The critical supercurrent I-c carried by a short (0.3 to 0.8 mu m) ballisti
c two-dimensional InAas-based electron gas between superconducting niobium
electrodes is studied. In relating the maximum value to the resistance of t
he weak link in the normal state R-n, a much lower value is found than theo
retically expected for a ballistic system. The energy scale which character
izes the observed temperature dependence is comparable to the energy associ
ated with the product of I-c and R-n. We point out that although the transp
ort between the electrodes is ballistic, in the InAs underneath the superco
nducting electrodes the transport is diffusive, an experimental case which
has not yet been studied theoretically. [S0163-1829(99)09741-6].