  We have investigated Andreev-reflection processes occurring at a clean
interface between a $p$-type semiconductor and a conventional superconductor.
Our calculations are performed within a generalized Bogoliubov-de Gennes
formalism where the details of the semiconductor band structure are described
by a $6\times 6$ Kane model. It is found that Andreev reflection of light-hole
and heavy-hole valence-band carriers is generally possible and that the two
valence-band hole types can be converted into each other in the process. The
normal-reflection and Andreev-reflection amplitudes depend strongly on the
semiconductor's carrier concentration and on the angle of injection. In the
special case of perpendicular incidence, Andreev reflection of heavy holes does
not occur. Moreover, we find conversion-less Andreev reflection to be
impossible above some critical angle, and another critical angle exists above
which the conversion of a heavy hole into a light hole cannot occur.
