A semiconductor die includes a barrier layer of type III-V semiconductor material, a channel layer of type III-V semiconductor material disposed below the barrier layer, the channel layer forming a heterojunction with the barrier layer such that a two-dimensional charge carrier gas is disposed in the channel layer near the heterojunction, a high-electron mobility transistor disposed in a first lateral region of the semiconductor die, the high-electron mobility transistor comprising source and drain electrodes that each are in ohmic contact with the two-dimensional charge carrier gas and a gate structure that is configured to control a conductive connection between the source and drain electrodes, and a capacitor that is monolithically integrated into the semiconductor die and is disposed in a second lateral region of the semiconductor die, a dielectric medium of the capacitor includes a first section of the barrier layer.