Energetics of quaternary III-V alloys described by incorporation and clustering of impurities

The energetics of alloy formation is generally modeled either by explicit sampling of the possible alloy configurations or by considering only noninteracting impurities in the dilute limit. We describe a model that bridges the two approaches by taking into account the thermodynamic probability to form small clusters by association of impurities, thereby extending the validity of the impurity model to higher concentrations. Since we express the alloy energetics in terms of pair and cluster binding energies there is no need for computationally intensive sampling over the full configuration space. The application to the Ga(1-x)In(x)P(1-y)N(y) highlights the importance of short-range ordering due to "small atom/large atom" correlation in such quaternary III-V alloys.