A field-effect transistor (FET) using a two-dimensional electron gas (2DEG) as an electron channel is fabricated from GaAs grown by molecular-beam epitaxy. The doping profile of the field-effect transistor is described by the Dirac delta (δ) function. The subband structure of δ-doped GaAs is calculated. The characteristics of the δFET are a high concentration of the 2DEG, a high breakdown voltage of the Schottky contact, a narrow distance of the 2DEG from the gate, and a high transconductance. These properties are analyzed. Preliminary results for the extrinsic transconductance and for the transit frequency are obtained from δFET's having nonoptimized structures.