A trench is formed in a monocrystalline silicon carbide substrate by amorphizing a portion of the monocrystalline silicon carbide substrate to define an amorphous silicon carbide region therein. The amorphous silicon carbide region is then removed, to produce a trench in the monocrystalline silicon carbide substrate corresponding to the removed amorphous silicon carbide region. The substrate may be amorphized by implanting ions into a masked substrate so that the implanted ions convert the unmasked portions of the substrate into amorphous silicon carbide. The amorphous silicon carbide may be etched using at least one etchant which etches amorphous silicon carbide relatively quickly and etches monocrystalline silicon carbide relatively slowly, such as hydrofluoric acid and nitric acid. The amorphizing and removing steps may be repeatedly performed to form deep trenches.