Statistical Model Applied To Ax By C1-x-y D Quaternary Alloys: Bond Lengths And Energy Gaps Of Alx Gay In1-x-y X (x=as, P, Or N) Systems

We extend the generalized quasichemical approach (GQCA) to describe the Ax By C1-x-y D quaternary alloys in the zinc-blende structure. Combining this model with ab initio ultrasoft pseudopotential calculations within density functional theory, the structural and electronic properties of Alx Gay In1-x-y X (X=As, P, or N) quaternary alloys are obtained, taking into account the disorder and composition effects. Results for the bond lengths show that the variation with the compositions is approximately linear and also does not deviate very much from the value of the corresponding binary compounds. The maximum variation observed amounts to 3.6% for the In-N bond length. For the variation of band gap, we obtain a bowing parameter b=0.26 eV for the (Ga0.47 In0.53 As)z (Al0.48 In0.52 As)1-z quaternary alloy lattice matched to InP, in very good agreement with experimental data. In the case of AlGaInN, we compare our results for the band gap to data for the wurtzite phase. 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