Role of Thermodynamics and Kinetics in the Composition of Ternary III-V Nanowires

Abstract

We explain the composition of ternary nanowires nucleating from a quaternary liquid melt. The model we derive describes the evolution of the solid composition from the nucleated-limited composition to the kinetic one. The effect of the growth temperature, group V concentration and Au/III concentration ratio on the solid-liquid dependence is studied. It has been shown that the solid composition increases with increasing temperature and Au concentration in the droplet at the fixed In/Ga concentration ratio. The model does not depend on the site of nucleation and the geometry of monolayer growth and is applicable for nucleation and growth on a facet with finite radius. The case of a steady-state (or final) solid composition is considered and discussed separately. While the nucleation-limited liquid-solid composition dependence contains the miscibility gap at relevant temperatures for growth of InxGa1−xAs NWs, the miscibility gap may be suppressed completely in the steady-state growth regime at high supersaturation. The theoretical results are compared with available experimental data via the combination of the here described solid-liquid and a simple kinetic liquid-vapor model.

Surface energy driven miscibility gap suppression during nucleation of III–V ternary alloys

“…In spite of the lack of justification for its application for solids 51 it remains very popular for modelling vapor-liquid-solid nucleation due to its simplicity. 14,24,31 The curve (iii) corresponds to the intermediate case calculated at δ = 0.5. Finally, a non-linear case can be considered within the convex model (iv) calculated at α = 1, while the curve coincides with the Vegard's law case at α = 0.…”

“…19,20 Despite a number of experimental investigations on the growth of nanowires with composition inside the miscibility gap, 21,22 the suppression mechanism in these nanostructures remain unclear. Some kinetic theories 23,24 assume that the miscibility gap might shrink under relatively high supersaturations in the liquid. Indeed, it has been shown that high concentrations of group V elements in the droplet can "straighten" the initially S-shaped liquid-solid composition dependence curve.…”

“…26 The composition-independence of the surface energy term of the critical nucleus is a standard assumption substantiated by the investigation by Wilemski, 27 where it was assumed that the component with the lower surface energy segregates to the surface so readily so that the nucleus always obtains the surface energy of that component. This is used in the majority of kinetic models based on the incorporation rate, 23,24,28 mass balance models, 29 equilibrium models 30 and nucleation-limited models. 14,31 The omitted surface energy term is a good approximation for the relatively large size of the stable growing clusters, making the surface energies insignificant.…”

“…At high supersaturation the final composition might differ from the one of the critical nucleus. 24 (iv) Finally, there is an uncertainty in the estimated values of the surface energies and the concentration of group V elements in the liquid. Despite these shortcomings, classical nucleation theory has proven to be valuable for modelling and understanding several aspects of nanowire growth.…”

Compositional Correlation between the Nanoparticle and the Growing Au-Assisted InxGa1–xAs Nanowire

“…Full details of the model are given in the Supporting Information (SI 1: Details about the model); here we present a summary of the important features of the model and compare them to experimental data. We base our model on another very recently published model, 22 which is kinetically limited at its core and in which the composition of the growing nanowire is determined by the relative rates of attachment of InAs and GaAs to a supercritical nucleus of a certain size. The model also, however, considers thermodynamics to determine, for example, the initial nucleus composition.…”