Theory of MBE Growth of Nanowires on Adsorbing Substrates: The Role of the Shadowing Effect on the Diffusion Transport

A new model for nanowire growth by molecular beam epitaxy is proposed which extends the earlier approaches treating an isolated nanowire to the case of ensembles of nanowires. I consider an adsorbing substrate on which the arriving growth species (group III adatoms for III-V nanowires) may diffuse to the nanowire base and subsequently to the top without desorption. Analytical solution for the nanowire length evolution at a constant radius shows that the shadowing of the substrate surface is efficient and affects the growth kinetics from the very beginning of growth in dense enough ensembles of nanowires. The model fits quite well the kinetic data on different Au-catalyzed and self-catalyzed III-V nanowires. This approach should work equally well for vapor-liquid-solid and catalyst-free nanowires grown by molecular beam epitaxy and related deposition techniques on unpatterned or masked substrates.