We study the spin-orbit coupling in the whole Brillouin zone for GaAs using both the $sp^3s^{\ast}d^5$ and $sp^3s^{\ast}$ nearest-neighbor tight-binding models. In the $Γ$-valley, the spin splitting obtained is in good agreement with experimental data. We then further explicitly present the coefficients of the spin splitting in GaAs $L$ and $X$ valleys. These results are important to the realization of spintronic device and the investigation of spin dynamics far away from equilibrium.

8 pages, 3 figures, Physica E, in press