Evaluation of matrix elements of the 8×8k⋅pHamiltonian withk-dependent spin-orbit contributions for the zinc-blende structure of GaAs

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Abstract
The k⋅p method of band-structure calculation provides a detailed description of a crystal’s energy dispersion near a high symmetry point in the first Brillouin zone. The resulting parameters of this calculation are a series of momentum matrix elements. Presented here is a set of band-structure parameters for the zinc-blende structure of GaAs at the Γ point that takes the lack of inversion symmetry into account as well as k-dependent spin-orbit contributions to the Hamiltonian. A comprehensive optimization was performed in order to satisfy effective mass data as well as conduction band spin-splitting data. It was found that the lack of inversion symmetry has a profound influence on the nonparabolicity of the conduction band and the contribution of the k-dependent spin-orbit effect cannot be ignored in the calculation of the effective mass of the conduction, light hole, and spin-orbit bands. © 1996 The American Physical Society.