According to an embodiment of a semiconductor device, the semiconductor device includes a semiconductor body having a main surface, the semiconductor body including a drift region of monocrystalline SiC, the drift region being of a first conductivity type, and a metallization arranged at the main surface. In a cross-section which is substantially orthogonal to the main surface, the semiconductor body further includes a contact region of the monocrystalline SiC directly adjoining the drift region and the metallization, and an anode region of a semiconductor material having a lower band-gap than the monocrystalline SiC. The contact region is of a second conductivity type. The anode region is in ohmic contact with the metallization and forms a heterojunction with the drift region.