Spin injection from Fe into Si(001): ab initio calculations and role of   the Si complex band structure
  We study the possibility of spin injection from Fe into Si(001), using the Schottky barrier at the Fe/Si contact as tunneling barrier. Our calculations are based on density-functional theory for the description of the electronic structure and on a Landauer-Buttiker approach for the current. The current-carrying states correspond to the six conduction band minima of Si, which, when projected on the (001) surface Brillouin zone (SBZ), form five conductance hot spots: one at the SBZ center and four symmetric satellites. The satellites yield a current polarization of about 50%, while the SBZ center can, under very low gate voltage, yield up to almost 100%, showing a zero-gate anomaly. This extremely high polarization is traced back to the symmetry mismatch of the minority-spin Fe wavefunctions to the conduction band wavefunctions of Si at the SBZ center. The tunneling current is determined by the complex band structure of Si in the [001] direction, which shows qualitative differences compared to that of direct-gap semiconductors. Depending on the Fermi level position and Schottky barrier thickness, the complex band structure can cause the contribution of the satellites to be orders of magnitude higher or lower than the central contribution. Thus, by appropriate tuning of the interface properties, there is a possibility to cut off the satellite contribution and to reach high injection efficiency. Also, we find that a moderate strain of 0.5% along the [001] direction is sufficient to lift the degeneracy of the pockets so that only states at the zone center can carry current. 
Phivos Mavropoulos