Energy-band structure of Ge, Si, and GaAs: A thirty-bandk∙pmethod

A 30-band $\mathbf{k}\mathbf{\bullet }\mathbf{p}$ method taking into account spin-orbit coupling is used to describe the band diagram of Ge, Si, and GaAs over the whole Brillouin zone on an extent of $5\mathrm{eV}$ above and $6\mathrm{eV}$ under the top of the valence band. The band diagrams provide effective masses in agreement with experimental data both for direct gap semiconductors (GaAs) and for indirect gap semiconductors (Ge, Si). This method also gives explicit expressions for Luttinger parameters and effective masses in the $\Gamma$ valley.