  Generalizing recent work, the Raman scattering intensity from a semi-infinite
superconducting superlattice is calculated taking into account the surface
contribution to the density response functions. Our work makes use of the
formalism of Jain and Allen developed for normal superlattices. The surface
contributions are shown to strongly modify the bulk contribution to the
Raman-spectrum line shape below $2\Delta$, and also may give rise to additional
surface plasmon modes above $2\Delta$. The interplay between the bulk and
surface contribution is strongly dependent on the momentum transfer
$q_\parallel$ parallel to layers. However, we argue that the scattering
cross-section for the out-of-phase phase modes (which arise from interlayer
Cooper pair tunneling) will not be affected and thus should be the only
structure exhibited in the Raman spectrum below $2\Delta$ for relatively large
$q_\parallel\sim 0.1\Delta/v_F$. The intensity is small but perhaps observable.
