A silicon carbide power device is fabricated by forming a p-type silicon carbide epitaxial layer on an n-type silicon carbide substrate, and forming a silicon carbide power device structure on the p-type silicon carbide epitaxial layer. The n-type silicon carbide substrate is at least partially removed, so as to expose the p-type silicon carbide epitaxial layer. An ohmic contact is formed on at least some of the p-type silicon carbide epitaxial layer that is exposed. By at least partially removing the n-type silicon carbide substrate and forming an ohmic contact on the p-type silicon carbide epitaxial layer, the disadvantages of using a p-type substrate may be reduced or eliminated. Related structures are also described.