Spin injection from a ferromagnetic metal into a semiconductor

We calculate the spin polarization of electrons injected from a ferromagnetic metal (F) into a semiconductor (SC) or a two-dimensional semiconductor electron gas (2-DEG) and the resulting magnetoresistance (MR) of a F/SC/F structure. Due to the conductivity mismatch between F and SC, efficient spin-injection can be obtained only by inserting a tunnel junction at the F/N interfaces. We find that a F1/SF/F2 structure can present a nonzero MR if the junction resistance is chosen in a relatively narrow range determined by the spin-diffusion length and resistivity of F and SC, the distance between the ferromagnets and the width of the conduction channels. The case of a 2-DEG is particularly favorable.