  An inherent difficulty in studying mesoscopic effects in
semiconductor--superconductor hybrid structures is the large Schottky barrier
which often forms at the interface. A large technological effort has been
invested in in improving the contact between the superconductor and the
two-dimensional electron gas (2DEG) of a semiconductor heterostructure, and in
recent years this has become possible for e.g. GaAs-Al, GaAs-In, and InAs-Nb
junctions. This development motivates quantitative theoretical modeling of
sample-specific transport properties. The aim of our work is to model the
conducting properties of a ballistic 2DEG-S interfaces with a QPC in the normal
region and also to take into account scattering due to a weak Schottky barrier
and/or non-matching Fermi properties of the semiconductor and superconductor.
