Band gap engineering of wurtzite and zinc-blende GaN/AlN superlattices from first principles

Based on all-electron density functional theory calculations, we systematically investigate the electronic structure of (0001)-oriented wurtzite (wz) and (111)-, (100)-, and (110)-oriented zinc-blende (zb) GaN/AlN superlattices, where the band gap, strength of the electric field and their correlation with biaxial stain as a function of the superlattice thickness are calculated. For the polar wz-(0001) and zb-(111) systems, the band gap values are found to continuously decrease with increasing thickness of the superlattice period due to the built-in electric field. By mapping the core-level shift, we demonstrate the presence of spontaneous polarization in both wz-(0001) and zb-(111) superlattices. The built-in electric field is calculated to be about $5.1\pm 0.3$ and $1.4\pm 0.4\text{MV}/\text{cm}$ in the “free-standing” (fully relaxed) wz-(0001) and zb-(111) superlattices, respectively. Strain-induced piezoelectric polarizations are estimated to contribute only about 5% for the wz-(0001) superlattice, and about 30% for the zb-(111) systems. The zb-(100) and (110) superlattices are characterized by flat core-level bands in the well and barrier regions. The zb-(100) superlattices are predicted to have a stronger quantum confinement than the zb-(110) superlattices. In both systems, confinement effects lead to a marked band gap increase with decreasing thickness of the superlattice period.