Conditions for efficient spin injection from a ferromagnetic metal into a semiconductor

We adapt the spin accumulation model of the perpendicular transport in metallic magnetic multilayers to the issue of spin injection from a ferromagnetic metal (F) into a semiconductor (N). We show that the problem of the conductivity mismatch between F and N can be solved by introducing a spin dependent interface resistance (tunnel junction preferably) at the $F/N$ interfaces. In the case of a $F/N/F$ structure, a significant value of the magnetoresistance can be obtained if the junction resistance at the $F/N$ and $N/F$ interfaces is chosen between two threshold values depending on the resistivity, spin diffusion length and thickness of N. The problem is treated for various geometries (vertical or lateral $F/N/F$ structures).