Molecular simulation study of miscibility of ternary and quaternary InGaAlN alloys

<jats:p>Molecular simulations are conducted to determine the limits of miscibility of a valence force field model for zinc-blende-structured In1−x−yGaxAlyN semiconductor alloys. The transition matrix Monte Carlo method is used to calculate the free energy of the model alloys as a function of temperature and alloy composition (considering both x and y ranging from zero to unity). Analysis of the free-energy surface provides values for the upper critical solution temperature of the ternary alloys: InGaN (1550 K), InAlN (2700 K), and GaAlN (195 K). The miscibility envelope of the quaternary alloy is determined at 773 K and 1273 K. The excess properties of the mixtures are calculated, and it is found that the excess entropy is negligible, and the excess enthalpy is nearly independent of temperature. Consequently, regular-solution theory provides a good description of the thermodynamic properties of the alloys, and comparison of the simulation results with the phase behavior previously reported using regular-solution theory finds good agreement. Structural properties of the ternary compounds are examined in terms of the local compositions. For InGaN it is found (surprisingly) that there is a slight preference for In atoms to have Ga atoms rather than other In atoms as neighbors, in comparison to a random mixture. The two other ternary compounds exhibit the expected behavior, in which the (small) deviations from random mixing tend to favor segregation of like atoms. Among the ternaries, GaAlN is found to show the greatest deviations from random mixing.</jats:p>