  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.
