A semiconductor device includes a substrate comprising a heterostructure configured to support formation of a channel during operation, first and second dielectric layers supported by the substrate, the second dielectric layer being disposed between the first dielectric layer and the substrate, a gate supported by the substrate, disposed in a first opening in the first dielectric layer, and to which a bias voltage is applied during operation to control current flow through the channel, the second dielectric layer being disposed between the gate and the substrate, and an electrode supported by the substrate, disposed in a second opening in the first and second dielectric layers, and configured to establish a Schottky junction with the substrate.