Density-functional calculations for III-V nitrides using the local-density approximation and the generalized gradient approximation C. Stampfl * and C. G. Van de Walle Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, California 94304 ~Received 7 October 1998! 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 perfor- mance of our pseudopotentials and various convergence tests are discussed. We find that the GGA yields improved physical properties for bulk Al, 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. @S0163-1829~99!06107-X# I. INTRODUCTION 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 ultra- violet ~UV! to the visible regions of the spectrum. This im- plies that the Al x Ga 1 2x InN alloy system can be used to fab- ricate 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! bond- ing. These materials can therefore be used for short- wavelength light-emitting diodes ~LED’s! laser diodes, and optical detectors, as well as for high-temperature, high- power, and high-frequency devices. Bright and highly effi- cient blue 7 and green 8 LEDs are already commercially avail- able, and diode lasers have been reported, emitting in the blue-violet range initially under pulsed conditions 9 and sub- sequently 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 plane- wave 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 band gaps in semiconductors, 11,12 as well as to overbinding. An additional problem for GaN and InN is that the LDA predicts that the Ga 3 d and In 4 d states overlap with the N 2 s band forming two sets of bands. 6 Recent experiments have shown, however, that the 3 d bands of GaN lie several eV below the N 2 s band. 13–17 The same problems may be expected for InN. This has been explained as being due to neglect in the LDA of a combination of self-interaction and final-state screening effects. 13 Use of the generalized gradient approximation ~GGA! in density-functional-theory calculations is currently receiving increasing attention as a possible improvement over the LDA. The GGA has generally been found to improve the description of total energies, ionization energies, electron af- finities of atoms, atomization energies of molecules, 18–20 and properties of solids. 21–24 Improvements have also been re- ported for adsorption energies of adparticles on surfaces 25,26 and for reaction energies. 27,28 Furthermore, the GGA has been shown to be crucial in obtaining activation energies consistent with experiment for H 2 dissociation. 29,30 The rela- tive stability of structural phases also appears to be better described for magnetic 31 and nonmagnetic systems. 32,33 Re- cent studies by Dufek and co-workers 34,35 for transition- metal oxides reported a significant improvement in the band structure when using the GGA. In an earlier publication, however, Leung, Chan, and Harmon 31 reported no significant change in the band structure between LDA and GGA results for the same materials. Thus the effect of the GGA on the band structure is still unclear. Given the large ionicity and wide band gap of the III nitrides, it is important to investigate the effects that the GGA may have on the electronic structure, in particular, whether it would lead to an improvement in the band gap. Since the GGA affects binding energies in other systems, one may also expect a difference in defect formation ener- PHYSICAL REVIEW B 15 FEBRUARY 1999-II VOLUME 59, NUMBER 8 PRB 59 0163-1829/99/59~8!/5521~15!/$15.00 5521 ©1999 The American Physical Society