Kinetic modeling of interfacial abruptness in axial nanowire heterostructures

Abstract

Kinetic modeling of the formation of axial heterostructures in III-V nanowires grown by the Au-catalyzed vapor-liquid-solid method is presented. We link the mass balance in the droplet to the crystallization rates of different III-V pairs at the liquid-solid interface. This allows us to describe how the chemical composition changes across a nanowire heterostructure and study the influence of the growth parameters on the interfacial abruptness. It is shown that, at high enough supersaturation in liquid, there is no segregation of different binaries in solid even for materials systems with strong interactions between III-V pairs, such as InGaAs. This leads to the suppression of the miscibility gaps by kinetic factors. The influence of the Au concentration on the interfacial abruptness is found to be complicated. Increasing the Au concentration widens the heterointerface at low Au content and narrows it at high Au content in a catalyst droplet. The model fits quite well the data on the compositional profiles across axial nanowire heterostructures based on both group III and group V interchange. Very sharp heterointerfaces in double of InAs/InP/InAs nanowire heterostructures is explained by a reduced reservoir effect due to low solubility of group V elements in the droplet.

Composition of Vapor–Liquid–Solid III–V Ternary Nanowires Based on Group-III Intermix

“…The group-V concentration in the droplet is in the order of 0.01 or even less, which is much lower than the total group-III concentration according to the data of Refs. [ 20 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 ]. This fundamental property holds regardless of the fact that the droplets catalyzing the VLS growth of InGaAs [ 15 , 29 , 31 , 32 ], InGaP [ 17 ], or InGaN [ 24 ] NWs are In-rich, while the droplets catalyzing the VLS growth of AlGaAs NWs are Ga-rich [ 20 , 29 , 31 ].…”

“…Here, and are the chemical potentials of A and B atoms in liquid in thermal units, which contain the chemical potentials of pure liquids and , logarithmic terms in concentrations and interaction terms and . These interaction terms generally depend on the atomic concentrations , , and (with the Au concentration given by ) [ 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 ]. The number of variables is reduced from three to two for self-catalyzed VLS NWs with .…”

“…The number of variables is reduced from three to two for self-catalyzed VLS NWs with . Within the regular solution model, the chemical potentials of AC and BC pairs in a solid are given by [ 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 ] where and are the chemical potentials of pure binaries AC and BC and is the pseudo-binary interaction parameter in thermal units (which may be -dependent). The temperature-dependent values are well-tabulated for each III–V ternary material [ 26 , 27 ].…”

“…Theoretical approaches developed so far (see Refs. [ 25 , 26 , 27 ] for a review) treat liquid–solid distributions connecting the composition of a VLS ternary A x B 1−x C, pseudo-binary (AC) x (BC) 1−x NW to the content of A atoms in liquid [ 20 , 28 , 29 , 30 , 31 , 32 , 33 , 34 ] or vapor–solid distributions connecting to the content of A atoms in vapor [ 14 , 21 , 24 , 35 , 36 ]. According to the general treatment given in Refs.…”

An Overview of Modeling Approaches for Compositional Control in III–V Ternary Nanowires

“…To this end, the seminal work of Biefeld [ 129 ] remains the only approach to access the behavior of vapor–solid distributions under a varying V/III flux ratio, but this model is restricted to the reaction-limited growth kinetics of epilayers and is not adopted for nanowires. Time-dependent generalizations of compositional models, which are used to model the interfacial abruptness in III–V nanowire heterostructures [ 21 , 111 , 115 , 116 , 127 , 148 ], were beyond the scope of this work (a review can be found, for example, in Ref. [ 142 ]).…”