A twenty-band $\mathbf{k}\cdot \mathbf{p}$ Hamiltonian taking into account the spin-orbit coupling is used to describe the valence band and the first two conduction bands all over the Brillouin zone. The basis functions are ${\mathrm{sp}}^3{s}^{*}$-like functions used in linear combination of atomic orbitals. To get the right dispersion up to the Brillouin zone edge, the influence of other bands $(d$ bands) is mimicked via Luttinger-like parameters in the valence band and in the conduction band. The method is applied to GaAs and Si. A satisfying agreement is obtained near the band extrema as well in the direct gap semiconductor (GaAs) as in the indirect gap semiconductor (Si). In particular, while the $\mathbf{k}\cdot \mathbf{p}$ Hamiltonian parameters are adjusted to get the longitudinal mass 0.92 of the silicon conduction band, the transverse mass, which results from the calculation without further adjustment, is equal to 0.19 which is the experimental value.

• Received 2 March 2001

DOI:https://doi.org/10.1103/PhysRevB.64.115207