  We compute the spin-active scattering matrix and the local spectrum at the
interface between a metal and a three-dimensional topological band insulator.
We show that there exists a critical incident angle at which complete (100%)
spin flip reflection occurs and the spin rotation angle jumps by $\pi$. We
discuss the origin of this phenomena, and systematically study the dependence
of spin-flip and spin-conserving scattering amplitudes on the interface
transparency and metal Fermi surface parameters. The interface spectrum
contains a well-defined Dirac cone in the tunneling limit, and smoothly evolves
into a continuum of metal induced gap states for good contacts. We also
investigate the complex band structure of Bi$_2$Se$_3$.
