8-BANK K.P MODEL OF STRAINED ZINCBLENDE CRYSTALS

Second-order Löwdin perturbation theory is used to calculate the interaction matrices for an eight-band kp model (near the point) of zinc-blende crystals under a uniform strain. The model treats the 6 conduction bands, 8 valence bands, and 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-bandvalence-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-bandvalence-band gap and large spin-orbit splitting, the four-band Luttinger model with strain is recovered. © 1990 The American Physical Society.