  In a point contact NS junction, perfect Andreev reflection occurs over a
range of voltages equal to the superconducting energy gap, producing an excess
current of $I_{exc} = (4/3)(2e\Delta/h)$. If the superconductor has a finite
width, rather than the infinite width of the point contact, one cannot neglect
superfluid flow inside the superconducting contact. The energy range available
for perfect Andreev reflections then becomes larger than the superconducting
gap, since superfluid flow alters the dispersion relation inside the finite
width superconductor. We find a maximum excess current of approximately
$(7/3)(2e\Delta/h)$ when the width of the superconductor is approximately 7/3
times the width of the normal metal.
