The two-dimensional electron gas concentration in InAs channel modulation-doped heterostructures can be controlled by using an In0.5Al0.5As0.56Sb0.44 quaternary alloy - doped with Si as a donor - as an electron-supplying layer. When lattice-matched with InAs, an electron concentration of more than 4 x 10(18) cm(-3) was obtained in the quaternary layer. The two-dimensional electron gas concentration of an undoped-In0.5Al0.5As0.56Sb0.44/undoped-heterostructure was 7 x 10(11)cm(-2) and that of a. Si-doped In0.5Al0.5As0.56Sb0.44/undoped-InAs heterostructure was 1.24 x 10(12) cm(-2). The electron mobility was Iom, though, due to the roughness of the heterointerface. If the interface can be made smooth: however, In0.5Al0.5As0.56Sb0.44 will be a useful material for forming the electron-supplying layer of InAs channel modulation-doped heterostructures.