Eight-band k⋅p model of strained zinc-blende crystals

Abstract

Second-order L\"owdin perturbation theory is used to calculate the interaction matrices for an eight-band k\ensuremath{\cdot}p model (near the \ensuremath{\Gamma} point) of zinc-blende crystals under a uniform strain. The model treats the ${\mathrm{\ensuremath{\Gamma}}}_{6}$ conduction bands, ${\mathrm{\ensuremath{\Gamma}}}_{8}$ valence bands, and ${\mathrm{\ensuremath{\Gamma}}}_{7}$ spin-orbit split-off bands. The model includes strain interactions arising from both the orbital and spin-orbit terms of the Hamiltonian. In addition to the usual Pikus-Bir deformation-potential constants, a, b, and d, which describe the coupling of the valence band to strain, two new deformation-potential constants arise, a' and b', which describe the coupling of the conduction band to strain. The constant a' couples the conduction band to hydrostatic deformations and the constant b', which results from a lack of inversion symmetry, couples the conduction band to shear deformations. The strain also introduces a k-dependent conduction-band--valence-band mixing that is linear in strain, in wave vector, and in the momentum matrix element between the conduction and valence bands. In the absence of strain, the eight-band Kane model is recovered. Under a finite strain, in the limit of a large conduction-band--valence-band gap and large spin-orbit splitting, the four-band Luttinger model with strain is recovered.