Incomplete Solubility in Nitride Alloys

Abstract

ABSTRACTA model based on the valence-force-field (VFF) model has been developed specifically for the calculation of the irascibility gaps in III-V nitride alloys. In the dilute limit, this model allows the relaxation of the atoms on both sublattices. It was found that the energy due to bond stretching and bond bending was lowered and the solubility limit was increased substantially when both sublattices were allowed to relax to distances as large as the sixth nearest neighbor positions. Using this model, the equilibrium mole fraction of N in GaP was calculated to be 6×l0−7 at 700°C. This is slightly higher than the calculated results from the semi-empirical delta lattice parameter (DLP) model. Both the temperature dependence and the absolute values of the calculated solubility agree closely with the experimental data. The solubility is more than three orders of magnitude larger than the result obtained using the VFF model with the group V atom positions given by the virtual crystal approximation, i.e., with relaxation of only the first neighbor bonds. Other nitride systems, such as GaAsN, AlPN, AlAsN, InPN, and InAsN were investigated as well. The equilibrium mole fractions of nitrogen in InP and InAs are the highest, which agrees well with recent experimental data where high N concentrations have been produced in InAsN alloys. Calculations were also performed for the alloy systems with mixing on the group III sublattice that are so important for device applications. Allowing relaxation to the 3rd nearest neighbor gives an In solubility in GaN at 800°C of less than 6%. Again, this is in agreement with the results of the DLP model calculation. This result may partially explain the difficulties experienced with the growth of these alloys. Indeed, evidence of solid immiscibility has recently been reported. A significant miscibility gap was also calculated for the AlInN system, but the AlGaN system is completely miscible.