which point sidewall nucleation is triggered, resulting in a shell expanding radially in the lower part of the wire. Factors that take into account the nonunity probability of inclusion of group III adatoms in the axially growing crystal are introduced. Moreover, a step-mediated growth is included to describe the axial evolution of the shell. The numerical values of the various parameters were assessed by fitting the model to experimental data on the morphology evolution of molecular-beam-epitaxy-grown GaAs and InAs nanowires.