An expression for the free energy of forming an island from a catalyst droplet in the vapor-liquid-solid growth of III-V nanowires is obtained. The effect of the droplet depletion with its group V (As) content is studied in the presence of material influx from vapor. Different growth regimes of a nanowire monolayer are theoretically analyzed, including the regime with the stopping size under very low As concentrations in liquid. It is shown that the island stops growing when the As content in the droplet decreases to its equilibrium value. The obtained results should be useful for understanding and modeling the growth kinetics of III-V nanowires, their crystal phase, nucleation statistics and length distributions within the ensembles of nanowires as well as the doping process.

Theoretical analysis is presented for vapor-liquid-solid growth of III-V nanowires in the presence of three competing processes of the group V deposition, surface diffusion of group III adatoms and nucleation of islands at the liquid-solid interface. A generalized equation for the nanowire growth rate is obtained which can be limited of one of the three processes depending on the growth environment. Different regimes of vapor-liquid-solid growth of III-V nanowires are analyzed depending on the group III and V influxes and nanowire radius.

A new analytic theory is developed for asymptotic stage of self-catalyzed growth of III-V nanowires (NWs) by molecular beam epitaxy (MBE), where NWs collect all group III atoms deposited from vapor. The shadowing NW length is derived which corresponds for the full shadowing of the substrate surface in MBE. The NW length and radius are derived depending on the effective deposition thickness and MBE growth parameters. It is shown that the NW length increases, and their length decreases with decreasing the array pitch and increasing the V/III flux ratio.