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 exchangecorrelation 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, N2 , 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. @S0163-1829~99! 06107-X# The group-III nitrides ~AlN, GaN, InN, and their alloys! have attracted much attention in recent years due to their great potential for technological applications ~see e.g., Refs. 1‐5, and references therein! In the wurtzite ~ground-state! structure, AlN, GaN, and InN have direct energy band gaps of 6.2, 3.4, and 1.9 eV, respectively, 3 ranging from the ultraviolet ~UV! to the visible regions of the spectrum. This implies that the AlxGa12xInN alloy system can be used to fabricate optical devices operating at wavelengths ranging from red into the UV. In addition, AlN and GaN have a high melting point, a high thermal conductivity, and a large bulk modulus. 6 These properties, as well as the wide band gaps, are closely related to their strong ~ionic and covalent! bonding. These materials can therefore be used for shortwavelength light-emitting diodes ~LED’s ! laser diodes, and optical detectors, as well as for high-temperature, highpower, and high-frequency devices. Bright and highly efficient blue 7 and green 8 LEDs are already commercially available, and diode lasers have been reported, emitting in the blue-violet range initially under pulsed conditions 9 and subsequently under continuous operation. 10 In order to help understand and control the materials and device properties, theoretical studies can be most valuable. A growing number of first-principles calculations have been performed for these materials over the past few years. Most of these calculations are based on density-functional theory employing the local-density approximation ~LDA! , either in an all-electron formalism or using the pseudopotential planewave approach. A number of studies have also been carried out using ab initio Hartree-Fock methods; however, these methods are much more computationally demanding than the LDA, and they significantly overestimate the band gap. It is well known that the LDA leads to an underestimate of the