  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 D'yakonov-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 D'yakonov-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)
