In combination with ordinary diffusive transport theory, knowledge of the relevant spin lifetimes allows us to identify the critical length scales for a spin transport device. The relevant spin relaxation mechanisms are reviewed by Fabian in this volume. In the doping range of interest for us, the dominant channel of spin relaxation is the D’yakonov-Perel’ (DP) mechanism , which corresponds to the randomization of spin during diffusive transport by precession around the instantaneous spin-orbit field. The bulk Dresselhaus spin-orbit coupling (due to the absence of inversion symmetry in GaAs) leads to a rapid decrease, proportional to ne-2, in the spin lifetime with increasing electron concentration ne [2, 4, 7]. The strong dependence on carrier density reflects the k3 dependence in the spin-orbit Hamiltonian. A maximum in the spin lifetime ts ~ 100 ns occurs at the MIT (2 × 1016 cm-3) at low temperatures, with a different set of mechanisms limiting the lifetime at lower dopings . The characteristic length scales for spin transport in the semiconductor are the spin diffusion length λs =√Dτs and drift length ld = µEτs. The characteristic mobility of n-GaAs at the MIT is of order 5000 cm2/V s. Assuming a barely degenerate electron gas one finds that λs is on the order of several microns.
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