Density-functional calculations for III-V nitrides using the local-density approximation and the generalized gradient approximation

We have performed density-functional calculations for III-V nitrides using the pseudopotential plane-wave method where the d states of the Ga and In atoms are included as valence states. Results obtained using both the local-density approximation (LDA) and the generalized gradient approximation (GGA) for the exchange-correlation functional are compared. Bulk properties, including lattice constants, bulk moduli and derivatives, cohesive energies, and band structures are reported for AlN, GaN, and InN in zinc-blende and wurtzite structures. We also report calculations for some of the bulk phases of the constituent elements. The performance of our pseudopotentials and various convergence tests are discussed. We find that the GGA yields improved physical properties for bulk Al, ${\mathrm{N}}_2,$ and bulk AlN compared to the LDA. For GaN and InN, essentially no improvement is found: the LDA exhibits overbinding, but the GGA shows a tendency for underbinding. The degree of underbinding and the overestimate of the lattice constant as obtained within the GGA increases on going from GaN to InN. Band structures are found to be very similar within the LDA and GGA. For the III-V nitrides, the GGA therefore does not offer any significant advantages; in particular, no improvement is found with respect to the band-gap problem.