Interplay of Kinetic and Thermodynamic Factors in the Stationary Composition of Vapor–Liquid–Solid IIIVxV1−x Nanowires

Abstract

Compositional control over vapor–liquid–solid III–V ternary nanowires based on group V intermix (VLS IIIVxV1−x NWs) is complicated by the presence of a catalyst droplet with extremely low and hence undetectable concentrations of group V atoms. The liquid–solid and vapor–solid distributions of IIIVxV1−x NWs at a given temperature are influenced by the kinetic parameters (supersaturation and diffusion coefficients in liquid, V/III flux ratio in vapor), temperature and thermodynamic constants. We analyze the interplay of the kinetic and thermodynamic factors influencing the compositions of VLS IIIVxV1−x NWs and derive a new vapor–solid distribution that contains only one parameter of liquid, the ratio of the diffusion coefficients of dissimilar group V atoms. The unknown concentrations of group V atoms in liquid have no influence on the NW composition at high enough levels of supersaturation in liquid. The simple analytic shape of this vapor–solid distribution is regulated by the total V/III flux ratio in vapor. Calculating the temperature-dependent desorption rates, we show that the purely kinetic regime of the liquid–solid growth occurs for VLS IIIVxV1−x NWs in a wide range of conditions. The model fits the data well on the vapor–solid distributions of VLS InPxAs1−x and GaPxAs1−x NWs and can be used for understanding and controlling the compositions of any VLS IIIVxV1−x NWs, as well as modeling the compositional profiles across NW heterostructures in different material systems.