Reconsideration of Nanowire Growth Theory at Low Temperatures

Abstract

We present a growth model that describes the nanowire length and radius versus time in the absence of evaporation or scattering of semiconductor atoms (group III atoms in the case of III-V NWs) from the substrate, nanowire sidewalls or catalyst nanoparticle. The model applies equally well to low-temperature metal-catalyzed or selective area growth of elemental or III-V nanowires on patterned substrates. Surface diffusion transport and radial growth on the nanowire sidewalls are carefully considered under the constraint of the total material balance, yielding some new effects. The nanowire growth process is shown to proceed in two steps. In the first step, the nanowire length increases linearly with time and is inversely proportional to the nanowire radius squared and the nanowire surface density, without radial growth. In the second step, the nanowire length obeys the Chini equation, resulting in a non-linear increase in length with time and radial growth. The nanowire radii converge to a stationary value in the large time limit, showing a kind of size-narrowing effect. The model fits the data on the growth kinetics of a single self-catalyzed GaAs nanowire on a Si substrate well.

Theory of MBE Growth of Nanowires on Reflecting Substrates

“…This is a special type of the Chini equation considered recently in Ref. [36], where it was used from the beginning of growth, assuming that all diffusive group III adatoms are collected by NWs from a "sticky" substrate surface. In our case, the solution is given by…”

The onset of tapering in the early stage of growth of a nanowire

“…This remarkable shape was modelled assuming no desorption of adatoms 13,14 . It is considered experimentally to be characterized by a long diffusion length along the nanowire sidewall, even if the radial growth starts with a delay with respect to the axial growth 24 . However, InP nanowires grown by Metal-Organic MBE exhibit a significant lateral growth [25][26][27] , which gives rise directly to the cone+cylinder shape and not to the pencil-like shape.…”

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

“…I will assume the absence of desorption of group III atoms from the substrate surface, NW sidewalls and catalyst droplets resting on the tops of VLS NWs, as discussed above. In the case of an adsorbing substrate, the diffusive growth species are collected by the droplet, NW sidewalls and also from a feeding ring of width on the substrate surface [ 18 , 21 , 23 , 26 , 29 , 38 ]. This can be called the diffusion length of group III adatoms, which describe the temperature-dependent surface mobility of these adatoms on a given substrate surface.…”

“…[ 14 ] for a review). Most works on this topic [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ], with only a few exceptions [ 30 , 31 , 32 , 33 , 34 , 35 ], addressed the growth kinetics of individual NW without accounting for the shadowing effect [ 30 ], which is very important in molecular beam epitaxy (MBE) and related directional deposition techniques where the material beams are inclined at an angle with respect to the substrate normal.…”