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

Abstract

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.

Modeling the Radial Growth of Self-Catalyzed III-V Nanowires

“…The latter depends on the diffusion length of group III adatoms on the NW sidewalls, which has always been a free parameter of modeling. Here, we notice that if (i) group III atoms cannot desorb from the NW sidewalls and droplet [ 15 , 27 , 28 ], and (ii) the axial NW growth rate is determined by the group V flux, as commonly assumed and confirmed experimentally [ 11 , 19 , 29 , 30 , 31 ], the radial growth of self-catalyzed III-V NWs can be described without any free parameters. Other assumptions of the model are not essential and can be refined.…”

“…For Au-catalyzed III-V NWs, foreign metal catalyzed III-N NWs or ZnO NWs, and catalyst-free III-V or III-N NWs, a more relevant approach has been developed in Refs. [ 27 , 28 ] without using the linear time dependence of the NW length. Any excessive group III flux should necessarily be used for radial growth.…”

“…The factor in these equations corrects the corresponding expressions of Refs. [ 27 , 28 ] for the difference in the elementary volumes in the solid and liquid phases (a value on the order of 2). This does not change the results of Refs.…”

“…This does not change the results of Refs. [ 27 , 28 ], where the contribution of the droplet volume into the overall material balance was considered negligible. Integration of Equation (6) with the initial condition gives showing that the length of self-catalyzed III-V NWs is simply proportional to the deposition thickness or growth time [ 19 , 23 , 29 ].…”

“…Using the recent theoretical results of Refs. [ 27 , 28 ], we develop the fully self-consistent growth model of self-catalyzed III-V NWs, which describes the experimental data on the morphological evolution of GaP and GaAs NWs on different substrates using growth details and no other free parameters. The model should be useful for understanding and controlling the radial growth of different III-V NWs within a wide range of conditions.…”