Spin injection and electric field effect in degenerate semiconductors

We analyze spin-transport in semiconductors in the regime characterized by $T\stackrel{<}{\sim}T_F$ (intermediate to degenerate), where $T_F$ is the Fermi temperature. Such regime is of great importance since it includes the lightly doped semiconductor structures used in most experiments; we demonstrate that, at the same time, it corresponds to the regime in which carrier-carrier interactions can assume a relevant role. We derive a general formalism which can be applied to ferromagnet/non-magnetic semiconductor junctions independently from the semiconductor regime. We analyze in details the combined effect of carrier density variation, applied electric field and Coulomb interactions on spin injection and concentrate on a {\it degenerate} regime peculiar to semiconductors, which strongly differs, as spin-transport is concerned, from the well known degenerate regime of metals.