Composition of III-V ternary materials under arbitrary material fluxes: The general approach unifying kinetics and thermodynamics
В. Г. Дубровский, Egor D. Leshchenko
Abstract
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 ${A}_{x}{B}_{1\ensuremath{-}x}C$ 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 $\ensuremath{\varepsilon}$ of the total flux of $A$ and $B$ atoms over the flux of $C$ atoms. At $\ensuremath{\varepsilon}\ensuremath{\ll}1$, the composition is kinetically controlled, while at $\ensuremath{\varepsilon}\ensuremath{\gg}1$ it becomes thermodynamically limited even at infinitely high binary supersaturations for $\mathit{AC}$ and $\mathit{BC}$ pairs. The model fits very well the compositional data on the $\mathrm{In}{\mathrm{Sb}}_{x}{\mathrm{As}}_{1\ensuremath{-}x}$ epilayers, $\mathrm{Al}{\mathrm{Sb}}_{x}{\mathrm{As}}_{1\ensuremath{-}x}$ epilayers, and $\mathrm{In}{\mathrm{Sb}}_{x}{\mathrm{As}}_{1\ensuremath{-}x}$ 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 $\mathit{AB}$-rich conditions for an ${A}_{x}{B}_{1\ensuremath{-}x}C$ 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.