By using a back-gate operation, a high-quality two-dimensional electron gas (2DEG) is formed in an undoped GaAs/AlGaAs inverted heterostructure. A high mobility of around3×106 cm2/V sat 1.6 K is obtained for the structure without any compensating surface doping. The electron density is controllable down to7×109 cm−2.The relation between electron density and mobility is studied for samples both with and without a surface gate. The obtained results indicate that background impurities and an inhomogeneity of the electric field coming from the surface govern the mobility in a low-electron-density region and that the interface inhomogeneity becomes important at a high electron density. ©1998 American Institute of Physics.