Electron spin relaxation in bulk III-V semiconductors is investigated from a fully microscopic kinetic spin Bloch equation approach where all relevant scatterings, such as, the electron--nonmagnetic-impurity, electron-phonon, electron-electron, electron-hole, and electron-hole exchange (the Bir-Aronov-Pikus mechanism) scatterings are explicitly included. The Elliot-Yafet mechanism is also fully incorporated. This approach offers a way toward thorough understanding of electron spin relaxation both near and far away from the equilibrium in the metallic regime. The dependence of the spin relaxation time on electron density, temperature, initial spin polarization, photo-excitation density, and hole density are studied thoroughly with the underlying physics analyzed. In contrast to the previous investigations in the literature, we find that: (i) In $n$-type materials, the Elliot-Yafet mechanism is {em less} important than the Dyakonov-Perel mechanism, even for the narrow band-gap semiconductors such as InSb and InAs. (ii) The density dependence of the spin relaxation time is nonmonotonic and we predict a {em peak} in the metallic regime in both $n$-type and intrinsic materials. (iii) In intrinsic materials, the Bir-Aronov-Pikus mechanism is found to be negligible compared with the Dyakonov-Perel mechanism. We also predict a peak in the temperature dependence of spin relaxation time which is due to the nonmonotonic temperature dependence of the electron-electron Coulomb scattering in intrinsic materials with small initial spin polarization. (iv) In $p$-type III-V semiconductors, ...... (the remaining is omitted here due to the limit of space)
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