In this paper, we focus on the role played by the relativistic and d-electron effects on the electronic structure of both wurtzite (α-InN), as well as, the zincblende (β-InN) modifications of indium nitride. Here we perform all-electron full-potential linearized-augmented plane-wave calculations with spin-orbit interaction. The In 4d electrons are treated both as core or as valence electrons. We compare the performance of the local-density approximation (LDA), the generalized gradient approximation (GGA) and the recently proposed non-empirical meta-generalized gradient approximation (Meta-GGA) in calculations of the structural and electronic properties of InN.

Band structures, densities of states, orbital-resolved densities of states, total and partial valence charge densities and ionicity factors are analysed in great detail. The calculated values of the energy gaps, bandwidths, spin-orbit and crystal-field splittings and the correct band degeneracies are compared to experimental and/or ab initio results.

The role played by relativistic effects and meta-GGA functional on the band structure is discussed. For the structural properties meta-GGA is more accurate and gives the best description of InN.

We found that several features of α-InN resemble those of β-InN. Most of the calculated band parameters, of band gaps, total and upper-valence bandwidths, and antisymmetric gap for α-InN are close to those of β-InN to within 1%. The charge distributions have similar features meaning that this material has the same ionicity factor in both structures even when In 4d were treated both as core or as valence electrons.

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