Predicted bond length variation in wurtzite and zinc-blende InGaN and AlGaN alloys

Valence force field simulations utilizing large supercells are used to investigate the bond lengths in wurtzite and zinc-blende $InxGa1−xN$ and $AlxGa1−xN$ random alloys. We find that (i) while the first-neighbor cation–anion shell is split into two distinct values in both wurtzite and zinc-blende alloys $(RGa−N1≠RIn−N1),$ the second-neighbor cation–anion bonds are equal $(RGa−N2=RIn−N2).$ (ii) The second-neighbor cation–anion bonds exhibit a crucial difference between wurtzite and zinc-blende binary structures: in wurtzite we find two bond distances which differ in length by 13% while in the zinc-blende structure there is only one bond length. This splitting is preserved in the alloy, and acts as a fingerprint, distinguishing the wurtzite from the zinc-blende structure. (iii) The small splitting of the first-neighbor cation–anion bonds in the wurtzite structure due to nonideal c/a ratio is preserved in the alloy, but is obscured by the bond length broadening. (iv) The cation–cation bond lengths exhibit three distinct values in the alloy (Ga–Ga, Ga–In, and In–In), while the anion–anion bonds are split into two values corresponding to N–Ga–N and N–In–N. (v) The cation–related splitting of the bonds and alloy broadening are considerably larger in InGaN alloy than in AlGaN alloy due to larger mismatch between the binary compounds. (vi) The calculated first-neighbor cation–anion and cation–cation bond lengths in $InxGa1−xN$ alloy are in good agreement with the available experimental data. The remaining bond lengths are provided as predictions. In particular, the predicted splitting for the second-neighbor cation–anion bonds in the wurtzite structure awaits experimental testing.