A semiconductor device of an embodiment includes a first layer, a second layer provided on the first layer, the second layer forming a two-dimensional electron gas in the first layer, a source electrode provided on the second layer, a drain electrode provided on the second layer, a gate electrode provided between the source electrode and the drain electrode on the second layer, and a first insulating layer provided between the gate electrode and the drain electrode on the second layer, the first insulating layer being a first oxide of at least one first element selected from the group consisting of Hf, Zr, Ti, Al, La, Y, and Sc, the first insulating layer containing 5×1019 cm−3 or more of at least one second element selected from the group consisting of F, H, D, V, Nb, and Ta.