Multibandk⋅pmodels for strained zincblende crystals: Application to the fine structure of ZnO

Abstract

The elementary-matrix blocks of multiband $\text{k}\ensuremath{\cdot}\text{p}$ 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 ${T}_{2}\text{\ensuremath{-}}{T}_{2}$ $pd$ -like coupling actually taken into account. We perform ab initio calculations in the local-density approximation including relativistic effects to estimate the coupling parameter ${\ensuremath{\zeta}}_{12}=250\text{ }\text{meV}$ that gives an amount of $pd$-like interband mixing of about 10%.