Statistics of Nucleation and Growth of Single Monolayers in Nanowires: Towards a Deterministic Regime

Abstract

The vapor–liquid–solid growth of semiconductor nanowires proceeds via the sequential nucleation and extension of biatomic monolayers at the interface between the solid wire and a liquid catalyst nanodroplet. In the case of III–V compounds, this mother phase contains only a small concentration of the volatile group V atoms. The growth regime where there is not enough such atoms available in the liquid at nucleation to complete a whole monolayer is studied experimentally and theoretically. Each monolayer cycle then consists in the rapid formation of a partial monolayer, followed by a slower propagation stage and by a waiting time preceding the next nucleation. The propagation and waiting times of long sequences of monolayers are measured in situ in a transmission electron microscope at three growth temperatures, in a single GaAs nanowire. The process is modeled and the statistics of the characteristic times are computed numerically and analytically. At low temperature, the weakness of group V desorption from the liquid should lead to a constant total monolayer cycle time, despite the stochasticity of the nucleation events. The modeling of the experiments yields values of several crucial growth parameters and provides guidance for the growth of nanowires in a deterministic regime.

In situ observations of size effects in GaAs nanowire growth

“…During the step-flow process the layer advanced across the LS interface by incrementally filling large sections of the LS interface switching between convex, concave and straight edged configurations (see video S1). This should not be viewed as a lack of temporal resolution of our system, since this type of step-flow behaviour is consistent with previous in-situ studies of nanowire growth [22][23][24] . Images and 2D schematic contours of the faceting of the bilayer for a nanowire not included in the main dataset are shown in Supporting Information SI-3.…”

“…This behaviour has been attributed to the low amount of As atoms in the droplet which is smaller than the amount of As atoms required to cover the whole LS interface 18 . In modelling this phenomenon has been termed the stopping effect, where it was shown that the amount of initial LS interface coverage was strongly dependent on the As flow 24,30,31 . Contrary to incubation time, our data shows that the step-flow time increases for decreasing nanowire diameter across the examined diameter range, as seen in Fig.…”

“…This has enabled improvement of theoretical models and contributed to increased understanding of existing experimental work. Additionally, several in-situ studies have focused further on investigating the layer-by-layer growth itself, demonstrating that it consists of two well defined processes, namely, step-flow and incubation (also sometimes referred to as layer propagation and waiting time, respectively) [22][23][24] . In III-Vs, an atomic layer advances across the liquid-solid (LS) interface during the step-flow process, after which there is a distinct waiting time known as incubation time.…”

Regulated Dynamics with Two Monolayer Steps in Vapor–Solid–Solid Growth of Nanowires

“…It was noted previously that the depletion which follows the nucleation and the rapid expansion of the island at the interface leads to an antibunching of the nucleation process. The characteristics of this depletion were analyzed further for a low incident flux − due to the quantitative approach which can be developed for the VLS growth of III–V nanowires. In this case, a basic process is thought to consist of two steps: (1) the increase of the concentration of group V atoms in the droplet until random nucleation and rapid expansion of the island fed by the excess of concentration and (2) a final expansion to the full ML controlled by the incoming flux.…”

“…As the nucleation of the steps is a random process, it raises the question of antibunching, particularly if the velocity of the steps is large, so that the propagation time is much shorter than the nucleation time. More recent studies have focused on the role of the postnucleation period, where the step propagation may be limited by refilling. − …”