Composition of III-V ternary materials under arbitrary material fluxes: The general approach unifying kinetics and thermodynamics

Understanding and controlling the composition of III-V ternary nanomaterials is essential for band-gap tunability and fabrication of functional nanoheterostructures. The kinetic approach developed so far is based on the assumption of C-rich growth of a ternary AxB1-xC material based on intermix of A and B atoms. This holds for epilayers based on group III intermix, but is not true for epilayers based on group V intermix or vapor-liquid-solid nanowires based on group III intermix. Herein, we develop a general growth theory and obtain a vapor-solid distribution which described the ternary composition under arbitrary material fluxes and for any III-V material. This vapor-solid distribution is a combination of the kinetic and equilibrium distributions, whose weights depend on the ratio epsilon of the total flux of A and B atoms over the flux of C atoms. At epsilon<< 1, the composition is kinetically controlled, while at epsilon << 1 it becomes thermodynamically limited even at infinitely high binary supersaturations for AC and BC pairs. The model fits very well the compositional data on the InSbxAs1-x epilayers, AlSbxAs1-x epilayers, and InSbxAs1-x nanowires under different total V/III flux ratios. It reveals some fundamental properties of the vapor-solid distribution beyond the assumption of decoupled binary fluxes. In particular, the vapor-solid distribution becomes purely thermodynamic and presents the miscibility gap below the critical temperature under AB-rich conditions for an AxB1-xC ternary regardless of the vapor supersaturation. The miscibility gap can be fully circumvented in the C-rich regime, where the solid composition is driven by the kinetic factors.