  The spin-dependence of the interface resistance between ferromagnetic Fe and
InAs is calculated from first-principles for specular and disordered (001)
interfaces. Because of the symmetry mismatch in the minority-spin channel, the
specular interface acts as an efficient spin filter with a transmitted current
polarisation between 98 an 89%.
  The resistance of a specular interface in the diffusive regime is comparable
to the resistance of a few microns of bulk InAs.
  Symmetry-breaking arising from interface disorder reduces the spin asymmetry
substantially and we conclude that efficient spin injection from Fe into InAs
can only be realized using high quality epitaxial interfaces.
