A field-effect transistor includes a channel layer having a channel and a carrier supply layer, disposed on the channel layer, containing a semiconductor represented by the formula Al.sub.xGa.sub.1-xN, wherein x is greater than 0.04 and less than 0.45. The channel is formed near the interface between the channel layer and the carrier supply layer or depleted, the carrier supply layer has a band gap energy greater than that of the channel layer, and x in the formula Al.sub.xGa.sub.1-xN decreases monotonically with an increase in the distance from the interface. The channel layer may be crystalline of gallium nitride. The channel layer may be undoped. X of the formula Al.sub.xGa.sub.1-xN of the carrier supply layer is greater than or equal to 0.15 and less than or equal to 0.40 at the interface.