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The wurtzite phase group III-Nitrides (AlN, GaN, InN) have attracted greatinterest due to their successful applications in the optoelectronics since the90's. In this paper we perform a comprehensive study of AlN, GaN and InNstructural elastic and electronic properties using hybrid and conventionalDensity Functional Theory, presenting a comparison of the features of the threecompounds. We perform a direct comparison of the features of their electronicstructures, including the inversion of the top valence band associated with anegative crystal field splitting and its relation to the challenges ofacceptor-doping on AlN systems. With the determination of elastic constants andthe Young modulus we provide a simple model to connect a deformation energyassociated with the parameter $u$ and the effective crystal-field splitting,showing a direct relation among internal strain and the crystal-fieldsplitting.

Strain and crystal field splitting inversion in III-Nitrides