 Split-off valence band

Spin-orbit coupling separates the $j=1/2$ valence states from the upper $j=3/2$ manifold at the zone centre in common cubic semiconductors. If its maximum lies ${\Delta }_{\mathrm{so}}>0$ below the upper valence band edge, its thermal electron hole population is suppressed by $e^{-{\Delta }_{\mathrm{so}}/(k_{B}T)}$ apart from effective density of states factors. Neglect requires $k_{B}T\ll {\Delta }_{\mathrm{so}}$; it is not valid at every temperature or in every material.