A newly fabricated three-terminal Josephson junction is coupled with a
n InAs-inserted-channel InAlAs/InGaAs heterostructure. The two-dimensi
onal electron gas (2DEG) confined in the inserted InAs layer has a hig
h mobility of 73890 cm(2)/V . s and a high sheet-carrier density of 1.
98 x 10(12) cm(-2) at 4.2 K. The supercurrent flows through the 2DEG a
nd can be controlled by gate voltage. The critical current and the nor
mal resistance as a function of gate voltage are measured and the shee
t-carrier density dependence of the critical current is obtained. The
experimental results for this dependence are explained by the supercon
ducting proximity effect theory and by the normal transport of the 2DE
G.