Multiband k⋅p models for strained zincblende crystals: Application to the fine structure of ZnO

The elementary-matrix blocks of multiband k⋅p models are derived for strained zincblende crystals using methods of group theory. The general viewpoint we adopted is exploited in two opposite directions: the global description of the first Brillouin zone and the fine structure of the valence-band maximum. First, full-zone models are completed: strain contributions originating from the orbital and spin-orbit parts of the Hamiltonian are included in the 30-band model while the next 54-band model is introduced. Second, a 16-band spin-orbit Hamiltonian is constructed for ZnO with zincblende-type structure. The reversed level order at the valence-band maximum is attributed to the T₂-T₂ pd -like coupling actually taken into account. We perform ab initio calculations in the local-density approximation including relativistic effects to estimate the coupling parameter ζ₁₂=250 meV that gives an amount of pd-like interband mixing of about 10%.