  Semiconductor-based Josephson junctions provide a platform for studying
proximity effect due to the possibility of tuning junction properties by gate
voltage and large-scale fabrication of complex Josephson circuits. Recently
Josephson junctions using InAs weak link with epitaxial aluminum contact have
improved the product of normal resistance and critical current, $I_cR_N$, in
addition to fabrication process reliability. Here we study similar devices with
epitaxial contact and find large supercurrent and substantial product of
$I_cR_N$ in our junctions. However we find a striking difference when we
compare these samples with higher mobility samples in terms of product of
excess current and normal resistance, $I_{ex}R_N$. The excess current is
negligible in lower mobility devices while it is substantial and independent of
gate voltage and junction length in high mobility samples. This indicates that
even though both sample types have epitaxial contacts only the high-mobility
one has a high transparency interface. In the high mobility short junctions, we
observe values of $I_cR_N/\Delta \sim 2.2$ and $I_{ex}R_N/\Delta \sim 1.5$ in
semiconductor weak links.
