Generalized valence-force-field model of (Ga,In)(N,P) ternary alloys

We present a generalized valence-force-field (VFF) model for the ternary III–V alloys ($\text{III}=\text{Ga}$, In and $\text{V}=\text{N}$, P) to predict the formation energies and atomic structures of ordered and disordered alloy configurations. For each alloy (GaInN, GaInP, GaNP, and InNP) the VFF parameters, which include bond-angle/bond-length interactions, are fitted to the first-principles calculated formation energies of 30 ternary structures. Compared to standard approaches where the VFF parameters are transferred from the individual binary III–V compounds, our generalized VFF approach predicts alloy formation energies and atomic structures with considerably improved accuracy. Using this generalized approach and random realizations in large supercells (4096 atoms), we determine the temperature-composition phase diagram, i.e., the binodal and spinodal decomposition curves, of the (Ga, In) (N, P) ternary alloys.

Figure 1

Calculated mixing enthalpies $\Delta H$ of 30 different structures (27 ordered $+3$ pseudorandom) at different cation/anion concentrations of the (a) GaInN, (b) GaInP, (c) InNP, and (d) GaNP alloys. The circles denote LDA results while the crosses denote TVFF results. The TVFF parameters were fitted to the LDA-calculated mixing enthalpies. The relative rms errors of the fitted energies with respect to LDA averaged over all structures are also shown.

Figure 2

(Color online) Average TVFF mixing enthalpy $\Delta H$ (solid curve and symbols) of (a) GaInN, (b) GaInP, (c) InNP, and (d) GaNP zinc-blende random alloys calculated using a 4096-atom supercell and ten random realizations at each composition. Also shown are the calculated energies of ordered structures (solid squares) and 32-atom SQSs (solid triangles) at different compositions—all were obtained using TVFF. Some of the lowest energy ordered structures, e.g., Q8/Q16 at compositions $x=0.25$ and 0.75 and chalcopyrite (CH) at $x=0.50$ are identified by arrows.

Figure 3

(Color online) Predicted temperature-composition phase diagram of (a) GaInN, (b) GaInP, (c) InNP, and (d) GaNP zinc-blende random alloys. The solid and dashed curves correspond to the binodal and spinodal decomposition lines, respectively. The consolute temperature $\left(T_C\right)$ and the corresponding alloy compositions $\left(x_C\right)$ are also shown.